Peter's homepage

Organization of problems

Two ants What's the shortest distance between two ants inside a room if they have to crawl along the inside surface?
Polygon Can you build a regular n-gon in 3 space with all angles 90? Get out the straws and pipe cleaners.
Arches The arches in the photo are all the same size but they seem to get smaller as they get farther from the camera. What sort of function describes this apparent size decrease? [This article has appeared in the Mathematical lens section of the Oct. 2007 issue of Mathematics Teacher, Vol 101.]
3-D view You know those pictures made up of dots that give you a 3-D vision if you relax your eyes? How do they work?
Cutting planes How many regions are created by the intersection of 5 planes?
Regions in the circle Take n points on the circumference and make all connecting lines. How many regions?
Cutcube Take a 4-dimensional hypercube, hang it by a vertex, and slice it in half with a 3-D hyperplane. What does the cross section look like?

HandshakeHow long does it take for everyone to shake hands with everyone else?
Stickers Every time you buy a package of gum you get a new sticker. How long till you fill the sticker book?
Sum of Cubes Variations on the formula for the sum of cubes.
Pascal Explorations with Pascal's triangle.
Fibonacci Playing with Fibonacci numbers.
Fibonacci modk Now we write the Fibonacci numbers mod k.
Fibonacci flowers and cones How do we account for the extraordinary appearance of Fibonacci numbers in nature?
Counting trains How many trains of length 10 can I make out of cars of length 1 and 2?
Even-odd Ten coins are tossed. Eyeore wins if the number of heads is even and Owl wins if the number of heads is odd. Is the game fair?
Even-odder Same game, but this time heads comes up 2/3 of the time.

First hit If A happens with probability p and B happens with probability q, what's the probability that A will happen befopre B?
Darts If on each throw I hit the bullseye with probability p, how many throws does it take on average to hit the bullseye?
Boys and girls If I know he has two children and I run into him downtown with a daughter, what's the probability that his other child is a boy?
Blood test If I test positive for a disease and the test is 98% reliable, what's the probability I have the disease?
Car and two goats The Monty Hall story complete with Marilyn's correspondence.
Horse race This is a game played at the Ex with 6 spinners. What's your expected net payoff?
Hitting 10 If I flip a coin again and again and get 1 for a head and 2 for a tail, what's the probability I'll hit 10?
Snap What's the probability of getting a snap with a standard 52-card deck?
Bridge hands What the probability of getting all four aces in a bridge hand?

Skunk As long as you stay in the game your payoff can increase, but there's also a chance you'll get knocked down to zero. Should you take what you've already got and run?
Card trick You do a bunch of things with the cards and and come up with some number, say 16. Then without looking, I tell you the 16th card in the deck. How do I do it?
Coffee and cream You want the coffee to be as hot as possible when you get around to drinkintg it. Do you put the cream in now or later?
Four wells In each well there is a glass either up or down. You get to reach in and alter the state of one or both. The table spins. Can you get all four up or down?
Prisoners and boxes To be spared execution, they must all find their names. It seems an impossible task. The solution is nothing short of extraordinary.