A problem discussed by Martin Gardner, Grant Sanderson, Bjorn Poonen, and the AMC 10 :)

My son was working on some old AMC 10 problems today and this problem gave him a bit of trouble. The problem is #18 on the 2007 AMC 10 b:

Problem.jpg

We’ve studied a similar problem before in these three projects:

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A Strange Problem I overheard Bjorn Poonen discussing

Bjorn Poonen’s n-dimensional sphere problem with kids

A fun surprise in Bjorn Poonen’s n-dimensional sphere problem

Related problems seem to be following me around this week, though. I saw one version when I bought Martin Gardner’s book at the Omaha public library book sale:

And another version when I watched Grant Sanderson’s latest video:

For tonight’s project we worked through the problem and talked about some of the fun ideas that come into the problem in higher dimensions.

Here’s the introduction to the problem:

Next my older son showed his solution to the problem. There were a few stumbles, but he got through it:

Next I had my younger son try to solve a similar problem – he also struggled a bit but eventually found the ideas necessary to solve it:

The next problem we looked at was the version of the problem in 3 dimensions. Once we solved that problem the boys had a good guess of how the problem would look in 4 dimensions!

Finally we played around with the strange ideas that come into play in 10 and 1206 (though I think we said 1063 in the video):

So, definitely a fun problem – from a nice 2d geometry problem to totally non-intuitive problem about higher dimensional spheres. Funny to run into it three times in the last week!

One thought on “A problem discussed by Martin Gardner, Grant Sanderson, Bjorn Poonen, and the AMC 10 :)

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