We Got A Problem #8: Super Ultra Mega Man!

The new toy craze is Mega Men, where kids buy a Mega Man in a box. The box won’t tell you which one it is, and kids open it up when they get home in hopes of getting one they don’t already have. (Sadly, eBay is not an option, since the only cool Mega Men are the ones still in their original packaging.)

There are ten toys in all, each equally likely when you buy a box. If you collect all ten, you can make Super Ultra Mega Man!

On average, how many Mega Men will you have to buy for your kid before he can finally collect them all?

(Stolen from PCMI 2007 Day 1 Problem #11: http://mathforum.org/pcmi/hstp/sum2007/morning/bowen/day1handout.pdf)


About Bowen Kerins
Bowen is a mathematics curriculum writer. He is a lead author of CME Project, a high school curriculum focused on mathematical habits of mind, and part of the author team of the Illustrative Mathematics curriculum series. Bowen leads professional development nationally, primarily on how math content can be taught with a focus on higher-level goals. Bowen is also a champion pinball player and once won $1,000 for knowing the number of degrees in a right angle.

2 Responses to We Got A Problem #8: Super Ultra Mega Man!

  1. suevanhattum says:

    Hmm, I want to modify this to be gender neutral. What’s a (conceivably) wildly popular sort of toy that could transform from 10 individuals to one biggie? Are dinosaurs equally interesting to boys and girls? “Get all 10 minisaurs and you can create your very own megasaur!” Or for Halloween, “get all 10 mini-ghouls and build your own mega-ghoul.” (My only child is a boy, so these ideas may still veer to that side of the spectrum.) I liked troll dolls when I was a kid, how about mini-trolls that combine to form a mega-troll? Yeah, I think I’ll go with that.

    Thanks for this problem. I’ll add it to my newly-begun stash for discrete math.

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