Most of these are a bit more difficult than the kind of puzzles I intend to put on my blog, but here's an easier one which I feel is appropriate.
Problem A1: Let f be a real-valued function on the plane such that for every square ABCD in the plane, f(A) + f(B) + f(C) + f(D) = 0. Does it follow that f(P) = 0 for all points P in the plane?If you are interested in seeing other Putnam problems, I refer you to the Art of Problem Solving Forum.
And here's another math puzzle, which is completely unrelated.
You play a game with me which involves flipping a coin. I flip the coin repeatedly until I get a heads. Let N be the number of times I flipped the coin. If N is even, we start the game over from the beginning. If N is odd, then you win N dollars. What is a fair price to play this game? (Hint: it's not $3)If you're wondering how I did on the Putnam, I expect to get four correct, just like last year.
See the solutions