40 Squares Problems

     Below are two additional "Matchstick Problems" that I thought up.

     In the problem shown on the left, you are to construct 40 squares using as many matches as possible. Find a configuration of squares that achieves this and determine the number of matches used. Are you sure that this is the best that can be done?

     In the next problem, shown on the right, you are to construct 40 squares using as few matches as possible. Find a configuration of squares that achieves this and determine the number of matches used. Are you sure that this is the best that can be done? Even though the two problems seem very similar, you probably found it a bit harder to solve this second problem. What do you think makes this one harder?

Matchstick Problems

© Charles F. Schmidt