Life is a Puzzle

Shortest Way to Help Grandma

Maria — Fri, 25 Jul 2014 08:11:00 +0000

Good news: The solution time has been extended till Friday as by technical reasons the newsletter didn't go on time.

You and your grandma live on the same side of the river. You need to find the shortest way to walk from your house to the river (with an empty bucket), fill the bucket with water and bring the water to your grandma. The river is fierce and you cannot swim in it. Disregard the fact that it is much harder to walk with a full bucket than with an empty one. Just look for the shortest path.

Note: the solution does not involve any equations, just one-two simple lines.... Feel free to print the image or redraw it. Submit your answers as images via email to me or in the comments on this blog post. Please explain your answer. The answers are accepted any time until midnight Eastern Time on Friday, on our Family Puzzle Marathon.

Friday is here and below is the answer drawing:

The shortest way is marked with a red line.
To find it draw a reflection of the grandma's house across the river and connect with a straight line Your house and the Reflection of Grandma's house. It surely is the shortest distance between these two points.
But Grandma lives on this side of the river! OK, just reflect the interval of the line from the river to Grandma's house.

What does it take to change an Army?

Maria — Fri, 04 Jul 2014 04:17:00 +0000

Here is a new great puzzle my coworker shared with me. By the way, he is in a delivery room right now waiting for his twin boys to emerge. All the best, Jonathan!

In a faraway land, the Queen's Army consists of 3 Corps.

Each Corp is composed of 3 Divisions.

Each Division of 3 Brigades.

Each Brigade of 3 Regiments.

Each Regiment of 3 Companies.

And finally each Company of 3 Soldiers.

Soldiers are either Air Force soldiers or Marines.

Now, the rules, from the bottom of the hierarchy to the top:

Each Company is composed of either:

2 Air Force soldiers and 1 Marine (in which case it is named The Air Force Company)

2 Marines and 1 Air Force soldier (in which case it is named The Marines Company)

Each Regiment is composed of either:

2 Air Force Companies and 1 Marine Company (in which case it is named The Air Force Regiment)

2 Marine Companies and 1 Air Force Company (in which case it is named The Marines Regiment)

and so on till:

Each Army is composed of either:
2 Air Force Corps and 1 Marines Corp (in which case it is named The Air Force Army)

2 Marines Corps and 1 Air Force Corp (in which case it is named The Marines Army)

At the present time the Queen's Army is Marines Army. However Queen's new lover is an Air Force pilot and he convinced the Queen to change the Army to the Air Force Army. The question is: what is the minimum number of soldiers that the Queen needs to change so that her Army will become The Air Force Army?

The answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Something to do with your kids this summer.

Maria — Fri, 27 Jun 2014 03:08:00 +0000

This came highly recommended from Peggy Orenstein, a well-know author.

She wrote:

Daisy (my daughter) and I are taking a 6-part online course by math guru Jo Boaler and it is truly life-changing. It is not only changing our relationship to math but to learning as a whole. Only 10-20 minutes per lesson, you can do it any time between now and December and it's FREE. I HIGHLY HIGHLY HIGHLY recommend it for students of any age and their parents!

I haven't tried this yet but plan on doing together with my 11-year old daughter this summer.

Hong Kong Elementary School Admission Test

Maria — Fri, 27 Jun 2014 02:34:00 +0000

Can you solve this in 20 seconds? If not, perhaps you are like I not ready for the 1st grade.

Try it on your iPad or a Smart Phone, this could help:)

The answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Standard heights for your kitchen counter, bar, dining table and other household items.

Maria — Fri, 06 Jun 2014 09:29:00 +0000

We are a tall family and over the years and few hellish renovations I gradually learn that we have to stand up for ourselves while convincing architects or Home depot employees in necessity of an extra height for our kitchen counters, vanities and toilets. A few cm do make a big difference for your comfort.

What are the standard household heights a how much freedom do you have?

Kitchen countertops: 36" standard. Tall people may prefer 37-38". Short people 32-35". To find the ideal countertop height, hold your elbows out at a 45-degree angle as if you were placing your hands on a counter. The distance from your hands to the floor is the ideal countertop height for you. However, beware that most appliances designed for 36" counter height.
Counter stools: 24".
Kitchen bar: 42-43".
Bar stools: 30".
Pendant lights should be hang 40-43" above the kitchen island.
Dining tables: 30".
Dining chairs: 17-19".
Bathroom vanity: 34-35".
Standard toilet: 16-17" height. Comfort height toilets for tall people or people with disabilities: 17-19" height.

Find more details in this Houzz article: Easy reference: Standard height for 10 household details.

Top image by Lynn Friendman, distributed under CCL.

An Olympic Torch Puzzle

Maria — Fri, 30 May 2014 07:37:00 +0000

Two people are running around the Olympic stadium in the same direction. One of them is a much faster runner than another. They have only one torch and they pass this torch to each other every time one of them is crossing another. They start from the same spot and the faster runner holds the torch at the start. At the end f the race, the faster runner made 50 loops, the slower 35. How many loops made the torch?

Hint: assume that instead of one torch they have another item (say a newspaper) that is starting in the hands of a slower runner and is being exchanged for a torch every time the runners pass each other.

This puzzle came from Israeli newspaper Haaretz.

The answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Tip image via Flickr, distributed under CCL.

Mother's Day Quiz

Maria — Fri, 09 May 2014 04:14:00 +0000

Life is a puzzle and we - moms - are experts at solving it with logic, humor, and numbers. This quiz by The Math Mom is celebrating moms who are wise, glamorous, efficient, and funny. Motherhood experience is required to answer. The Quiz was originally posted on boston.com

Puzzle #1: Handbag Mania

Mothers, daughters, grandmothers - we all have our passions. One mother could not go to the store without buying a handbag. Leather, plastic, cloth - she loved them all. When asked after a recent shopping expedition "How many did you buy?" she answered: "Three quarters of their number plus three quarters of a bag." How many did she purchase?

Choices:

3
30
13
None

Think a bit, then scroll down to see the answer.

Correct answer is 3.
Three quarters of their number plus three quarters of a bag is: 3/4 times 3 + 3/4 = 3

Puzzle #2: Mom vs Dad Race.

Mom and Dad are running on a high school track, but in opposite directions. They notice that their meeting point keeps shifting by three steps in the direction Mom is running. Who is a faster runner?

Choices:

Image by Ed Yourdon, distributed under CCL.

Correct answer: Mom, she does the whole track distance plus three steps while dad is running the track distance minus three steps in between their meeting times around the track.

Puzzle #3: Speedy Breakfast

You are making grilled cheese sandwiches on a pan that is just wide enough for two slices of bread. It takes 1 minute to grill one side of each sandwich. Can you make three of those sandwiches in just 3 minutes and send your kids out of the door just in time for the school bus?

Choices:

Sure you can;
No, you need at least 4 minutes. Gotta drive the kids yourself.

Correct answer: Sure you can. This is tricky. Name the sandwiches A, B, and C.
Minute 1: Grill one side of sandwiches A and B.
Minute 2: Grill the second side of sandwich A and the first side of sandwich C. Sandwich A is ready.
Minute 3: Grill the second sides of sandwiches B and C. All three sandwiches are ready.

Puzzle #4: Cookies Heaven

Twelve mothers from a kids' activity class decide to get acquainted through a baking party. They agree that each will bring homemade or store-bought cookies to share and each will try one cookie from everyone else. While tasting each other's cookies, each pair will have a little chat getting to know each other. How many cookies are consumed altogether at this party?

Choices:

Correct answer: 132.
Each of the 12 moms tried 11 cookies that the other moms brought: 12 x 11 = 132

Puzzle #5: Eggs for Breakfast

To make breakfast for yourself, you bring a big pot of water to a boil and then boil one egg for 4 minutes. How long would it take you to boil five eggs to feed your whole family?

Choices:

4 minutes
8 minutes
20 minutes

Correct answer: 4 minutes.

The boiling time is the same if you put all the eggs in the pot at the same time.

Puzzle #6: Sport for Moms

You are a soccer mom, a swim mom, a lacrosse mom, a runner's wife, a Shape Magazine subscriber, and have a family gym membership. Does this guarantee that you can look your family physician in the eye and say that you get enough exercise?

Choices:

Sure: Soccer, swimming, lacrosse, running, gym - you are obviously well aware of the importance of physical activity!
Absolutely not: Just because you make time for others to play sports doesn't mean you have time to do it yourself!

Correct answer is: Absolutely not!

Puzzle #7: Your Good Night Sleep

What are your chances of a good night sleep if there is 30 percent probability that your baby will cry in the middle of the night, a 20 percent probability that your son will have nightmares and come into your room, and a 10 percent chance that your husband will be snoring after the giant steak he consumed at dinner?

Choices:

Zero
50 percent
70 percent

Image by Micah Taylor, distributed under CCL.

Correct answer: 50 percent. For you to have a good night sleep none of these events should occur. No crying AND no nightmares AND no snoring = 0.7 times 0.8 times 0.9 = 0.504 or about 50 percent.

Puzzle #8: A Working Holiday

This may have happened to you. Take Veterans Day, Martin Luther King Day, Presidents Day - or any other holiday observed by your child's day care but not observed by some private companies. If both you and your spouse work and you have not lined up a babysitter, you are facing a puzzling day. Assuming you have flexible hours, can you arrange the day so that you and your spouse will each work an 8-hour day and split childcare?

Choices:

Correct answer: Yes. All three go to sleep at the same time. Mom and Dad wake up after 8 hours of sleep. There are 16 hours are left in the day. Mom watches the child for 8 hours while Dad works for 8 hours. Then, dad watches the child for the remaining 8 hours while Mom works for 8 hours.

Puzzle #9: A Rotten Egg

You buy a dozen eggs. After a few days, you notice that just a few are left and you buy a dozen more. You fill up all the empty egg spots in your refrigerator, then refill and buy more as necessary. But if you don't keep track properly, some will get rotten before you eat them. Which practice will leave you with some rotten eggs?

Choices:

Pick eggs for use from the right side of the refrigerator, shift eggs to empty spots to the right, refill egg on the left.
Leave eggs in the cartoon. When you buy a new cartoon, put it under the old one.
Mark eggs with numbers using a pencil.
Just pick eggs randomly, refill empty spots when you buy new eggs.

