A nice “possible / impossible” problem from the 2007 AMC 8

Ran across this problem from the 2007 AMC 8 today:

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Here’s a direct link to the full exam on Art of Problem Solving’s site:

The 2007 AMC 8 on Art of Problem Solving’s website

I thought the problem would make for a great discussion this morning. We began by discussing the first two choices:

and here’s a discussion of the last three choices:

I love using old contest problems with my kids. One reason is that I’m not that great at coming up with good problems on my own, and the old AMC problems tend to be really good. I especially like this problem because it gets kidsthinking about numbers and talking about mathematical reasoning. Fun little project!