15 puzzle scrambles are not random state

[benwh1]

The distribution of the pieces is not uniform and the scrambles are easier than they should be. I generated 500 scrambles, and they had an average optimal solution length of 50.64, which should only happen with probability ~0.000000000000000476.

This is the distribution of pieces over 10000 scrambles:

Bar n in the m'th bar chart shows the number of scrambles where the 'n' tile ended up in position 'm' e.g. the leftmost bar in the bottom right bar chart shows the number of scrambles where the blank ended up in the top left (position 1)