Alumni Newsletter: Spring '98

Sample Problems:

Because of the positive response to the Quest problems in ou previous issue, we are including two more problems, this time with the answers included inside.

Assignment 1

A monk seeking enlightenment begins to climb the path to the top of a mountain at 6am. At 6pm he arrives at the top and spends the night in contemplation. He starts down at 6am and arrives at the start at 6pm. Prove that, no matter how fast he walks or how many times he rests, there is a time on the second day when he is at the exact same spot that he was at that time on the first day.

Assignment 2

A checkerboard has 64 squares. You are given a set of dominoes, each of which covers exactly two squares. Someone removes two diagonally opposite squares from the checkerboard and asks you to cover the remaining squares with your dominoes. The dominoes are required to lie flat and to be confined to the remaining squares. Can it be done?

Answers are available.