We Got A Problem #12: Tile Shufflin’

Online word games, such as Scrabble, now let you “shuffle” your tiles with the touch of a button.  As far as I can tell, when you click the “shuffle” button the 7 tiles are randomly rearranged into any of the 7! = 5040 different orderings.

And there’s an animation of the tiles moving.  Well… sort of.  Because, sometimes one or more of the tiles doesn’t move, because they are in the same position before and after the shuffling.

How does the probability of having one stuck tile compare to the probability of having no stuck tiles? How does the probability of having one stuck tile compare to the probability of having two stuck tiles? Three? Four?

A Scrabble variant called Lexulous gives players eight tiles instead of seven.  What happens then?

What is the approximate probability of having no stuck tiles?

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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. 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.

One Response to We Got A Problem #12: Tile Shufflin’

  1. I find it interesting enough of a problem to explore..Do your students? Do we always need to come up with these questions to be answered (explored?)? If you present the topic of the shuffling you see on Scrabble and Words W/ Friends, will you have students sometimes generate the inquiry?

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