When the game starts, Alice and Bob go into separate soundproof rooms — they cannot communicate with each other in any way. They each flip a coin and note whether it came up Heads or Tails. (No funny business allowed — it has to be an honest coin flip and they have to tell the truth later about how it came out.) Now Alice writes down a guess as to the result of Bob’s coin flip; and Bob likewise writes down a guess as to Alice’s flip.

If either or both of the written-down guesses turns out to be correct, then Alice and Bob both win as a team. But if both written-down guesses are wrong, then they both lose.

Can you think of a strategy Alice and Bob can use that is guaranteed to win every time?

There is an unmarked grave and two tall oak trees. Walk from the grave to the left tree, counting the number of steps. Upon reaching the left tree, turn left by 90 degrees and walk the same number of steps. Mark the point with a flag. Return to the grave. Now, walk towards the right tree, counting the number of steps. Upon reaching the right tree, turn right by 90 degrees and walk the same number of steps. Mark this point with another flag. The treasure lies at the midpoint of the two flags.A party of sailors reached the island. They find a pair of tall oak trees merrily swaying in the wind. However, the unmarked grave is nowhere to be found. They are planning to dig up the entire island. It'll take a month. Can they do any better?

*int f(int x)*in C that satisfies f(f(x)) == -x? Without globals and static variables, of course.

^{3}unit cubes. Prove that if one unit cube is removed from T, then the remaining solid can be decomposed into pieces.

*each and every*prisoner. What is their strategy?

*deterministic*strategy?

The Puzzle Toad at CMU has challenging puzzles. William Wu's Puzzles Page at Berkeley has myriad puzzles with a discussion board. Cut the Knot has dozens of high quality articles on mathematics, puzzles and games. Puzzles by Erich Friedman has cute puzzles; he also maintains Math Magic, Erich's Packing Center and Ambigrams. Archives of Ed Pegg Jr's Math Games in MAA make interesting reading. Age of Puzzles is a nicely done website with classic puzzles, diagrams and references. Sam Lloyd website: A few of his puzzles have tastefully been compiled at this website. SOMA cube has dozens of SOMA cube configurations. List of books by Martin Gardner. Select puzzles for high school students: SNAP Math Fair. Another small collection. A nice collection of problems at mathproblems.info. Another collection of puzzles. Yet another collection by Tanya Khovanova. Some problems by Mihai Patrascu. Several ingenious puzzles at MathOveflow.Net. Prisoner and Hat Puzzles. Surprises! Surprises! Surprises!. MSRI Archives (puzzles in each newsletter). Nice C Puzzles by Gowri Kumar. Interesting articles on various problems.