Correct answer: Random picking. If you pick eggs randomly and refill empty spots with new eggs, there may be a stinking rotten egg that never got picked.

Puzzle #10: I'm a mother, I'm a sinner, I'm a saint.

Remember the song by Alanis Morissette? You are a professional woman (20 percent of the time), a mother (20 percent of the time), a wife (10 percent of the time), a daughter (5 percent of the time), a sleeping angel (25 percent of the time), a good friend (3 percent of the time), a line cook (4 percent of the time), a house maid (5 percent of the time), a self-indulging queen (3 percent of the time), a neurotic guilt-ridden mess (2 percent of the time), and a driver (3 percent of the time). Is this all possible?

Choices:

Correct answer: Yes. Of course the answer is yes! We all do it, somehow.

Happy Mother's Day!

Fair Split of the Rent

Maria — Fri, 02 May 2014 05:20:00 +0000

Do you know Joe, Jay and Jim? They are renting a 3-bedroom apartment in Cambridge and have to split the $3,000 monthly rent.
$1,000 each?
But the trouble is that all 3 bedrooms are of a different size.
Divide the rent based on a room size?
Good idea! However one room has two windows, second has only one and the third one has a fire escape in front of its window. Joe really wants the last one for his cigarette breaks but he is wiling to pay no more than $900 for it.
Apparently math could help them!

Recent New York times article describes an algorithm that could be used in such situations. Take an equal-sided triangle where every vertex represents a totally unfair situation when one person pays for one room only the whole $3,000 rent. Subdivide this triangle into smaller ones and interpolate rent linearly into every new vertex. See below:

Now go over all the vertices and for each vertex ask either one of the roommates which room he prefers at such rent split. Apparently there always will be a triangle where every roommate has picked a different room. The fair rent subdivision lies somewhere in this triangle. Read more about the algorithm in the New York Times article: To divide the rent, start with a triangle.

And try the New York Times interactive rent division calculator: Rent Division Calculator.

Top image from Rentcafe.

Riddles

Maria — Fri, 02 May 2014 03:49:00 +0000

Lets try as an appetizer the riddle my coworker shared with me:

The more you take from it, the larger it becomes. What is it?

And now munch on a few number riddles sent by Lulu:

I am worthless as a leader, but when I follow a group their strength increases tenfold. By myself I am practically nothing, neither positive nor negative.
A word I know, six letters it contains, subtract just one and twelve remains.
Five hundred begins it, five hundred ends it, five in the middle is seen. First of all figures, the first of all letters, take up their stations between. Join all together, and then you will bring before you the name of an eminent king. (hint: use non-Hindu-Arabic numbers)

They are short but not necessarily easy. You can ask your kids for help. Please reference puzzle numbers in your answers. The answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Tip image via Flickr, distributed under CCL.

Marathon Birthday Puzzle

Maria — Thu, 24 Apr 2014 14:55:00 +0000

This week my friend Irina complained to me that her son's 17th birthday fell on the Boston Marathon Day and friends weren't able to come and celebrate with them in their Brookline home until the roads opened. Previous such coincidence was 17 years ago when her son Daniel was just born in the Beth Israel Hospital that is right along the marathon route and all the visitors got delayed till the end of the marathon festivities. Irina mused that I could probably calculate when the next such coincidence would happen and I thought why not turn it into a puzzle.

Daniel's birthday is April 21.
Boston Marathon is held on Patriots Day that is 3rd Monday in April.
Is Irina correct that the Boston Marathon coincided with Daniel's birthday only twice: in 1997 when he was born, and now in 2014? When is the next time such a coincidence will happen?

Image from Flickr, distributed under CCL.

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Must See Movies

Maria — Fri, 04 Apr 2014 03:23:00 +0000

One friend is telling another:
- I am going to recommend you 5 movies each of which will completely turn your life upside-down.
One month later:
- Did you see my movies?
- Yes, I did.
- What do you think?
- Oh, I should have stopped after the ....

Your task is to complete the last sentence and provide the explanation to your answer.
This puzzle came from my co-worker Ira.

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Best Time For Lunch

Maria — Thu, 03 Apr 2014 17:07:00 +0000

No matter where you work, at some point during the day you have to gobble something to refuel your energy. Most of us at least occasionally leave our desks for a lunch in a cafeteria or a restaurant. Frequently accompanied by coworkers or friends.
What's the best time to go out for lunch?

When one is hungry?

Probably.

When a majority of the people in the lunching group are hungry?

Perhaps.

But what if 5 minute of waiting till your colleague will finish his non-urgent email may cost you 20 extra minutes of waiting at the salad bar, or leave you without the daily special or a table to sit at.

People that are very particular about what they eat and when usually develop mathematical theories that define when they need to start heading towards food. Below are a few of the theories I heard.

Most of the people decide to go out for lunch at round hours or half-past an hour: 12:00, 12:30, 13:00, 13:00. This results in "waves" of crowding a few minutes past these times. To avoid the crowds try to come a bit ahead of either wave: 12:20 or 12:50.
To guarantee the specials, the seat and the fresh salad bar come ahead of the crowds: leave your desk at 11:53 so that you could be among the first customers at noon.
Do not follow your instincts. Most of the people seek salad on Mondays recovering after the weekend feast, soup on a rainy or cold day, light fare in warm weather, turkey in October-November. Avoid these trends to guarantee a quick lunch.

When do you head for lunch? Share your thoughts or theories.

A Simple Magic Square

Maria — Thu, 27 Mar 2014 16:32:00 +0000

Magic squares are tables of numbers where sums of every row, every column and both diagonals produce the same number. No, they were not invented by Ben Franklin, but have been around for thousands of years before. Take a look at this one on Gaudi’s Sagrada Família church in Barcelona:

Now, a little Magic Square puzzle suggested by our reader Lulu:

There is a 3 X 3 table with 9 cells in it and we are required to fill in the table with numbers from 1 to 9. Each number can be used only once. The numbers have to be placed in such a manner that they add up to 15 horizontally, vertically and diagonally. Can you do it?

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Four Women and Four Hats Puzzle

Maria — Fri, 07 Mar 2014 08:04:00 +0000

Once upon a time four women bought four hats. All the hats were black inside. Two of them were while on top and two black on top as in the picture below. In this game, three women (Beth, Iris, Michelle) were asked to stand inside the room facing each other's back, and the fourth (Katy) was left behind the wall. Everyone was allowed to look only forward. Michelle saw Beth and Iris'es heads. Iris only Beth's head. Beth and Katy were facing the non-reflective wall. Then the hats were placed on their heads.

No woman knew what color hat she has, only that there are two white and two black hat overall. They were asked to figure out their hat color. No guessing was allowed, just pure logic and definite answer. They were all very savvy. After a minute of silence one of them announced her hat color. And she was absolutely right. Who was it and how did she figure it out?

This puzzle came from my daughter's friend (10-years old) and they had great time enjoying it at school. You can do it as well!

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Oscar Ropes Puzzle

Maria — Fri, 28 Feb 2014 03:03:00 +0000

We are done with the winter Olympics and now are looking forward to the Oscar's entertainment.

As we saw in the previous puzzle, the most interesting stuff happens away from the main arena and escapes the media attention:) And what do we have on the margins of the Oscar ceremony? VIP ropes and poles that guard the Red Carpet attendees, of course.

This a puzzle about two poles, 5 feet high each, and a rope connecting these poles. The rope is 6 feet long and at its lowest point is 2 feet above the ground. The question is: how far away are those poles?

This puzzle came from my son's friend Adam. Thank you!

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

An Olympic Puzzle

Maria — Thu, 13 Feb 2014 15:28:00 +0000

February 2014. Russia, Sochi.
Taxi drivers in the city are very busy bouncing all the athletes and spectators in-between the Olympic village and the city. This is a puzzle about two taxis: say Green and Yellow. Green taxi starts from the village and goes toward the city exactly at the same time when Yellow taxi leaves the city in the direction of the village. They drive toward each other and meet (for the first time) 5 km from the village. Each delivers its passengers and immediately returns back with the new riders: Green taxi now drives from the city to the village while Yellow taxi returns from the village to the city. They meet (for the second time) 3 km from the city.
The question is very simple - how far is the Olympic village from the city?
Here is the sketch created by Kimberly Rose that should help you.

Note that this puzzle is fictional and Googling the real distance will not provide the answer. The puzzle is adapted from a summer boat puzzle from my favorite book of puzzles:

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

How does it work?

Maria — Fri, 07 Feb 2014 06:45:00 +0000

Here is a number magic trick that came to me via mail.
All of you, math detectives, are invited to unveil its magic with your logic.

Take the last digit of your mobile phone number.
Multiply this digit by 2.
Add 5 to the result.
Multiply what you got by 50.
Now, you may need a calculator. Add to the previous result 1763. And if you already celebrated your birthday in 2014, add another 1.
Last step! Subtract the year of your birth.

You should now have a 3-digit number.

Its first digit is the last digit of your mobile phone number and the next two digits are your age!

How does it work? Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

All About Anne

Maria — Fri, 07 Feb 2014 06:42:00 +0000

As customary on TheMathMom's website we are honoring each of our 50-puzzle points winner with an exclusive interview. This week it is Anne.

Q: Dear Anne. Does your work have anything to do with math?

I am recently retired and after working in a hospital I spent most of my career as a visiting nurse for my county. Of course I had to use math for medication administration and proper dosage. When going into a home there was much problem solving and creativity involved which I enjoyed. The home environment, especially on a new visit, does not have all the health amenities of a hospital and you must figure out how to proceed with what is there, which can be very little and/or not as hygienic as you need or would prefer. You must also problem solve to assist the patient in following instructions and adapting them to a sometimes challenging household environment or because of personal reservations.

Q:If you could go back, what profession would you choose and why.

I love the basis of the healthcare field (forget about the insurance, politics, etc!). It is based on science, something new is always being discovered, it is challenging and it helps people. If I could choose again I would definitely choose a scientific field, maybe healthcare again or something in astronomy or physics or medical research, and I think it would be fun to be a detective or someone who can crack sophisticated codes!

Q: Is there a childhood mentor who infused your interest in math?

I would have to say my parents. My father was an engineer and my mother was a science major in college so their interest in things math/science related was always there. I guess you take for granted your father's tinkering, contraptions and the lack of repairmen coming to the house! They definitely supported and encouraged a full math/science curriculum for me when it was not the usual way for a girl. I loved the subject matter but not the fact that I could be the only, or one of a few, girls in the class ...... but I continued and was a math major in college.

