Saw a neat tweet from Joel David Hamkins at the end of last week:
I thought it would be fun to talk through the knight’s tour problems with the boys today and end by showing them the infinite problem. I ran into trouble almost immediately when we began to talk about the tours on the 3×3 and 4×4 boards. The difficulty they had explaining was a big surprise to me. We ended up talking about the 4×4 problem for almost 30 min.
Tonight I sat down with each of them and asked them to talk me through the problem and explain why the knight’s tour on the 4×4 board was impossible. You can see that my older son (in 8th grade) was able to explain the problem pretty well, but my younger son (in 6th grade) still really struggled.
Here’s what my older son had to say:
Here’s what my younger son had to say:
Definitely a much harder problem for kids than I thought. Hopefully will have some time during the week to explore this and maybe a few other tour problems with them.