The list is long… feel free to help me narrow it down.

pi
pic
pie
pig
pin
pip

pit
pix
epic
pick
pics
pied
pier
pies
pigs
pike
pile
pill
pimp
pine
ping
pink
pins
pint
piny
pipe
pips
pita
pith
pits
pity
pixy
spic
spik
spin
spit
spiv
topi
aping
aspic
cupid
epics
lipid
lupin
opine
opium
piano
picks
picky
piece
piers
piety
piggy
pigmy
pikes
pilaf
pilau
piled
piles
pills
pilot
pimps
pinch
pined
pines
piney
pings
pinko
pinks
pinky
pinny
pints
pious
piped
piper
pipes
pipit
pique
piste
pitas
pitch
pithy
piton
pitta
pivot
pixel
pixie
pizza
pupil
rapid
sepia
spice
spics
spicy
spied
spiel
spies
spiff
spike
spiks
spiky
spill
spilt
spine
spins
spiny
spire
spite
spits
spivs
tapir
tempi
tepid
topic
topis
vapid
alpine
apiary
apiece
armpit
aspire
biopic
copied
copier
copies
coping
cupids
depict
doping
duping
empire
epilog
espied
espies
expire
expiry
gaping
hatpin
hippie
hoping
hyping
impish
limpid
lipids
loping
lupine
lupins
magpie
moping
myopia
myopic
octopi
opiate
opined
opines
papist
pianos
piazza
pickax
picked
picker
picket
pickle
picnic
piddle
pidgin
pieced
pieces
pierce
piffle
pigeon
pigged
piglet
pigpen
pigsty
pilaff
pilafs
pilaus
pilfer
piling
pillar
pillow
pilots
pimped
pimple
pimply
pincer
pinged
pining
pinion
pinked
pinker
pinkie
pinkos
pinned
pipers
piping
pipits
pipped
piqued
piques
piracy
pirate
pistes
pistil
pistol
piston
pitied
pities
pitons
pittas
pitted
pivots
pixels
pixies
pizzas
pulpit
pupils
rapids
rapier
raping
rapist
ropier
roping
scampi
spiced
spices
spider
spiels
spiffs
spiffy
spigot
spiked
spikes
spills
spinal
spines
spinet
spiral
spires
spirit
spited
spites
stupid
supine
taping
tapirs
tenpin
tiepin
topics
torpid
tropic
typify
typing
typist
umpire
unpick
upping
uppity
utopia
wapiti
weepie
wiping
yuppie
alpines
armpits
aspired
aspires
aspirin
bagpipe
beeping
biopics
bopping
bumpier
bumping
burping
camping
capital
capping
carping
cesspit
chippie
cockpit
compile
cooping
copiers
copilot
copings
copious
coppice
copping
cupping
damping
depicts
despise
despite
dippier
dipping
draping
dumping
eloping
empires
epicure
epigram
epilogs
episode
epistle
epitaph
epithet
epitome
expiate
expired
expires
fleapit
foppish
gasping
gawping
griping
groping
groupie
gulping
guppies
gypping
hairpin
happier
happily
harpies
harping
harpist
hatpins
heaping
helping
hippies
hopping
hospice
humping
impiety
impinge
impious
insipid
inspire
jumpier
jumping
keeping
kingpin
kipping
lapping
leaping
limping
lisping
loopier
looping
lopping
lumpier
lumping
lumpish
lupines
magpies
mapping
mopping
nappies
napping
nipping
nitpick
opiates
opining
opinion
papists
peeping
pepping
pianist
pianola
piazzas
picador
piccolo
pickaxe
pickers
pickets
pickier
picking
pickled
pickles
picnics
picture
piddled
piddles
pidgins
piebald
piecing
pierced
pierces
pigeons
piggery
piggies
pigging
piglets
pigment
pigmies
pigpens
pigskin
pigtail
pilaffs
pilfers
pilgrim
pilings
pillage
pillars
pillbox
pillion
pillock
pillory
pillows
piloted
pimento
pimping
pimpled
pimples
pinball
pincers
pinched
pinches
pinging
pinhead
pinhole
pinions
pinkest
pinkies
pinking
pinkish
pinkoes
pinnies
pinning
pioneer
piously
pipette
pipping
piquant
piquing
piranha
pirated
pirates
pistils
pistols
pistons
pitched
pitcher
pitches
piteous
pitfall
pithead
pithier
pithily
pitiful
pitting
pitying
pivotal
pivoted
pizzazz
pooping
poppies
popping
preppie
pulping
pulpits
pumping
puppies
pushpin
rapidly
rapiers
rapists
