Posted by Robin on Thursday, January 28, 2010 at 12:21pm.
How many ways can seven basketball players of different heights line up in a single row so no player is standing between two players taller then herself?

8th math  drwls, Thursday, January 28, 2010 at 12:49pm
Two would be ascending or descending order.
Twelve more would be ascending or descending order, with any one of the nottallest going to the other end.
I can think of four others that involve flipping and inverting more than one to the opposite side. Maybe you can think of others. Add them up

8th math  drwls, Thursday, January 28, 2010 at 1:23pm
By seeing how many arrangements I could make with N players, I found that for N = 1, 2, 3, 4, and 5 players, the number of arrangements is 2^(N1).
If this trend continues, the number of possible arrangements of N = 7 players is 2^6 = 64. Figuring it out with numbers (1 through 7) is easier than doing it with "straws" of different length.
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