Q: Do you think math helps you in your daily life?

I definitely think math helps in your daily life, from simple things like cooking, sewing, smart shopping to home repairs and financial decisions to a certain way of thinking that solves problems.

And may I add that my children are grown and my days as a Math Mom are over. Neither child avoided math and, in fact, took many advanced mathematics courses. My son in an engineer with an MBA and my daughter is a neuropsychologist, both professions where math is used. I have two grandchildren now and, while I know their parents will raise them with an appreciation for math, I have moved on to Math (Grand)Mom!

Anne is the 8th person to reach such a celebrity status on our pages. Before her there were: Kim, Tom, Jerome, Ilya, TracyZ, Anne-Marie, and Wang.

Parrots and Cages puzzle

Maria — Fri, 17 Jan 2014 03:31:00 +0000

You have 42 parrots and 7 cages of various sizes. Lock all the parrots inside the cages so that no cage is empty and each cage contains an odd number of parrots.

A hint: this puzzle requires some unusual thinking.

Warning: the solution is below.

At first it seems simple: 42 divide by 7, 6 parrots in each cage. But the number of parrots in each cage should be odd. OK, let's try 1 parrot in each of the first 6 cages. How many parrots are left? 42-6=36. Put 36 in the last cage. Again, not an odd number.

Now we note that in general, there is no way that 7 odd numbers could be added to produce an even number. So, there must be a trick! A trick that does not involve the numbers.

And the trick is to place cages inside each other. There was a note of cages being of different sizes. So, place one parrot inside a small cage, place this cage inside a large cage. Both cages have odd number of parrots. You are left with 41 parrot and 6 cages. Now, it is easy. Anyway you do it, it works. Just keep numbers odd.

You can try this puzzle now on your friends and family if you are not afraid to be beaten. A simpler version of it is to pack 6 presents inside 7 boxes of various sizes so that no box is empty.

Enjoy!

A Homeland Puzzle

Maria — Fri, 17 Jan 2014 03:01:00 +0000

Homeland.
We started watching these series a year ago after they got great reviews in the media and among our friends. It took us a few episodes to get into the drama but the excellent acting and unexpected story-line twists turned us into addicts. Occasionally, I nervously rushed to the news in the mornings expecting last night's episode events to have happened for real and wanting to know what was next. After the dramatic finale of the season 2 we were orphaned, left on our own for the summer.

By September of last year, our renovations drama replaced the Homeland emotions and we have completely forgotten about the promised continuation of the series and missed the beginning of season 3. Luckily on Thanksgiving a friend uttered something that made me remember these great series. On December 1st, we started catching up, watching the previously aired season 3 episodes 5 days per week while each of the 12 episodes of this season was released weekly on TV starting from September 29th. My question is whether we were able to catch up with the TV releases and watch the season 3 finale, biting our nails, on December 15th on Showtime or we missed it and a co-worker spoiled the suspense next day at work.

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon. You can also email me your drawings to maria@themathmom.com

A puzzle that 99% will fail to answer.

Maria — Fri, 10 Jan 2014 07:33:00 +0000

This came from my son who got it from someone else at school.

I solved it quickly and texted him the answer just as I was getting into my car for work.

He wrote: "Wrong" and sent me a ridiculous solution.

I typed: "Ohh boy, how could you miss it! I will beat you up at home:)" and started driving.

Stuck in traffic I thought back to it and the 99% that are getting it wrong and suddenly realized that his answer is in fact correct!

I texted: "Apology! Now that my head has cooled off I see that you were right."

He wrote: "Hahahahahaha".

No one at my work got it right either. Could you?

There is at least two solutions. Let's call them: my and my son's. Both are kind of correct. But his is more original.

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

A Holiday Greeting for You from You

Maria — Fri, 03 Jan 2014 05:05:00 +0000

My mom is our family poet and a writer who has been composing little humorous personalized sonnets for almost every birthday, wedding, anniversary or other significant events in our family and her work clusters. Last weekend she worked on a non-rhymed New Year greeting, and the fact that the year 2014 is a year of the Horse in Chinese calendar gave her a lot of ideas to write about. Here it is, loosely translated from the Russian;

We already work hard as a workhorse; pull the plow as peasant horse; strive to come to the finish line first , like a racehorse; fear losing our jobs as an old horse; easily bought by sweets like a circus horse; devoted to our owner (employer , children, friends ) as domestic horse.
Therefore we are ready to welcome the 2014 NEW YEAR!
And let every home and every heart find a place for a small horseshoe, which will bring us a little luck and much happiness!
Be healthy, as a young horse, racing all year long.
and so long....

She sent the greeting by email to me and seven of her closest friends from Israel and Russia on December 30th. A day later she received an email with her own greeting from one of my dad's friends who resides in Florida. Interestingly the text was edited to exclude parts about life in Israel that were not so applicable to the Florida retirees. What are the chances for an email to go around the globe (at least once) and among millions of potential recipients, and come back to the original writer!

Actually, this is not so rare. Something similar may have likely happened to you.
While our world is inconceivably large, our circle of friends is rather small and typically based around age, interests, education, socio-economic status. And some of our friends' friends are likely to know each other. Moreover, there are those of us who serve as "network hubs", social butterflies with extremely large circle of friends and acquaintances that goes outside of their age, interests, education and socio-economic status, which allows to connect people from different networks together.

In Hollywood this paradigm is known as 6-degrees of separation from Kevin Bacon, stating that any actor could be linked to the well-known Kevin Bacon with up to 6 steps. Mathematicians are counting their "proximity" to Paul Erdős in Erdős numbers. This prolific Hungarian mathematician apparently spent large portion of his life travelling around and writing papers with those who would give him room and board. He published more than any other mathematician in history. LinkedIn has used this chain-of-connections concept to help anyone reach almost everyone for a professional contact.

Going back to our New Year week, let's contemplate our enormous world being tightly connected and inter-dependent, and how anything good we do could spread around bringing so much happiness and ricocheting back to us just when we need it. Happy New 2014, the Year of the Horse.

Happy Holidays! Next year challenge - think outside of a box.

Maria — Fri, 27 Dec 2013 03:03:00 +0000

Happy holidays to all my dear readers!
Thank you so much for your loyalty, comments and ideas. Please keep them coming.
Wishing you a healthy and successful year.
Today I would like to tell you a story and give you and myself a New year challenge: Lets try thinking outside of a box.

the story:
You have likely heard of a field of cryptography that is dealing with secure data storage, transfer and access. It is applicable to anything from protecting your personal medical information, sending online payments to breaking into the Pentagon computers. In the past century very complex algorithms have been developed to encode and decode such secure data. Many algorithms are using extra-large prime numbers. $150,000 dollar prizes were announced to people that could find such large primes consisting of hundreds of thousands of digits. Even since the Second World War cryptography has been a very hot field and many brilliant scientists are working in it.

A group of them just published a ground-breaking study announcing that you can decode the encrypted message that your computer is sending or receiving by ... looking outside of the computer box. You don't need to break into the computer, instead concentrate outside of the box, just listen to it. Computer at the end is just a machine that process any keystroke into series of bits that are translated into electrical signals: on and off. And as we all know these on-off switches usually makes tiny noise. In the computer case this noise could be captured by any smartphone microphones. So, if you are a secret agent you can spy on your enemy by accidentally leaving a smartphone near his laptop, taping and transferring the noise to your computer and de-crypting the data at home.
This is one of those things when many other scientists and lay people probably think: It is so simple. Why haven't we thought about it before? We have been concentrating so hard and deep inside the box that we forgot about the outside options.

Next year - let's try to thinking outside of the box. At work or at home, let's try to step aside and find creative unconventional solutions to any challenge we may face.
Happy New 2014!

Holiday Cookies: the chemistry and math of making them. Plus, a recipe.

Maria — Wed, 18 Dec 2013 14:21:00 +0000

How the ball of dough flattens, spreads and bubbles in the oven?
Why tasting raw dough is like playing a Russian roulette?
Why your cookies won't brown at the standard 350F?
How could you figure out that they are ready without using a kitchen timer?

All the answers and much much more interesting details are in this TedEd video:

But wait, there is more:
When you use melted butter instead of the room temperature butter chunks, the dough will spread out faster in the oven creating larger diameter cookies. At the same time meted butter will create more but smaller sized air pockets (holes) making the cookies chewier. Source: molecular biologist Liz Roth-Johnson, UCLA.

And the biggest secret is to make the dough 3 days ahead and refrigerate it for about 36 hours prior to shaping and baking in order to allow all the ingredients slowly penetrate each other and achieve better dough consistency. More details on that are in this NYTimes article.

Finally, as we learned all the science, let's try making the cookies.
My friend and excellent baker Sherene Michlin recommended two of her favorite recipes. One that is adapted from NY baker Jacques Torres and requires two types of flour, two types of sugar and very precise measurements. NYTimes subscribers could find it here.
Another: basic, straight-forward, no-fail - is from the NESTLE website. I am posting it below.

Ingredients:
2 1/4 cups all-purpose flour
1 teaspoon baking soda
1 teaspoon salt
1 cup (2 sticks) butter, softened
3/4 cup granulated sugar
3/4 cup packed brown sugar
1 teaspoon vanilla extract
2 large eggs
2 cups (12-oz. pkg) NESTLÉ® TOLL HOUSE® Semi-Sweet Chocolate Morsels
1 cup chopped nuts

Directions:

preheat oven to 375° F.

combine flour, baking soda and salt in small bowl. Beat butter, granulated sugar, brown sugar and vanilla extract in large mixer bowl until creamy. Add eggs, one at a time, beating well after each addition. Gradually beat in flour mixture. Stir in morsels and nuts. Drop by rounded tablespoon onto ungreased baking sheets.

bake for 9 to 11 minutes or until golden brown. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely.

Enjoy!

Bermuda Triangle Puzzle

Maria — Fri, 13 Dec 2013 04:17:00 +0000

I should warn you that this is a tricky one. It came via Facebook and god knows what devil invented it but as all the good puzzles it is carefully retold through generations and social networks.

Two triangles consist of exactly the same shapes. Shaped are rearranged in a different order in the bottom triangle and suddenly... one square disappears. How did this "Bermuda Triangle" swallowed the square?

