Po-Shen Loh’s coin problem

Last year I saw this amazing presentation from Po-Shen Loh at the Museum of Math:

In the presentation Loh does something that seems close to impossible. He takes a difficult problem from the International Mathematics Olympiad (problem #5 from 2010) – a problem on which roughly 2/3 of the 2010 IMO participants received 0/7 points! – and turns it into a fantastic public lecture.

Tomorrow I’m going to give a talk at the East Coast Idea Math camp and I’m using problem in Loh’s lecture for one part of my talk. For our Family Math project today I used the problem in the first part of Loh’s talk with my kids.

Here’s how it went.

(1) First I introduced the problem and the boys gave their initial reaction:

(2) Having found a value of 63 cents in the last video next we tried to see if we could find some other values by moving the coins in different ways. We also had a nice discussion about how you could determine if 63 was the maximum value.

(3) Before talking more about why 63 is the maximum value, I wanted to have my younger son try an new approach to the game just to see if we’d ever find a value other than 63.

(4) Finally, we wrapped up by talking about one way you can see that the value of this game is 63. One lucky coincidence is that my younger son was learning about different bases this week. That coincidence helped him see the connection between this game and binary counting fairly quickly.

So, I love Loh’s presentation. It is so cool (and inspiring) to see him take a super challenging IMO problem and turn it into a public lecture. I won’t walk the kids all the way through the solution of the original problem tomorrow, but I will use Loh’s approach to create a big discussion about the 2nd part of the problem. Can’t wait to see what values the kids find for the 2nd game.


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