Recreational math, a few videos

You can check out Neller & Presser’s 2004 paper which Ben refers to in the video here.

I seem to recall the box game above from when I was a child, and I think I actually tentatively reached a similar conclusion as Bradlow did in the video, namely that one of the example combinations displayed on the box did not seem to be possible to reach through any legal sequence of box manipulations/moves. One of my uncles used to be a math professor and I think we actually discussed this game at one point, but if we did it’s many years ago so details are very hazy – Bradlow’s line of reasoning sounds familiar but that may just be due to the fact that a ‘parity argument’ of the type he introduces in the video seems to often be useful in the context of implicit game theory existence proofs like these, even though we did not in fact go into such details back then.

Either way Bradlow did the math and if you encounter someone who claims he managed to solve the example discussed in the video you’ll know two things: 1. S/he cheated, and 2. s/he most likely did not do the math.

The cat and mouse game is a great illustration/example of how combining different strategies may sometimes lead to the solution of a problem that might not be solveable by any single strategy in the choice set on its own; considering combinations of different strategies will always increase the choice set, and/but sometimes it’ll do so in surprisingly unintuitive yet helpful ways.