Fill free to print the pictures and play with them, use a ruler. Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon. You can also email me your drawings to maria@themathmom.com

A Better Deal

Maria — Fri, 06 Dec 2013 02:55:00 +0000

I love shopping for my girls nowadays and buying items in bright pastel colors that will brighten the monochromatic pallet of the winter. In the last couple of days we made a few special trips to pick warm boots and pants. At first I purchased a couple of toddler pants in a strip mall for a "buy one, get second one half price" deal:

Two days later I finally organized the baby's closet and realized I need many more warm pants for the day care and home. In a run-by shopping after a movie I bought three more colorful pairs at a different store that had a "buy 2, get 1 free" offer.

Taking all the tags off I realized that all the pants had the same original price. But what purchase was a better deal or were they all the same? Each of my older kids had a different opinion on that. What do you think?

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Girl Rising

Maria — Sun, 22 Sep 2013 05:49:00 +0000

October 11st the UN's International Day of the Girl celebrating the power of education that transfers lives of girls all around the world. While our cultural stereotypes are preventing our daughters from being strong in math and going for degrees that will ensure their economic independence, cultural traditions or poverty in many other countries preventing girls from receiving any education at all. A new groundbreaking documentary Girls Rising, directed by Academy Award nominee Richard Robbins, tells the stories of 9 extraordinary girls from 9 countries. It is written by 9 celebrated writers and narrated by 9 renowned actresses. You can check for the screenings near you or organize your own screening:

Aside from the movie Girl Rising is a campaign and its website help you to create a curriculum that teaches students to think critically about issues related to girls education, ways for each to realize their own potential and and our global responsibilities. Click to bring Girl Rising to your school.

A Nail Cutting Puzzle

Maria — Fri, 09 Aug 2013 07:47:00 +0000

One mom told me recently that she cuts about 100 nails weekly. All coming from her own family.
Four young kids and her own nails.
The math is going like that:
Five people times (10 hand nails+ 10 feet nails) = 5 x 20 = 100

Counting this I started to appreciate my older kids' abilities to use the nail cutter themselves. My two-year old though is giving me a very hard time with every nail-cutting attempt. I have to catch her, sit her on my lap in front of a TV screen or capture her attention with ridiculous stories while carefully concentrating on her tiny hands and feet. And even then, her patience rarely lasts for more than 5 fingers.
I have heard that it is even harder with cats and dogs.

What is your nail math?
Do you have any advice on streamlining the process?

Image by GeoFx via Flickr, distributed under CCL.

Renovations Math, Smiles and Tears

Maria — Fri, 26 Jul 2013 08:28:00 +0000

They told us - be careful; renovations always take twice longer than expected, cost twice more than you planned, stress your work and family life to an unprecedented level and double your chances for divorce. We thought: Nonsense! It is just the stairs and a suite on the roof; a few months of work, with contractor and architect from our extended family. I thought I could keep an eye on the whole project while assembling the posts from this blog into a book. Life showed that they were absolutely right.

It all went like in the kids' classic: "If you give a mouse a cookie." Stair redesign led to flooring changes and required a new kitchen layout; while we were at it we extended the kitchen into the garage that demanded new garage doors; since the floors were open we were advised to renew the pipes; then came the bathrooms and the doors. It all got so expensive that we gave up on the roof suite dreams and re-planned for it in the basement. At the end we thought that perhaps the original stairs were OK but with 5 workers and a cement mixer inside the house it was too late:).

Double the time and double the budget but still married, we are now only in the middle of the process. My book dreams were put aside, as well as summer travel. Museum and park visits got replaced with tile, parquet and furniture shopping. The whole adventure did give us a lot of valuable construction knowledge that unfortunately will not come to use as we swore to never ever renovate again.

As I was immersing in, more and more renovation math shoved on me daily by general contractor and designer. I was trying to keep our kids involved and stimulated by occasionally translating to them these real life math puzzles:

If it took 3 days to destroy all the walls, how long may it take to build new ones? 1) 3 days. 2) one week 3) three months. #3 is the correct answer.
Which room is bigger? Calculate the area and compare.
Can you help me figure out how much tile will we need for your room? What about the whole basement (split into rectangles and calculate)?
What is the length of the railings that we will need to order for the roof?
How many stairs are we going to have? Our old stairs were surprisingly cumbersome: uneven, too high, slightly tilted. To lower the stair height we had to increase the overall staircase area extending it into the kitchen. The new stairs were supposed to be 7" each so my daughter and I calculated the number of these new stairs: (ceiling height + ceiling-to-second-floor thickness) /7
How many 6" tiles could you fit into a 60" x 60" area? 100? We were wrong! There is a 3mm-wide grout in-between every tile connection.
How many parts a bathtub shower and faucet may possibly have? More than you could see and imagine!
How many white colors do you think exist in this world? One? Wrong again! But they all would look the same to you if it were not for your designer biasing your perception.

I am sure you all have your own share of renovations math puzzles or experiences that I invite you to share with us to make me feel a little bit better.

Handcuff Your Kids

Maria — Fri, 26 Jul 2013 07:45:00 +0000

We are half-way through the summer vacation and you may be running out of ideas, resources and patience for how to entertain your kids while making sure their brains do not melt in front of screens, and they don't fight each other the rest of the time. Here is a short trick that will show them who is the boss, force them to collaborate, yet will leave them giggling.

Handcuff your kids. Yes, you heard me well. Use two ropes. Make sure not to tie them too tight to their wrists.

Now, tell your kids that they are free as soon as they will figure out how to untangle the ropes. No scissors or knives allowed. Let them hug and dance around each other for a while, then lead them to the solution that you can see here.

Summer Learning Activities from PBS Kids

Maria — Fri, 12 Jul 2013 08:01:00 +0000

Summer is officially here and for most of us it is an opportunity to do things we couldn't do throughout the school year - take it easy, spend more time outdoors, do something adventurous, learn new skills, and spend more time with the friends and family. It is a time to see who really your kids are, what they like and where they need a bit more confidence, tell them about things you like and teach them to manage their leisure time with some structure. Below is a list of resource links from the PBS Kids of fun summer science and math activities.

PBS KIDS Lab Home Activities:

http://pbskids.org/lab/home

Keeping Kids’ Math Skills Sharp All Summer Long

http://www.pbs.org/parents/cyberchase/math-fun-more/using-math-at-home/summer-skills/

Fun Summer Science Projects:

http://www.pbs.org/parents/education/science/tips/summer-science-projects/

Transitioning family from summer to school:

http://www.pbs.org/parents/education/going-to-school/back-to-school/transition/

13 Ways to sneak learning into summer fun

http://www.pbs.org/parents/summer/13-ways-to-sneak-learning-into-summer-fun/

Simple Tips for Summer Math Learning

http://www.pbs.org/parents/education/math/math-tips-for-parents/summer-math/

Creative Car Game for Summer Road Journeys

http://www.pbs.org/parents/summer/road-trip-games-for-kids/

Summer crafts

http://www.pbs.org/parents/crafts-for-kids/category/seasonal/summer-crafts/page/2/

A Bar Joke and a Bar Puzzle

Maria — Fri, 12 Jul 2013 07:31:00 +0000

First, let me start you on a joke.

A man has been coming to the bar weekly and ordering four small glasses of Scotch. The bartender offered him to take two large glasses instead of four small as it would come cheaper, but the man explained that they are four brothers living far apart from each other. Last time they met they decided that whenever each of them drinks, he should order four glasses to celebrate their brotherhood and imagine them all drinking together.
One day the man came to the bar and ordered three glasses. The bartender started on his condolence assuming that one of the brothers has passed away, but the man quickly rebutted that everyone is alive only he has recently been at his annual checkup and the doctor told him to stop drinking.

Now, to the puzzle that our fan Ilya spotted somewhere on Facebook (or at the bar?) and thought you would like:

Three very logical people walk into a bar. The bartender asks "Do you all want a drink?"
The first person says "I don't know."
The second person says "I don't know."
The third person says "Yes!"

Question is, what explains such strange answers by these logical people, and why do they actually make perfect sense?

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Image by marsmet511 used under CCL.

The Shopping Cart Paradox

Maria — Sat, 29 Jun 2013 04:36:00 +0000

We all have done it thousands of times. But I have thought it through only now. There is a serious issue.
A paradox, I'd say. The shopping cart paradox... The more you buy, the more pronounced this paradox becomes. You pay at the cashier, bag all your groceries and carefully place them in the shopping cart arranging the heaviest items on the bottom and anything breakable, smashable, squeezable on the top. If you do your family shopping only once a week and especially if you have diaper-age kids, chances are your cart is full to the top.

top: anything fragile, smashable, squeezable
bottom: heavy items

Now, you come to your car and start transferring the bags into your trunk. What bags are on top of the cart? The bags with the breakable, smashable, squeezable items! The only choice you have is to put them at the bottom of your trunk. What goes next? The bags with the heavy items that will undoubtedly break, smash and squeeze the bread, yogurts, eggs and peaches on the bottom. You see the flipping grocery cart-car paradox? Of course you are aware of this. So, you naturally try to sort the bags as you place them, spreading the bags around the trunk or the shopping cart. Some of us are even using the ground or a second cart as a temporary placeholder, flipping the bag order once again: lighter to the ground, heavier in the trunk, then placing lighter ones on top. We make it work, but it is far from optimal. It seems that some creative solution is required here to save us all from this ridiculous weekly process.

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Image by Polycart used under CCL.

The Power of Ten, by Eames.

Maria — Fri, 21 Jun 2013 06:31:00 +0000

The Eames Chair: one of the design gems of the 20th century, a unique combination of beauty and comfort. Designed in 1956 and continuously produced by Herman miller ever since; available at the Design Within (Without?) Reach for $3,500+.

Turns out that the designer couple behind this legendary chair, Charles Eames and Bernice Alexanda ("Ray") Eames, were interested not only in furniture but also textiles, photography and film. Fascinated by the relative size of things around us and our perception of the universe they created an interesting short movie called Powers of Ten. It starts with a couple on a lakeside picnic near Chicago and every 10 second shows the same scene from 10 times further out until the galaxy is visible only as a speck of light. It then quickly goes back down to the picnicking couple and zooms deep into the men's skin. Short and powerful! Click on the image below to open the film in a new window. Watch with the kids.