rapping
rasping
reaping
respire
respite
ripping
romping
ropiest
sandpit
sappier
sapping
scrapie
seeping
shaping
sipping
sloping
sniping
soapier
soaping
soppier
sopping
souping
spicier
spicing
spiders
spidery
spiffed
spigots
spiking
spilled
spinach
spindle
spindly
spinets
spinier
spinner
spinney
spirals
spirits
spiting
spittle
supping
swiping
tamping
tapioca
tapping
temping
tenpins
tiepins
tipping
topiary
topical
topping
topspin
tropics
typical
typists
umpired
umpires
unpicks
utopian
utopias
vamping
vampire
warping
waspish
weepier
weepies
weeping
wimping
wimpish
yapping
yelping
yipping
yuppies
yuppify
zapping
zipping
allspice
aspirant
aspirate
aspiring
aspirins
atypical
bagpipes
bleeping
blimpish
blowpipe
bumpiest
canopied
canopies
capitals
cesspits
champing
champion
chappies
chapping
cheeping
chippies
chipping
chirpier
chirpily
chirping
chomping
choppier
chopping
clamping
clapping
clasping
clipping
clumping
cockpits
codpiece
compiled
compiler
compiles
conspire
copilots
coppiced
coppices
cramping
creepier
creeping
crimping
crispier
crisping
cropping
croupier
cupidity
cuspidor
decrepit
depicted
despised
despises
dippiest
drippier
dripping
droopier
drooping
dropping
earpiece
epicures
epidemic
epidural
epigrams
epigraph
epilepsy
epilogue
epiphany
episodes
episodic
epistles
epitaphs
epithets
escaping
escapism
escapist
expiated
expiates
expiring
eyepiece
flapping
fleapits
flipping
floppier
flopping
frumpier
frumpish
grasping
gripping
groupies
grouping
grumpier
grumpily
hairpins
happiest
harpists
helpings
hornpipe
hosepipe
hospices
hospital
impinged
impinges
impishly
inspired
inspires
intrepid
jalopies
jumpiest
kingpins
lapidary
limpidly
linchpin
loopiest
lumpiest
lynchpin
ninepins
nitpicks
occupied
occupier
occupies
opinions
panpipes
perspire
pianists
pianolas
picadors
picayune
piccolos
pickaxes
picketed
picketer
pickiest
pickings
pickling
pictured
pictures
piddling
piercing
piffling
pigments
pigsties
pigswill
pigtails
pilaster
pilchard
pilfered
pilgrims
pillaged
pillages
pillared
pillions
pillocks
pillowed
piloting
pimentos
pimiento
pinafore
pinching
pinewood
pinheads
pinholes
pinioned
pinkness
pinnacle
pinpoint
pinprick
pinwheel
pioneers
pipeline
pipettes
pipework
piquancy
piranhas
pirating
pitchers
pitching
pitfalls
pitheads
pithiest
pitiable
pitiably
pitiless
pittance
pivoting
pizzeria
plopping
plumping
preppies
prepping
primping
propping
pushpins
quipping
rapidity
respired
respires
sandpits
sappiest
scalping
scooping
scorpion
scraping
sharpish
sheepish
shipping
shopping
skimpier
skimping
skipping
slapping
sleepier
sleepily
sleeping
slipping
sloppier
sloppily
slopping
slumping
slurping
snappier
snappily
snapping
snappish
snipping
snooping
soapiest
soppiest
spiciest
spiffing
spillage
spilling
spindles
spiniest
spinners
spinneys
spinning
spinster
spiraled
spirally
spirited
spitball
spiteful
spitting
spittoon
stamping
steeping
stepping
stickpin
stomping
stooping
stopping
stumpier
stumping
stupider
stupidly
supinely
swampier
swamping
swapping
sweeping
swooping
swopping
tailpipe
tailspin
terrapin
thespian
thumping
toppings
torpidly
tramping
trapping
tripping
tromping
trooping
tropical
trumping
turnpike
typified
typifies
umpiring
underpin
unpicked
usurping
vampires
vapidity
weepiest
whelping
whipping
whooping
whopping
whupping
windpipe
woodpile
wrapping
aspirants
aspirated
aspirates
autopilot
blowpipes
capillary
champions
chippings
chirpiest
