March 16, 2013 Leave a comment
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?