Indian Math Trick

Maria — Fri, 21 Jun 2013 05:42:00 +0000

A few days ago my son excitedly rushed to show me a trick he learned via Facebook. It was called an Indian Math Trick probably because Indians are very good and confident at math and you have to be both to do the tricks.

Here is the trick:
Take two large two-digit numbers, for example 97 and 86. It is a pain to multiply them without calculator, right?
Computers do it easily: 97 x 86 = 8342
Can someone human to do it in his/her head?
Turns out anyone can:
Take complements of these numbers that bring each to 100: for 97 it will be 3, for 86 it is 14.
Multiply these compliments and you get the last two digits in your desired result: 3 x 14 = 42
Now add these two compliments: 3+14=17 Subtract this number from a 100 and you will get the first two digits in your number: 100-17=83
8342

Pretty impressive!
Now, tell me why it works and when?

Image is by Partha Sarathi Sahana distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Who is Faster?

Maria — Fri, 14 Jun 2013 06:06:00 +0000

My kids love racing each other: on foot, bikes, roller skates or scooter.
They also love arguing: you are older, so you have to give me a headstart, your legs are longer, but you are lighter.
Well, my son is 13 and is 6'8", my daughter is 10 and is 4'9".
How can I help them decide who is faster, factoring their age and size?

Image by Shanti Knapp, distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

All About Tracy

Maria — Thu, 13 Jun 2013 13:11:00 +0000

This week we are cheering to Tracy Z. who slowly and consistently climbed toward 50 puzzle points, and honoring Tracy with an exclusive interview.

Congratulations, Tracy! As you were answering these questions, you were preparing to go camping on the Cape Cod. In this picture you sent you are also hiking with a baby in tow and what seems like a giant backpack. What an amazing energy!

This picture is of me and one of my kids on a trip that we take every winter. We and friends hike into a very rustic cabin (no electricity, no plumbing) in VT for a long weekend, and carry all our gear in via backpacks and sleds. We’ve been doing it since pre-kid days. I spend a lot of time for work and at home in front of computers. Many of my fondest memories though come from the times when I unplug the computer and get outside for a weekend, a week, or longer. I love hiking, biking, kayaking, and cross-country skiing and snowshoeing.

Tracy, have you ever had a big or little life dilemma that you solved with math?

Little: I’ve used math to estimate a number I can’t actually fully compute. For example, in a contest to guess the number of peanuts in a very large bag, I came closer than anyone else and won the whole bag. It was too much to eat.

Bigger: At my house, we once wanted to estimate where a property line was located without having to hire a surveyor. We wanted to know which trees were on our property and which were on an adjacent property. We found survey markers for two corners (A & B) on one side of the property and used very long pieces of string and triangle geometry to estimate the border on an adjacent side of the property. Here are the details: We took the straight line distance between A and B (let’s call the distance x) and assumed the adjacent border from corner A to the unknown point C would be a right angle to side AB (the assessors’ property maps suggested the angle was 90% or very close to it). We created a string of length x and a second string of length (sqrt(2))*x. We tied the x- length string at corner A, and tied the (sqrt(2))*x-length string at corner B. At corners A and B, we then rotated the two strings until they intersected when each string was fully extended. This intersection point was point C. Once we knew C, we knew side AC was on the property border. AC was long enough to go past the trees in question, but if it had not been, we could have run another longer string along AC as far as needed.

Have you ever did any miscalculation using logic and numbers in real life?
One type of miscalculation I make far too frequently is underestimating how long it will take me to get somewhere, such as for an appointment. I think about what time the appointment starts, and then make the assumption that that time it will take me to get there will be the minimum time that such a trip would take under ideal conditions with no delays of any kind. I allow for little margin of error and as a result I am often a wee bit late. Fortunately, I had just a few times where I have been very late. Too bad personal teleportation is not yet an option.

Do or did you ever use math professionally?

I use math personally and professionally almost every day. I was a math major in college. In my professional life, I have had positions gathering and analyzing data regarding: the energy and cost savings of energy-efficient household appliances; the population, economic, and land use trends for regions and communities; and the contributing factors behind motor vehicle crashes and fatalities. I currently work in a research laboratory that conducts studies of driver behavior (such as driver distraction) in driving simulators and on-road environments. We collect a variety of data on our participants during their sessions, including their demographic and driving histories, and their eye movements, head movements, their travel speed, acceleration, and lane deviation while driving, and use this data to develop training programs to improve drivers’ skills.

Some people say that best ideas come to them in the shower, for some it is while they are asleep, for some - while they are jogging. For you, what conditions, mood or environment are the most optimal to tackle a hard puzzle?

I get many of my best ideas for how to proceed on a hard problem when I outside walking or biking. I also get great ideas, especially for Math Mom puzzlers and other brain teasers, by talking them over with my spouse or kids. They love math and logic puzzles as much as I do.

To whom or what you are attributing your interest in math – a teacher, parent, TV program?

There are two people to whom I attribute my interest in math and logic. The first is John Powers, a wonderful teacher who mentored me in middle school. He encouraged me to create a book of logic puzzles and to develop a curriculum to teach logic skills to kindergarteners and first graders. The second is Dr. Arthur Eisenkraft, my high school physics teacher. He frequently had us put down our textbooks and engage in real-life exercises to better understand the concepts he was teaching us. We’d have labs where we threw and hit baseballs (studying speed and distance); dropped objects out of 3-story windows (gravity), and honked car horns while driving at different speeds (Doppler effect). He made science and equations live. Dr. Eisenkraft now runs a center at UMass-Boston that focuses on improving the teaching and learning of science and math for all students, from kindergarten through graduate school.

Thanks, Tracy!
Curious to know more about our other puzzle-solvers? See our previous interviews: All About Ilya, All About Jerome, All About Anne-Marie, All About Tom, and All About Kim.

Party Head Count

Maria — Fri, 07 Jun 2013 06:31:00 +0000

A few months ago we celebrated our son's Bar Mitzvah party. This was the first large-scale formal celebration that was held not in our back yard (unlike our wedding and a few other big bashes we have had). And the food was not the usual potluck or Trader Joe's or grilled meat, but a pre-tasted catering selection. I spent a month picking a place with nice vibe, good views, reasonable food and price, and plentiful parking space. And, by the way, the place was half-a-way across the globe, in Israel, where most of our family and quite a few friends live. We celebrated in Tel Aviv, on the banks of the Yarkon river, in the restaurant space of the Daniel Amihai Rowing center, which looked magnificent in the evening and had even better views from inside, of the city skyline and Mediterranean sunset.

About a week before the event we had to provide the exact head count. We were told that this would be the minimum amount of people we will pay for. Even if only half of these guests will show up, we will have to pay for the ordered amount as the chef will prepare the food for that amount. Should a few extra guests pop up, we will pay for each of their portions as well, on top of the agreed upon amount. Inexperienced in such situations and dealing with relatives that we haven't seen in a while and customs we are no longer used to, we were not sure how exactly to estimate the expected head count most precisely. We invited 120, but how many will show up? The answer seemed to lay somewhere between 70 and 125.

Price-per-person depended on the number of people we reserve for:

less than 100 guests - $80 each
more than 100 guests - $64 each

in addition to the price-per-person, there was a service fee:
$100 for each waiter that serves 10 people
the more people will show up, the more waiters we would need

We tried to call and email everyone (no RSVP customs in Israel) carefully inquiring who is coming, but then we realized that some mathematical thinking and less precision could save us some money and time. How?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

What is Wrong with This Prudential Ad?

Maria — Fri, 31 May 2013 02:45:00 +0000

Prudential is running a new advertising campaign titled "Let's get ready for a longer retirement"
The text under the picture says:
A typical American city. 400 people. And a fascinating experiment. We asked everyday people to show us the age of the oldest person they've known by placing a sticker on our chart. Living proof that we are living longer. Which means we'll all need more money to live in retirement. and so on.

While I agree that statistically we are living longer than our predecessors and we need to save more for our retirement, I doubt this experiment proves it.

I can imagine how it all came to be:
- Folks, let's emphasize that we are dying at an older age, and need to save more.
- But, Bob, we cannot talk about death in an ad campaign.
- Yeah, let's find something positive in us growing older, sicker, lonelier, absolutely dependent.
- Well, everyone is excited to hear about someone in the stress-less mountains making it to a 100.
- Great idea, let's talk about the oldest person you know!

So, why this chart is not a living proof of us living longer?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Bat Mitzvah Favors, Messy And Full of Math.

Maria — Thu, 23 May 2013 15:28:00 +0000

This is a guest post by my very good friend Ellina who is celebrating her daughter's Bat Mitzvah in a few weeks.

In a strange and unexpected moment of creative inspiration (channeling my inner Martha Stewart, which I didn't know I could!), I decided to make chocolate-covered Oreos as favors for my daughter's Bat Mitzvah party, where we will have 70 kids in attendance. Some strong math should really have been involved in my decision, but I usually shy away from having to calculate anything, so I thought I'd "be creative" and "enjoy the process." What is there to do - buy a few packs of Oreos, dip them in chocolate, use food coloring spray and stencil to "Mazel Tov" on each, pack them in bags of 3, and here we go - 70 delicious and festive favors.

I was told that there is a person who charges $2 per cookie when she does this, and I thought it was an exorbitant price. I needed 70 x 3 = 210 of those and wasn't ready to pay $420 for that.

Preparing the project, I created a list of supplies:

I have three molding trays that make 6 Oreos each, so I can make 18 at a time
I have three different decorative stencils -- one says "Bat Mitzvah", one says "Mazel Tov!", and one is a Star of David -- every favor will get three cookies, one of each design
There are 36 Double-Stuf Oreos in one package
A package of chocolate melt wafers is 14 oz.
A can of pearl white food coloring spray (that is used to spray the stencil design onto each cookie) is 15 oz.
Each set of 3 cookies will go into a little cellophane baggie, tied with a piece of decorative ribbon (about 8" of ribbon per baggie)
Ribbon comes in rolls of 9 feet
Baggies come in packs of 100 (so I will need only one pack -- this one is easy!!)
Each baggie will have a piece of cardstock stuffed into it, as "decorative backing" for the cookies.
Cardstock comes in sheets of 12" x 12"
Each baggie will need a 4" x 4" piece of colored cardstock
I want to alternate lavender and light blue cardstock (trying to stick to the party's color scheme of lavender, white, and light blue)

Just in time, the AC Moore store was having a sale on chocolate melt wafers (normally 2.49/bag, sale price of 1.99/bag), so I stocked up, got 12 bags. The first time. Little did I know that I will have to go back two more times, for wafers and other ingredients... 16 bags of wafers total.