choppiest
clippings
codpieces
compilers
compiling
conspired
conspires
copiously
coppicing
creepiest
crispiest
croupiers
cuspidors
decamping
depicting
depiction
despising
drainpipe
drippiest
drippings
droopiest
droppings
earpieces
empirical
encamping
epicenter
epicentre
epicurean
epidemics
epidermis
epidurals
epigraphs
epileptic
epilogues
episcopal
epitomise
epitomize
equipping
espionage
expiating
expiation
eyepieces
floppiest
frumpiest
galloping
gazumping
gossiping
groupings
grumpiest
hairpiece
happiness
hiccuping
hornpipes
hosepipes
hospitals
impinging
impiously
incipient
insipidly
inspiring
kidnaping
linchpins
lolloping
lynchpins
marsupial
nitpicked
nitpicker
occupiers
overspill
palpitate
perspired
perspires
picketers
picketing
picnicked
picnicker
pictorial
picturing
piecemeal
piecework
piggeries
piggyback
pigheaded
pigmented
pilasters
pilchards
pilfering
pillaging
pillboxes
pilloried
pillories
pillowing
pimientos
pimpernel
pinafores
pineapple
pinewoods
pinioning
pinnacles
pinpoints
pinpricks
pinstripe
pinwheels
pioneered
piousness
pipelines
pipsqueak
piquantly
piratical
pirouette
pistachio
pitchfork
piteously
pitifully
pittances
pituitary
pityingly
pizzerias
pizzicato
porcupine
precipice
recapping
recipient
recouping
reshaping
respiring
revamping
sandpiper
scorpions
scrapings
scrappier
scrapping
scrimping
scrumping
showpiece
shrimping
skimpiest
sleepiest
sloppiest
snappiest
spiciness
spiderweb
spikiness
spillages
spillover
spindlier
spineless
spinnaker
spinsters
spiraling
spiralled
spiriting
spiritual
spitballs
spittoons
standpipe
stickpins
stockpile
strapping
stripping
stroppier
stroppily
stumpiest
stupidest
stupidity
suspicion
swampiest
tailpiece
tailpipes
tailspins
terrapins
therapies
therapist
thespians
timepiece
toothpick
topically
torpidity
transpire
trappings
turnpikes
turpitude
typically
typifying
underpins
unhappier
unhappily
unpicking
untypical
unzipping
walloping
waspishly
whippings
windpipes
woodpiles
wrappings
yuppified
yuppifies
altarpiece
aspidistra
aspirating
aspiration
auspicious
autopilots
beekeeping
capitalise
capitalism
capitalist
capitalize
capitation
capitulate
catnapping
championed
chirpiness
chirruping
clothespin
conspiracy
conspiring
cornucopia
crosspiece
decapitate
depictions
depilatory
despicable
despicably
developing
dispirited
drainpipes
empiricism
empiricist
entrapping
enveloping
epicenters
epicentres
epicureans
epiglottis
epileptics
epistolary
epitomised
epitomises
epitomized
epitomizes
expiration
floppiness
grumpiness
gyroscopic
hairpieces
hiccupping
hospitable
hospitably
impishness
insipidity
kidnapping
marsupials
mouthpiece
myopically
nitpickers
nitpicking
palpitated
palpitates
percipient
perspiring
pianissimo
pianoforte
picaresque
piccalilli
pickpocket
picnickers
picnicking
piercingly
pigeonhole
piggybacks
pilgrimage
pillorying
pillowcase
pillowslip
pimpernels
pincushion
pineapples
pinpointed
pinstriped
pinstripes
pioneering
pipsqueaks
pirouetted
pirouettes
pistachios
pitchforks
pitilessly
porcupines
precipices
propitiate
propitious
recipients
regrouping
respirator
sandpipers
scalloping
schlepping
scrappiest
sheepishly
showpieces
sleepiness
sloppiness
snappiness
snappishly
spiderwebs
spillovers
spindliest
spinnakers
spiralling
spiritedly
spiritless
spirituals
spitefully
standpipes
stockpiled
stockpiles
stroppiest
suspicions
suspicious
tailpieces
telescopic
therapists
timepieces
toothpicks
