| 10 Head Puzzle: There are a bunch of pennies laid out on a table, 10 of which have heads face up, the rest having tails. Without being able to see or detect which are the pennies with heads, how do you separate the N pennies into two groups so that each group has the same number of heads? |
| Geography Puzzle: Gia Graphy has a map showing a cluster of states in the U.S. She has labled each state with a number equal to the number of states bordering it on the map. Prove that the number of states which have been labeled with odd numbers is even. |
| Martian Base: When the first Martian to visit Earth attended a high school algebra class, he watched the teacher show that the only solution of the equation 5x^2 - 50x + 125 = 0 is x = 5. "How strange" thought the Martian. "On Mars, x=5 is a solution of this equation, but there is also another solution." If Martians have more fingers than humans have, how many fingers do Martians have? |
| Series: Find the missing number in the following sequence: 10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, ?, 100. Hint 1: The next two numbers after 100 are 121, 10000. |
| Blackbox: Given a blackbox that outputs a polynomial - with all coefficients being positive - how many numbers need to be input to determine the polynomial? (This one seems to be open to interpretation--I think the box contains a polynomial: you give it the value of x, and it spits the value of f(x).) |
| Hat Puzzle: You have three people, who are each given either a red hat or a blue hat, and then put into a room. They can communicate before their hats are put on, but not once they're hats are on. Each one cannot see what color hat they have on, but they can see the hat color of the other two people. Once in the room, they each simulataneously guess their hat color or pass. If one or more people guess their hat color correctly and none guess incorrectly, they each get a million dollars. If any of them guesses incorrectly, or all of them pass, they get nothing. What is the best strategy for guessing, for which they optimize their chance of winning money? If you figure that out, then try it for 7 people. |
| Contestant A & B: Contestant A is given the sum of two numbers, X and Y. She knows that sum but not X and Y. Contestant B is given the product of X and Y. Once again, she knows the product but not the factors. Both contestants are trying to determine X and Y. And each contestant knows that the other was provided with either the sum or product of X and Y. Their conversation goes like this: contestant A - I don't know X and Y contestant B - I don't know either, but I know that you don't know contestant A - now I know contestant B - now I know, too. Both A and B are very good at math. |