perplexus.info :: Probability : Checkerboard Chance Conclusion II

Checkerboard Chance Conclusion II (Posted on 2022-05-16)

Reuben has a 4x4 checkerboard. He uses scissors to cut out each square from the board. He then randomly arranges the 16 pieces into four rows and four columns.

Disregarding rotations, determine the probability that this layout is in a precise checkerboard pattern.
How will the answer change if rotations are taken into consideration?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

8! * 7! / 15! = 1/6435 ~= 0.000155400155400155
If it's required that the top left be a specific one of the two colors, the probability is 1/2 this, or 1/12870 ~= 7.77000777000777 x 10^-5
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
soln	Steven Lord	2022-05-16 14:05:00
solution	Charlie	2022-05-16 10:42:35

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