Alumni Newsletter: Spring '98

Answers to sample problems

Answer to problem 1:

You can do this problem by using something called the Intermediate Value Theorem but we prefer the following simpler argument. Imagine that, by some miracle, he goes up and down on the same day. The monk going up must meet the monk going down.

Answer to problem 2:

The usual checkerboard has alternately colored squares, for example, black and white. Two diagonally opposite squares have the same color. We may suppose the missing squares to be white. Then there are 30 white squares and 32 black squares remaining. Each domino covers exactly one white and one black square. Thus, the dominoes must cover an equal number of black and white squares. It can't be done.