Got 6 spray bottles of white food coloring -- with the way my spraying was going, I knew I'd need a few! Got 4 more during a later trip.

Double-Stuf Oreos were also on sale (normally 3.69/box, sale price of 2.99/box), I got 7 boxes and then went back for another 4 (36 cookies in each, I needed to make a total of 210, but underestimated the amount of broken cookies, eat-while-I-work cookies, cat-stole-and-dropped-down- off-table-to-share-with-dog cookies, and family-sneaking-finished- product-late-at-night cookies).

Found cute ribbon for only $1 per roll (9 feet each), but all I could find was 3 rolls (will not be enough, as I need 8" per baggie, and need to make 70 baggies, which would mean almost 6 full rolls). Tried to find 3 additional rolls later that would be the same, scared away fellow shoppers as I frantically clawed my way through the $1 ribbon bin -- alas, to no avail. Will end up with two types of ribbons closing up the baggies. Keep reminding myself that kids don't care.

Then, I planned the actual steps and slowly perfected them through trial-and-error:

Melt chocolate wafers (three 30-second intervals in the microwave)
Pour a bit of the chocolate melt into one cookie mold slot

Put Oreo into cookie mold, and push down to get the chocolate to come up around the sides
Pour a bit more chocolate over the top, and spread to cover up the cookie
Tap the bottom of the mold a few times to get air bubbles out, and to ensure the chocolate has spread evenly around/over the cookie
Repeat for remaining 5 cookies in the mold
Put into freezer for 15 minutes

Repeat with remaining two mold trays, ending up with 18 cookies
Pop out cookies, take a stencil (one of the three choices), place over cookie, spray with food coloring

Put 18 cookies into large ziplock bag, make bag airtight by sucking all air out with a straw
Store bag in kitchen cabinet
Repeat while tolerating rolling-eye expression from daughter and husband
Curse Martha Stewart.

Now, you are probably starting to wonder what got me thinking that this could be fun. Well, so did I, but this was already too late into the adventure. The kitchen was an ugly mess. Every few hours I was going into sugar-induced shock from breathing cheap candy wafer fumes, and food coloring spray fumes. I then run to the fridge, took pickles out of a jar and ate them to decrease the sugar overload. Ate them quickly, to balance out the sugar. At that point it is important to recognize that the assembly of the favors was still to come....

Favor Assembly Steps:

Take pre-cut piece of cardstock, put into cellophane baggie
Put three cookies (one with each design) into baggie, with cardstock as background
Take pre-cut pieces of ribbon
Tie ribbon into knot
Repeat

The final result:

Overall time investment: 35 hours so far.

Total money spent: about $110 .
Chocolate consumed: 1 pound+

59 done, 11 to go... I've somehow miscalculated my sets of 18, so I now have too many Magen Davids, 7 Bat Mitzvahs (need 11), and no Mazel Tovs at all... Bought one more box of Double-Stuf Oreos...

Honestly, when this is done, I don't think I'll be able to be anywhere near another Oreo for what is likely to be years... :-)

Plan on bringing the not-yet-assembled pieces to a Memorial Weekend retreat to get the extended family help me put it together. Need to feed them ice cream before to prevent any pieces being eaten.

Exhaustion and excitement are up.

Time to the party: 2 weeks
Next on my list: video montage and table centerpieces.

From TheMathMom: Ellina - I am sure these elaborate multi-week home preparations make the anticipation even more special and the whole event much more personal and memorable.

St Patrick’s Day Math Pop Quiz

Maria — Thu, 14 Mar 2013 06:10:00 +0000

Prepare for St Patrick's Day with this fun math pop quiz. A simpler version of this quiz was originally created for and published by Boston.com in 2011. Here is the old link.

Puzzle #1 Two Airplanes Puzzle

A Boston man decides to surprise his friend in Ireland for St Patrick’s Day and boards a plane for Dublin. Meanwhile, his Dublin friend has the same idea and boards a plane for Boston. The Dublin-bound plane is flying at 565 miles per hour and the Boston-bound plane at 485, because it is bucking a jet stream. Which plane will be closer to Dublin when they meet above the Atlantic?

Answers:

Boston-to-Dublin plane;
Dublin-to-Boston plane;
same distance

Correct answer is 3. At the point when they meet, of course they will each be the same distance from Dublin.

Puzzle #2: The Snake Myth

Legend holds that St. Patrick banished snakes from Ireland. It's true that no snakes exist in Ireland today. What do you think most likely have happened:

Snakes were scared of St Patrick and slowly slid away; assuming they were traveling 5 miles per hour, in 60 hours they could cover the 300-mile length of Ireland.
It was the Pied Piper that run all thee snakes away.
Snakes never lived in Ireland, since it is an island surrounded by icy waters and snakes never had an opportunity to migrate there

Answer #3 is correct

Puzzle #3: Root Beer Puzzle

You bought a homemade root beer kit in celebration of St Patrick’s Day. But you decide to skip reading the directions and just mix up everything in the kit. As soon as you plug the bottle and shake it, the brownish mix starts growing with an astronomical speed. It looks like it is doubling in volume every minute. If you start with one glass (250ml) of mix, how long will it take to expand and fill the whole 2-liter bottle?

Answers: 8 min, 4 min, 3 min

Correct answer is 3 min. If the mix is doubling in volume every minute, then after the first minute 250ml will grow into 500ml, after the second minute 500ml will grow into 1000ml and after the third minute 1000ml will make 2000ml, which is the whole bottle.

Puzzle #4: Tough Luck

The three-leaf clover (shamrock) has been a symbol of Ireland for hundreds of years. Very rarely a clover with more than three leaves can be spotted. It is believed that encountering it brings good luck. It is actually a tough luck to find as there are approximately 10,000 three-leaf clovers for every four-leaf clover. But you promised one for your friend. If you are searching in a one-acre field that has 500 clovers per square foot, how many square feet of field you are likely to crawl and scan before you find the lucky clover?

Answers:

1,000
500
20

Correct answer is 3) 20. You are likely to look through approximately 10,000 clovers to find the four-leaved one. If there are 500 clovers per square foot, then you will crawl 10,000/500=20 square feet.

Puzzle #5: Parade Puzzle

St. Patrick's Day Parade starts at 1pm and goes at approximately 3mph through the South Boston. You are watching the parade start on TV but still want to experience it for real midway through, 1 mile from its start. It is a 15min walk from your apartment, but you are really hungry. Do you have extra 5 min to grab a lunch on your way?

Answers:

Forget about lunch, run as fast as you can.
Sure you do.

Correct answer: 2. With a speed of around 3mph, it will take the parade 20min to move 1 mile. 15min to walk and 5min to get a lunch.

Puzzle #6: The Celtics' logo

The name Boston Celtics reflects the city's Irish heritage. Celtics logo was designed by Red Auerbach's brother, Zang, in the early 1950s. He assembled the familiar leprechaun with the words Boston Celtics arched around it in a circle. You surely saw this logo hundreds of times. Do you recollect how many three-leaf clovers are featured on the leprechaun?

Answers:

Correct answer: 12 (3 on the hat, 2 on the tie and 7 on the vest)

Puzzle #7: Grandma’s Recipe

Every St Patrick’s Day you are making soda bread for a family dinner. Your favorite grandma’s recipe lists ingredients for a loaf-shaped 12” x 5” x 3” pan. You just threw the rusty pan out and only have a square 9” x 9” x 2” pan. Will the dough overflow?

Answers:

Correct answer: 1) Go look for another pan or use 2/3 of the ingredients. It will overflow. Your original pan had a 12x5x3=180 cubic inch volume. The new square pan has 9x9x2=162 cubic inch.

Puzzle #8: I can see you, can you see me?

Your band has been invited to participate in the St Patrick’s Day Parade. You are rushing to Parade start point in the car and finish applying make-up at the red lights, looking in the rear view mirror. While applying lipstick you see in the rear view mirror the eyes of the driver from a car behind you. He seems to be staring at you. Can he see your beautification routine?

Answers:

yes he can
no way, he is in the car behind

Correct answer is 1) The driver in the car behind you sees at least part of your face reflected in your rear view mirror (unless your car back is tinted). Light is reflected with the same angle it falls on the mirror. If I can see you, you can see me.

Puzzle #9: Celtics Pride

The TD Garden has 17 NBA championship banners hanging from the rafters, one for each of the NBA championships Celtics team has won (most than any other NBA team). Celtics team was formed in 1946 and championships were held from 1947. At this rate, would they win their 34th championship by 2075?

Answers: a) yes b) no

Correct answer is a): The Celtics won 17 games in the past (2010-1947+1) = 64 years. With the same winning rate, it will take another 64 years for 17 more wins: 2011+64=2075

Puzzle #10: The Magical Year

Your father was telling you about the memorable Celtics NBA final when the TV cameras zoomed in on the year at the end of the game, then slowly zoomed out and rolled (rotated) revealing, to his amazement, that the year number is the same upside down. Which year and game this was?

Answers:

1969
1991
1961

Correct answer is 3) 1961 will be 1961 upside-down if 1’s are written as lines.

I Can See You Breathing

Maria — Thu, 28 Feb 2013 06:13:00 +0000

This is fresh from the oven - terrific new technology from the MIT Computer Science team.

You know how it is easier to recognize someone from a caricature than from a photograph? This is because caricaturists exaggerate our imperfections and exasperation help our brain to do the match. What if we can apply such exaggeration to other fields? For example, what if we can exaggerate small motions? A hand tremble, eye movement, chest raising while breathing, blood pulsation on the neck or cheek? Computer Scientists from the MIT propose to process a video stream with such motions and use some surprisingly simple math to detect and amplify these motions so that they will be clearly visible to our eye. This is the beginning of a great technology. Technology that can allow you to easily check whether your baby is breathing by just glancing at the video camera, check his pulse without EKG, observe your body's blood flow without going to an alternative medicine clinic, define guilt during a trial through involuntary eye movements, and even verify whether Batman is still alive. Check the clip:

Playful Family Statistics

Maria — Wed, 27 Feb 2013 04:38:00 +0000

This came via Facebook. It is written by Orit G. in Hebrew.
Since it is so funny and true, plus it is family statistics, I decided to translate it for your enjoyment:

Questions that kids are asking mom:

Mom, where is my towel?
Mom, what are you making to eat?
Mom, when are you coming back?
Mom, what time is it?
Mom, what day is today?
Mom, where is my pencil?

