`I found two eight-move solutions to entropy. Second is a slight
variation of the first.`

`Number the board as`

` 1 2 3 4`
` 5 6 7 8`
` 9 10 11 12`
`13 14 15 16`

`The solutions are`

`6 2
and
6 2`
`10 6
7 6`
`11 15
11 15`
`7 3 4
10 11 3 4`
`6 8 16
6 8 16`
`15 3
15 3`
`2 1
2 1`
`3 15 13
3 15 13`

`where a line reads: move from first number - by way of any middle
numbers - to the final number.`

`I suspect that you have seen these already - I did not find any
more. Found these by working backward - much easier than going forward.
Given time, might run a program to find all 8, 9, etc move solutions.`

`Very cute idea.`