New Puzzles

What time is it?

Sun, 19 May 2013 01:28:47 +0000

"What time is it, Rory?" asked Cory one lazy day. "When I checked my watch this morning, the hour hand was where the minute hand is now, and the minute hand was one minute before where the hour hand now sits. I notice both hands are now at exact minute divisions." What is the time now? When did Rory check this morning?

Tessellated Pictures

Sun, 19 May 2013 01:24:59 +0000

I have lots of photo prints, in two sizes: (a) 4 x 6 inches, and (b) 5 x 7 inches. I put photos up on the wall, each one can be vertical or horizontal, so that they tile into a big rectangle (with no overlapping or cutting, of course).

i) Prove I can't make a 19 x 19-inch "photo-square."

II) Show me how to tile the 29 x 29 photo-square.

Two special numbers

Sun, 19 May 2013 01:22:02 +0000

The product, the quotient, and the difference of two real numbers are all the same. Find the sum of the two numbers.

Winoc Sells

Fri, 17 May 2013 22:55:23 +0000

Winoc sells four types of products. The resources needed to produce one unit of each and the sales prices is listed below:

Resource Product 1 Product 2 Product 3 Product 4

Raw Material 2 3 4 7

Hours of labor 3 4 5 6

Sales Price ($) 4 6 7 8

Currently, 4,600 units of raw material and 5,000 labor hours are available.To meet customer demands, exactly 950 total units must be produced. Customers also demand that at least 400 units of product 4 be produced. What is the solution that maximizes Winoc's sales revenue?

Whether to produce desks, tables, or chairs

Fri, 17 May 2013 01:49:45 +0000

Resource Desk Table Chair Availability

Lumber 8 board ft 6 board ft 1 board ft 48 board ft

Finishing 4 hours 2 hours 1.5 hours 20 hours

Carpentry 2 hours 1.5 hours 0.5 hours 8 hours

Selling Price $60 $30 $20

Given the constraints listed in terms of time and wood available, how many of each object should be produced to maximize revenue?

SteelCo

Fri, 17 May 2013 01:38:54 +0000

Steelco has received an order for 100 tons of steel. The order must contain at least 3.5 tons of nickel, at most 3 tons of carbon, and exactly 4 tons of manganese. Steelco receives $20/ton for the order. To fill the order, Steelco can combine four alloys, whose chemical composition and cost is given in the table below:

Alloy (%)

Content 1 2 3 4

Nickel 6 3 2 1

Carbon 3 2 5 6

Manganese 8 3 2 1

Cost/Ton ($) 12 10 8 6

Steelco wants to optimize profit (revenue-costs) obtained from filling the order. How much of each Alloy content type must they produce to achieve optimal profit?

Solve the cryptogram II

Fri, 17 May 2013 01:21:01 +0000

18,8,21,24 22,24 2,1,1,25, 4,17,25 8 3,8,13,13 13,8,21,24; 18,8,21,24 22,24 3,4,9,24,10, 4,17,25, 8 3,8,13,13 25,8,24. 3,12,4,9 4,22 8?

The large punctuation is meant to be maintained when you resolve this cryptogram. The small commas is only meant to separate the numbers they go together as a single word.

Like last time, i don't care if you can translate this cryptogram. I want the correct answer in code.

Number Logic Puzzles Part 2

Fri, 17 May 2013 01:09:37 +0000

Paper Scissors Rock

Thu, 16 May 2013 13:54:50 +0000

There are satchels where 2 has paper, 2 has scissors and 2 has rock inside.
2 contestants picks up one satchel each, open them to determine who wins.
Then picks up another to determine who wins. 2 wins is needed to determine
the winner of the contest. What is the chance of winning 2 in a row ?

Driving man's delight - 2 a harder puzzle

Wed, 15 May 2013 19:16:32 +0000

I owe it to the Den to post at least one of these without error.
Possibly this one does that.

Give the longest route (sequence of city numbers) that visits all the cities
(a) not returning to starting city (sum of 7 distances - starting point matters)
(b) returning to starting city (sum of 8 distances - starting point does not matter)

This puzzle has more choices than the first one.

Cities lie clockwise on the perimeter of a 6x6 square:

6--O------O-------+--------O
   |3     4               5|
   |                       |
   |                       |
4--+                       +
   |                       |
   |                       |
   |                       |
2--O2                     6O
   |                       |
   |                       |
   |1              8      7|
0--O-------+-------O-------O
   |       |       |       |
   0       2       4       6

+----+---+---+
|City| x | y |   Distances:
+----+---+---+   8.485 1-5 3-7
| 1 | 0 | 0 |   7.211 2-5 3-6 3-8 4-7
| 2 | 0 | 2 |   6.325 1-4 1-6 2-7 4-8 5-8
| 3 | 0 | 6 |   6.000 1-3 1-7 2-6 3-5 5-7
| 4 | 2 | 6 |   5.656 4-6
| 5 | 6 | 6 |   4.472 2-4 2-8
| 6 | 6 | 2 |   4.000 1-8 2-3 4-5 5-6
| 7 | 6 | 0 |   2.828 6-8
| 8 | 4 | 0 |   2.000 1-2 3-4 6-7 7-8
+----+---+---+

Walking man's delight

Wed, 15 May 2013 00:26:19 +0000

Enough with traveling salesman who hate long road trips.

Mario Andretti has joined the team, and he loves to drive!

His route today comprises eight towns, placed at the corners of an octagon.

Here are their coordinates:

Edit: 7 and 8 are labeled incorrectly. They should be switched.

+---+-+-+

City x y

+---+-+-+

1 0 2

2 0 4

3 2 6

4 4 6

5 6 4

6 6 2

7 4 0

8 2 0

+---+-+-+

The inter-city distances, to save some calculations, are N-S and E-W distances of 6, along with four different diagonal distances of 2.828, 4.472, 5.657 and ~~6.083~~ 6.325

If Mario begins driving at city 1 (coordinates 0 2) and drives until he has visited them all, how far will he be able to drive, and what city will he visit last?

If his objective is to return to his hotel in City 1 after visiting the other cities, how long of a trip could he accomplish?

The Best Performer

Tue, 14 May 2013 23:43:52 +0000

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

The Average Wage

Tue, 14 May 2013 23:40:56 +0000

The average hourly wages of men and women in company A are $21 and $16, respectively. The average hourly wages of men and women in company B are $20 and $15, respectively.

If twenty percent of company A employees are men, and forty percent of company B employees are men, which company pays a higher average wage to their employees?

Falsely accused correctly

Tue, 14 May 2013 23:08:10 +0000

Verdict Is Guilty Verdict is not Guilty

Committed Crime 80% 20% False Negative

Innocent of Crime 10% False Positive 90%

The above chart shows the rate that individuals are correctly found guilty or innocent of crimes in a particular jurisdiction.

If 1% of the population of residents in this county were tried in court, what are the chances that someone was correctly charged with crime?

The Mathematical Milkman

Tue, 14 May 2013 22:53:21 +0000

The school children were returning to their homes when they met the mathematical milkman, who propounds the following problem:

In one of the two cans there is milk which is so rich with cream that it becomes absolutely necessary to dilute it with a little water to make it wholesome.

Therefore, in the other can there is some pure spring water, now I proceed to pour spring water from can No. 1 into can No. 2 sufficient to double its contents, and then repour from No. 2 into No.1 enough of the mixture to double the contents.

Then to equalize matters, I again pour from No. 1 into No. 2 to double the contents of No. 2 and find the same number of gallons of milk in each can, although there is one more gallon of water in can No. 2 than there is milk, so I want you to tell me how much more water than milk is there in can No. 1?