Questions that kids are asking dad:

Dad, where is mom?

How to Help Your Kids Handle Test Stress

Maria — Thu, 21 Feb 2013 05:11:00 +0000

It may be a dance or piano recital, SAT test or mid-term exam for your kids; a job interview or important conference call for you. Perfectly prepared, you became more anxious as time gets close and fail to deliver at your best. Does it mean that you or your kid are just not built for stressful situations and should avoid them altogether?

Last week I stumbled upon a very important article in NYTimes by Po Bronson and Ashley Merryman "Why Can Some Kids Handle Stress While Others Fall Apart" In case you don't have a subscription or time to read all 6 pages, here is a short summary.

Some of us are striving in a competitive stressful environment (school tests, sport or arts competitions) while others worry and perform worse than they could in a regular "peaceful" surrounding. Turns out that people of this second type can be trained to embrace the stress and out-perform on a long run. So the answer in not less testing but more testing of the right kind.

Few recent studies pinpointed an "anxiety-related gene" that can have either Worrier or Warrior state. Since we all inherit one gene from our mother and one from our father, a quarter of the population has two Worrier genes, a quarter has two Warrior genes and a half of the population has one of each genes.

Worrier gene gives us cognitive advantage: better reasoning, concentration, higher IQ. And this advantage appears to increase with the number of years of education. However, this advantage disappears at the time of stress and leads to under-performance.

Warrior gene, on opposite, lights up at the time of competition. People with to Warrior genes are "like Superman emerging from the phone booth in times of crisis; their abilities to concentrate and solve problems go up." (BC professor Adele Diamond)

Should Worrier types avoid stress altogether? No. "In fact, shielding them could be the worst response, depriving them of the chance to acclimate to recurring stressors. Training, preparation and repetition defuse the Worrier’s curse." (UCSD professor, Douglas C. Johnson) Some early studies show that " Worrier-genes can still handle incredible stress — as long as they are well trained. Even some Navy SEALs have the Worrier genes, so you can literally be a Worrier-gene Warrior. "

"There are many psychological and physiological reasons that long-term stress is harmful, but the science of elite performance has drawn a different conclusion about short-term stress. Studies that compare professionals with amateur competitors — whether concert pianists, male rugby or female volleyball players — show that professionals feel just as much anxiety as amateurs. The difference is in how they interpret their anxiety. The amateurs view it as detrimental, while the professionals tend to view stress as energizing. It gets them to focus."

Studies show that a similar mental shift helps students in test-taking situations. Grades of the students improved only after their were told to see stress as beneficial.

"David and Christi Bergin, professors of educational and developmental psychology at the University of Missouri, have begun a pilot study of junior high school students participating in math competitions. They have observed that, within a few weeks, students were tackling more complex problems than they would even at the end of a yearlong class. Some were even doing college-level math. That was true even for students who didn’t like math before joining the team and were forced into it by their parents. Knowing they were going up against other teams in front of an audience, the children took ownership over the material. They became excited about discovering ever more advanced concepts, having realized each new fact was another weapon in their intellectual arsenal.

Maybe the best thing about academic competitions is that they benefit both Warriors and Worriers equally. The Warriors get the thrilling intensity their minds are suited for, where they can shine. The Worriers get the gradual stress inoculation they need, so that one day they can do more than just tolerate stress — they can embrace it. And through the cycle of preparation, performance and recovery, what they learn becomes ingrained."

So, what can help any Worrier to do better at a test time? It is:

training, preparation and repetition
change of attitude toward stress - looking at it as excitement, energizing physiological process
participation in more tests, especially group-type confidence-boosting academic competitions

Top image by db photography, distributed under CCL.

How Long Should Your Phone Number Be?

Maria — Wed, 13 Feb 2013 08:14:00 +0000

Arranging a carpool recently I was surprised to discover that the father of my daughter's friend has a very suspicious and easy to remember number ending with "9999." Inquiring whether he is anyone very important to be assigned such a number, I received a straight answer from his 9-year old daughter: "He got this number as a payback after being very mad at his cell service."

Most of us cannot keep more than 4 digits in a memory for too long. Why then our phone numbers should be so long we have to bribe or threaten phone providers to get an easy-to-remember number?

As you may have guessed the answer is in math, simple and applicative. Exactly the type of math that many argue should be taught at school. Blessed with a free afternoon this week, I decided to try the following on my 9 and 12 year old kids.

Imagine that we have just 10 people spread around the world. Just 10 people, no one else. And a fully functioning cell phone system. Do these people really need 10-digit phone numbers to dial each other?
Since there are only 10 of them, we can give them 1-digit numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

But as soon as eleventh person is born and grows mature enough to get her/his phone number, we need to use number 10. And we add to all the other numbers 0 in front: 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10.
Then another person (twelfth) grows and gets number 11.
We can continue adding up more phone customers till a hundredth person gets number 99.

So, we see that:
1 digit is enough for 10 people.
2 digits - 100 people.
continuing this we get:
3 digits - 1,000 people.
4 digits - 10,000 people.
etc.

How many people live in our home state of MA? 6.5 million. Let's see how many digits do we need so that everyone can get a unique phone number.
5 digits are enough for 100,000 people.
6 digits - 1,000,000 people. Still less than we need.
7 digits - 10,000,000 people.

So, using 7 digits in a phone number will allow us to create 10 million various phone numbers that will be more than enough for all the people of MA. And guess what, check your home phone number. Not counting the 3 area code digits, it is exactly seven digits long! Someone thought it through.

Now, imagine that you want to establish a new cell phone service in Russia. How long should your numbers be? I let my kids to Google Russian population (160 million) and come up with a 9 digit answer.

Then we tried China with 1 billion 344 million people and realized that we need 10 digits.

Now think car license plates or zip codes. Imagine yourself planning a Mars colony. How many digits in their phone numbers, flying saucer license plates and zip codes would you need?

Top image by Ed Yourdon, distributed under the CCL.

Matchmaking - how does it work?

Maria — Thu, 31 Jan 2013 11:49:00 +0000

Imagine that you have four daughters and you want to marry them. You carefully select four guys and let each of your daughters spend some time with each guy. Then all the daughters and all the guys mark their potential partners in the order of their priorities. How do you use this ranking to match your daughters to the guys to create four stable couples? Couple is considered stable if each of your daughters is happy with her partner and she wouldn't rather be with some other guy who simultaneously also prefers her to his current match.

Or take another matching game. Four medical residents need to be matched to work in the hospitals. Each of the residents spent some time practicing at each of the four hospitals in the program. Then all the residents and all the hospitals mark each other in the order of their preferences. Your task is to use this rating to create a satisfactory match, sending one resident to each of the four hospitals. Each resident should be sent to a hospital where he is happy. It may not necessarily be her or his first choice but there should be no other hospital that he would rather be at that simultaneously also wants him more than the current resident you sent there.

Try playing such match-making and when you are done, watch this video. Click to see Harvard Postdoc Emily Riehl explains the optimal matchmaking algorithm for such situations. You can share this with your 10+ year old kids.

You can also see the explanation of the same algorithm applied to the National Resident Matching Problem via this link.

Note that while this algorithm is simple and is always guaranteed to converge to the optimal result, the algorithm is not symmetric. The optimal solution for girls is different than the optimal solution for boys, and optimal solution for residents differs from the optimal solution for hospitals.

Top image by imaekelley, distributed under CCL.

Prime Number Pop Quiz

Maria — Fri, 25 Jan 2013 05:04:00 +0000

The year 2013 has just started and while writing a check or holiday cad you may have noticed that 2013 is odd. It ends with 13 that many would rather skip. It contains all the digits in a range of 0-3 with no repetitions, however it is not a number you would call beautiful. Definitely odd. Perhaps even prime...
Is it prime?
Nope, 2013 is divisible by 11, 3 and 61!
Dare to take a quiz about prime numbers?
If you need some muscle-buildup before the quiz, here is an article about recent prime year 2011 I wrote for The Boston Globe: 2011 is a sexy prime.

Ready for the Quiz?
Here we go:

1.Puzzle #1: Prime Olympics

True or false: Number of rings in the Olympic emblem is prime.

Answer: True, there are 5 rings and 5 is a rime number.

Puzzle #2: Leap Prime

True or false: Leap year cannot be a prime number year.

Answer: true, leap year numbers are divisible by 4.

Puzzle #3: Infiltrator

Which of the following four numbers is not a prime: 1, 37, 911, 991.

Answer: 1 is not prime because prime should have two different divisors: 1 and itself. However, long time ago 1 was considered to be a prime.

Puzzle #4: What are primes?

Which one of the following is a correct definition of a prime number:

–

Odd number ending with 1, 3, 5, or 7.

Any number present in the multiplication table. Multiplication table is a “base” of all the numbers.

Number that can be divided by only two distinct divisors.

Number that looks the same left-to-right and right-to-left.

Answer: #3.

Puzzle #5: Prime Flowers.

True or false: Number of petals in any flower is always prime.

Answer: false. There are 4 petal flowers, 4 is not a prime.

Puzzle #6: Even Primes

True or false: No even number is prime because all even numbers are divisible by 2 in addition to divisors of 1 and itself.

Answer: this is false because 2 is a prime number. The only even prime. It is divisible by 1 and 2.

Puzzle #7: Math Magic

True or False: This trick can only be done in the prime year such as 2011: Take the age you were in 2011, add the last two digits of the year you were born and get a number that ends with 11 or 111.

Answer: This trick will work for any year that ends with 11 such as 1911. And 1911 is not prime: 1911 = 3 x 7 x 7 x 13 Therefore the magic statement is false.
In general, if you add your age to the year you are born you will always get current year. So in 2011 it will end with 11, as well as in 1911 and 3311.

Puzzle #8: Prime Senate.

Number of Democrats in the US Senate is a prime number as well as the number of Republicans in the US Senate.

Answer: This is true. There are 47 Democrats and 53 Republicans currently in US Senate.

9.Puzzle #9: Prime 108

True or false: Famous “Prime 108” restaurant in Nashville, TN located in the Union Station is named after prime number 108 that is the number of entries on their menu.