topicality
transpired
transpires
unhappiest
uninspired
unoccupied
unwrapping
worshiping
yuppifying
altarpieces
aspidistras
aspirations
bookkeeping
capillaries
capitalised
capitalises
capitalists
capitalized
capitalizes
capitations
capitulated
capitulates
caterpillar
centerpiece
centrepiece
championing
clothespins
compilation
conspicuous
conspirator
crosspieces
decapitated
decapitates
decrepitude
dilapidated
dispiriting
empirically
empiricists
epidermises
epitomising
epitomizing
hospitalise
hospitality
hospitalize
impiousness
insipidness
inspiration
kidnappings
kneecapping
landscaping
malapropism
mantelpiece
mantlepiece
masterpiece
microscopic
mouthpieces
opinionated
outcropping
overlapping
palpitating
palpitation
participial
photocopied
photocopier
photocopies
pianofortes
pickpockets
pictorially
picturesque
pigeonholed
pigeonholes
piggybacked
pigheadedly
pilgrimages
pillowcases
pillowslips
pincushions
pinpointing
pirouetting
pitchforked
pituitaries
precipitate
precipitous
preoccupied
preoccupies
propinquity
propitiated
propitiates
respiration
respirators
respiratory
sellotaping
serendipity
showjumping
sideswiping
spinelessly
spiritually
stockpiling
stroppiness
stupidities
subtropical
telescoping
timekeeping
transpiring
trepidation
underpinned
unhappiness
uninspiring
untypically
videotaping
wiretapping
worshipping
archetypical
backslapping
capitalising
capitalistic
capitalizing
capitulating
capitulation
caterpillars
centerpieces
centrepieces
championship
compilations
conspiracies
conspirators
decapitating
decapitation
depilatories
dilapidation
doorstepping
epidemiology
epiglottises
epigrammatic
frontispiece
glockenspiel
handicapping
hospitalised
hospitalises
hospitalized
hospitalizes
housekeeping
inauspicious
inhospitable
inspirations
malapropisms
mantelpieces
mantlepieces
masterpieces
misanthropic
outcroppings
outstripping
oversleeping
overstepping
palpitations
peacekeeping
perspicacity
perspiration
photocopiers
pigeonholing
piggybacking
pigmentation
pitchforking
pitilessness
precipitated
precipitates
propitiating
propitiation
propitiatory
propitiously
prototypical
psychotropic
recapitalize
recapitulate
redeveloping
semitropical
sheepishness
showstopping
sidestepping
spinsterhood
spiritualism
spiritualist
spirituality
spitefulness
stereoscopic
stereotyping
suspiciously
underpinning
capitulations
championships
conspicuously
decapitations
eavesdropping
frontispieces
glockenspiels
goosestepping
horsewhipping
hospitalising
hospitalizing
inconspicuous
inspirational
kaleidoscopic
misanthropist
perspicacious
philanthropic
picturesquely
piezoelectric
pigheadedness
precipitately
precipitating
precipitation
precipitously
recapitalized
recapitalizes
recapitulated
recapitulates
serendipitous
spectroscopic
spinelessness
spiritualists
stereotypical
transpiration
underpinnings
antiperspirant
aromatherapist
capitalisation
capitalization
conspiratorial
epidemiologist
hypnotherapist
inauspiciously
misanthropists
philanthropist
precipitations
radiotherapist
recapitalizing
recapitulating
recapitulation
antiperspirants
aromatherapists
conspicuousness
epidemiological
epidemiologists
hospitalisation
hospitalization
hypnotherapists
inconspicuously
microscopically
philanthropists
physiotherapist
picturesqueness
psychotherapist
radiotherapists
recapitulations
conspiratorially
counterespionage
physiotherapists
psychotherapists
recapitalization
kaleidoscopically

