My younger son was working through the 1989 American Junior High Mathematics Exam this morning and got stuck on this problem:
Here’s a link to the entire exam on Art of Problem Solving’s website:
I thought this problem would make for a nice project since there are a couple of good mathematical ideas in it, so we sat down to talk about it. My younger son talked through his approach first:
My older son went next and had a different approach:
To wrap up we talked about how the answer would change if the problem was set up with a slightly different arrangement of the cubes and the boys found their way to an important idea in geometry:
I’m really happy that the old AMC problems are available – they are a wonderful resource to use to find challenging but accessible problems for kids.