Answer: false. 108 is not a prime number (108=54x2). The restaurant is named for a Bully 108, the first steam engine to chug through Union Station, and "prime" alludes to the high-quality ingredients used to compose the dishes.

10.

Puzzle #10 A Special Year.

True or false: Current year is rather special. It is prime in the Gregorian calendar – year 2013; prime in the Islamic calendar – year 1434. And prime in the Hebrew calendar – 5773.

Answer: false. 2013, 5773 and 1434 are not prime numbers.

This quiz was created by TheMathMom for the Boston Globe in 2011. Link.

Food shopping: optimizing it all but still enjoying it.

Maria — Thu, 10 Jan 2013 09:36:00 +0000

From time to time everyone of us has to reconsider our food shopping strategies. You either move to a new area, have a new baby, or send old baby away for college, get laid off from work, start a new demanding job, or simply discover new stores in the neighborhood. Either way your old shopping strategy falls apart and you have to piece it back again ensuring everything is covered, feasible and optimal.

You want to remember it all - baby products, kids' breakfast foods, fruits and vegetables, meats, breads, dinner components, cleaning supplies - and renew it all on a weekly basis. What is your strategy for accomplishing this?

For a few years I have been encouraging you to create and utilize a Master Shopping List and even posted my list for you to copy and edit. I advised to check the supplies before leaving for the store, crossing everything you don't need to get, take a pencil with you to the store and check-mark the items as you drop them into a cart. But guess what, I am seriously questioning this strategy now.

It may be the new baby that we got that requires a load extra items; or the frequent long lines in the meat department, but I came to realize that my weekly shopping became an impossibly tedious and dull process that I am always trying to postpone. It takes me about an hour to zigzag the supermarket and efficiently gather all the items on my list. But approximately after 30 min it stops being fun. The pleasures of smelling fresh produce, trying samples, browsing through and discovering new products or combinations, planning the meal in my head - all expire at about 30 min from the store entry and all my senses shut down. I feel like a pawn in a reality show trying to mark off all the remaining items in a least possible time. At about 60 min threshold I get angry and start transferring my anger to the foods in my basket. A very sad beginning of the food as a pleasure process.

I discover that I enjoy short specialized shopping trips much more than I enjoy one long exhaustive food purchase. Biweekly stops at a bakery, weekly order from a fruit and vegetables farm, one or two quick specific visits to the supermarket (breakfast stuff only, dinner products, diary and meat items). I still do shopping lists but not the long master shopping list that I believe turns me into a food soldier. I create short lists of absolutely-do-not-forget products and try keeping the number of items in them below 20. This way I can keep my eyes on the shelves rather than in the list and let me mind explore and discover, noting, touching and smelling the items. I feel that I am adding fun as a new component to my overall shopping puzzle that already included time and money optimization, overall product coverage and product quality. The new strategy is definitely more time consuming but the fun factor makes it much less strenuous.

I think long shopping lists are still great for some people (aka food soldiers) and some situations. If, like my father, all you want is to restock on the items your wife asked without adding any frivolities, you cannot accomplish it without a long list. If you have to assemble an elaborate meal consisting of tens of obscure ingredients, you need the list and the focus on the list. You cannot avoid the long list also when coming back from a vacation. But for the rest of the days I insist on making my food shopping an adventure. What about you?

Image via Flickr, distributed under CCL.

Math-phobic Glossary of Math Terms

Maria — Thu, 03 Jan 2013 10:41:00 +0000

I decided to start 2013 with something playful. Over the years I have heard from many of my girlfriends that they feel quite uneasy with math. Below is my attempt to define math as something relevant, fun and hip. Please share it with the women in your life. And, let me know what you think about it.

Random : an arbitrary piece of clothing you are picking from your closet without even looking at the mess in it. Beware - if you cheat and feel the material type, buttons, zippers or, god forbid, take a peak - it will be a preudo-random item.

Average : Something you first want but then try to avoid to be.

Positive numbers: height extensions that high heels provide to you.

Negative numbers: The depths your pumps sink into the ground when you find yourself at the back yard party.

Infinity : the amount of sweets that your kids consume while you are away.

Parallel: your Sunday plans to your husband's Sunday plans during the football season. Absolutely nothing in common.

Perpendicular: your plans for the same Sunday to your teenager's plans. He needs you as a driver but for the rest please stay as far as possible.

Arithmetic series: your clothes' size, sampled every decade.

Geometric series: dramatically increasing amounts of gray hair you observe monthly on your head.

Integral: the amount of cork in your platform shoes.

Derivative: the steepness of the arch of you heel.

Signal-to-noise ratio: proportion of the neatly folded items to the messy stuff in your closet.

Median: you, dividing your kids' quarrels.

Acute angle: a narrow corner where you frequently want to hide.

Obtuse angle: a corner where you really are - observed and exposed.

Square Root: size of the present inside the holiday gift box, as compared with the size of the box.

Pythagorean Theorem:something to consider if your bed is too short for you. Perhaps you can fit on diagonal - it is just a square root of the sum of squares of the sides.

Fraction: you get what you get and you don't get upset.

Sine function: pessimist's happiness curve (indifferent and cautious at first, regularly surprised to the good but always finds a reason to push the mood back down).

Cosine function:optimist's happiness curve (happy to start with, regularly disappointed, but always brings his spirits back up).

Exponential growth - the speed rumors travel.

Parabola: the complimenting soft shape of your shirt's neckline exposing a bit but not too much.

Logarithm: how much does it take to make two (or more) kids to do what you planned.

Factorial: all your exes, numbered and multiplied.

Correlation: the coefficient of your marriage describing how strongly two strangers can connect and continuously affect each other.

Equation: your life with its ups and downs, some stable constants and a few unknowns.

Common denominator: greatly compromised choice for a family movie night.

Top image by she was, distributed under CCL.

Life Jokes Sweetened by Math

Maria — Thu, 27 Dec 2012 11:32:00 +0000

This is my assembly of jokes that arrived to me from various places on Earth and in different languages. I was carefully choosing life jokes that are sweetened by math rather than jokes about mathematicians or math ignorance. If you have anything to add - please add it in the comments below this post.

The speed with which woman says nothing when asked "What's wrong?" is inversely proportional to the severity of the anger that is coming.

I am not so good at "Scissors, paper, stone". Tried practicing in front of the mirror but it is very frustrating.

I bought pills for raising IQ, but couldn't figure out how to open the bottle.

A real optimist even at the cemetery sees pluses instead of crosses.

Bob, a 70-year-old, extremely wealthy widower, shows up at the Country Club with a breathtakingly beautiful 25-year-old woman. His buddies at the club are all aghast. At the very first chance, they corner him and ask, "Bob, how'd you get the trophy girlfriend?"

Bob replies, "Girlfriend? She's my wife!"

They are knocked over, but continue to ask.

"So, how'd you persuade her to marry you?"

"I lied about my age," Bob replies.

"What, did you tell her you were only 50?"

Bob smiles and says, "No, I told her I was 90."

We, women, have the hardest time finding a job. Everyone wants to hire a 18-year old with a 30-year experience, high education and grownup kids.

No, I am not so fat. My hubby says that I have a perfect figure.

Dear, but your hubby is a mathematician. For him, the perfect figure is a sphere!

My wife has just two complaints: first, she has absolutely nothing to wear. And second, she's run out of closet space to keep it in.

Bob bought a donkey from an old farmer for $100. The farmer agreed to deliver the donkey the next day. The next day the farmer drove up and said, “Sorry, but I got some bad news. The donkey died.”

“Well then, just give me my money back.”

“Can’t do that, I went and spent it already.”

“OK then, just unload the donkey.”

“What are you gonna do with him?”

“I’m gonna raffle him off.”

“You can’t raffle off a dead donkey!”

“Sure, I can. Watch me. I just won’t tell anyone he’s dead.”

A month later the farmer met up with Bob and asked, “What happened with the dead donkey?”

“I raffled him off. I sold 500 tickets at $2 a piece and made a profit of $898.”

“Didn’t anyone complain?”

“Just the guy who won. So I gave him his $2 back.”

Logical confusions:

Sign on an aircraft exit door: "If you cannot read these instructions, call a stewardess."

A fortune cookie note says: "Don't take advice from a fortune cookies."

And lastly: We do not stop laughing because we grow old, we grow old because we stop laughing.

So, Happy upcoming 2013 and much laughter for you all in it: with your friends, parents, spouse, kids, co-workers, TV, smartphone or radio. Do not miss any opportunity.

Top image by melthork, distributed under CCL.

Life is a Puzzle

Shortest Way to Help Grandma

What does it take to change an Army?

Something to do with your kids this summer.

Hong Kong Elementary School Admission Test

Standard heights for your kitchen counter, bar, dining table and other household items.

An Olympic Torch Puzzle

Mother's Day Quiz

Fair Split of the Rent

Riddles

Marathon Birthday Puzzle

Must See Movies

Best Time For Lunch

A Simple Magic Square

Four Women and Four Hats Puzzle

Oscar Ropes Puzzle

An Olympic Puzzle

How does it work?

All About Anne

Parrots and Cages puzzle

A Homeland Puzzle

A puzzle that 99% will fail to answer.

A Holiday Greeting for You from You

Happy Holidays! Next year challenge - think outside of a box.

Holiday Cookies: the chemistry and math of making them. Plus, a recipe.

Directions:

Bermuda Triangle Puzzle

A Better Deal

Girl Rising

A Nail Cutting Puzzle

Renovations Math, Smiles and Tears

Handcuff Your Kids

Summer Learning Activities from PBS Kids

A Bar Joke and a Bar Puzzle

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.Image by marsmet511 used under CCL.

The Shopping Cart Paradox

The Power of Ten, by Eames.

Indian Math Trick

Who is Faster?

All About Tracy

Party Head Count

What is Wrong with This Prudential Ad?

Bat Mitzvah Favors, Messy And Full of Math.

St Patrick’s Day Math Pop Quiz

I Can See You Breathing

Playful Family Statistics

How to Help Your Kids Handle Test Stress

How Long Should Your Phone Number Be?

Matchmaking - how does it work?

Prime Number Pop Quiz

Food shopping: optimizing it all but still enjoying it.

Math-phobic Glossary of Math Terms

Life Jokes Sweetened by Math

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Image by marsmet511 used under CCL.