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## Checkerboard Chances 2

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #42307 Fun: (2.14) Difficulty: (2.81) Category: Probability Submitted By: billy314

Timothy has a four by four checkerboard. He uses scissors to cut out each square from the board. He then randomly arranges the pieces into four rows and four columns. What is the probability that this layout is in a checkerboard pattern?

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 marie7771 Jul 22, 2008 Complicated, but I got it! first comment woo hoo Herman Nov 24, 2008 I went about this a different way, actually. The prob that the first square was correct was 8/16. The prob that the next square selected was correct was 8/15. The next, 7/14, and so on. Multiply all of that out, then multiply by two, since the first square can be black or red (turn the board). lookagain Nov 10, 2010 There are (16 choose ways to assign one of the colors and then 1 way to assign the remaining color. There are two set-ups of the checkerboard (white left corner or black left corner). So the probability is 2/(16 choose . HFmanager Nov 19, 2010 I don't necessarily agree with this. It is assumed here that the 2 different red squares are uniquely identifiable, but shouldn't they be identical? So the number of ways the checkers can be arranged is 16!/(8!x8!), and there are only two arrangements that can have alternating red and black squares (i.e. RBRB...RB and BRBR...BR). So the answer should be 2x(8!x8!)/(16!). Am I right?