Thursday Math Tea

A few weeks ago, as we gathered for tea and scones (thanks, Jeffrey!), one of the students came in with a problem posed in an education class, which we then attempted to solve. Here's the deal.

Take a square and put positive integers at each of the corners. (Choose numbers between 1 and 99.) Now at the midpoints of each side of the square, write down the absolute value of the difference of the two neighboring corners. Finally, join the midpoints to make a new square. Repeat.

In the problem posed to the education class, the final figure has seven squares (I think), one inside the other. This is a problem that is used in grade school classrooms, and the (stated) goal is to find numbers for the outermost square, so that the number zero never shows up anywhere in the final figure. (The actual goal is to get the students to practice their subtraction.)

Well, that sounded like an easy problem, so we set to it. After some deliberations we came up with a solution, then proceeded to ask lots of related questions. (A real mathematical spirit filled our students.) One thing the students there were able to prove, is that given enough concentric squares, any starting configuration eventually ends with all zeros.

Final note: We have a Thursday tea every week as long as classes meet that day. Tea starts at 3:00 pm in the Math Lab. Please feel free to join us if you are in the area.