Dr. Conway developed a sweet method to determine the day of the week for any day in history.  It takes some practice.  Dealing just with the current year is pretty simple, provided you know the Doomsday. 

Doomsday 2012 is Wednesday*.

• This means that the following dates are all Wednesday: 4/4, 6/6, 8/8, 10/10, 12/12. 
  What day of the week is Christmas 2012?  13 days past a Wednesday… must be 1 day before a Wednesday.
• If you work nine to five at the local 7-11, you can remember four more Wednesdays: 9/5, 7/11, 5/9, 11/7.
• Einstein’s birthday = Pi Day = 3/14 = Wednesday.
• The last day of February (2/29 this year) is a Wednesday.
• Lastly, 1/4 is Wednesday (3 out of 4 years it’s the 3rd… but on leap years it’s the 4th).

What day of the week is your birthday? Halloween?  Independence Day? 

*In case you’re interested, the link up top does a thorough job of teaching the method, but here’s the quick version. Start with the century day.  For 2000 it is Tuesday (2).  Then look at the 2-digit year, 12, and ask how many 12’s are in it. (1). What is the remainder? (0) How many 4’s are in this number? (0). Add up (2)+(1)+(0)+(0) = 3 = 3rd day of the week = Wednesday. 

Craziness? How about one more example from the future: 2055.  Century day is still (2).  How many 12’s in 55? (4). What is the remainder? (7).  How many 4’s in this number? (1).  Add q‘em up: (2)+(4)+(7)+(1) = 14.  Take out multiples of 7 and you get 0.  The 0th day of the week is Sunday. Now you can find the day of the week for any date in 2055.

Given this information, will there be another numerically interesting year for us, or is this it?  We can’t look forward to all being powers of 2 again, but perhaps there’s something else in store for us?

So I started using this pattern, and challenge you to find an even more efficient way to pack stars in a plane.

Step 2: Effect > Distort & Transform > Transform.  Make sure to preview, then make some copies of that leaf and scale ‘em down.  Add a reflect X, scale dimensions down to 90%, and put some Move Vertical, and with some tweaking you should get a fern-looking thing.

Why does this remind me of the geometric series elves?

Step 3: Object > Expand Appearance so that the effect becomes materialized.  Select all, right-click and group that sucker.

Step 4: Now for the fractal part: iterate!  I rotated my tree-looking thing 90º clockwise so it resembled the initial leaf.  Then I repeated the transformation to make a bunch of these tree things with a scale factor of 90%. 

With 50 copies of a shape made of 50 parts, you’ll notice your computer start to slow down a bit.  I decided to stop while I was ahead… not a perfect fractal, but good enough for your Christmas card.

Start by drawing something… in this case, an elf.  Say he has a height of one unit.  Select your drawing, right-click, and group it.

Now hit up the Effects > Distort & Transform > Transform

Here’s where it gets cool.  First click Preview, then put a number in the Copies box (I used 100 to approximate infinity).  This will create a bunch of copies of the original, but since they’re all the same size, you can’t see them.  Change the horizontal and vertical scales to 50%, and space out the elves by increasing the Move>Horizontal slider.  Drop the vertical slider so that the elves are on the same baseline.

You can now see that each elf is half the height of the previous.  This is a geometric sequence.  To find the value of the series, we need to add the heights of the elves, which we can do by adjusting the horizontal and vertical sliders to stack the elves on top of each other (make sure to have students make a prediction first).

All that’s left is to see how tall that stack of elves on top of the first one is.  Remember that the big elf is one unit, so let’s use him as the measuring stick.  Copy and paste the big elf, then turn off his transformation effect and drag him up to measure the series.

Students should see that the sum of the heights of all the little elves is equal to 1 big elf, which is to say 1/2 + 1/4 + 1/8 + … = 1.

That ego-maniacal Yertle, proclaiming himself king of all that he sees, calls for a stack of 500 turtles to sit upon.

And now Yertle the Turtle was perched up so high,
he could see forty miles from his throne in the sky

So tell me: how tall is each turtle?  Assume the earth is a sphere with radius 4000 mi, that Yertle and the reset of the turtles are a uniform height, and that Yertle’s eyes are on the top of his head.  The first correct solution (posted as a comment) will earn a cool drawing of the solver on top of Yertle.