# Talk:15 puzzle solver

## Mathematical meaning of minimum

The meaning of minimum has been discussed see: Minimum. It means 52 not 58, assuming fewest is a synonym for minimum. I think the task description should call for 'minimum solutions to random 15 puzzles' (see below)--Nigel Galloway (talk) 10:28, 6 October 2017 (UTC)

## Mathematical meaning of random

Unlike minimum, which I am surprised that anyone thinks means anything other than 'reduced to the least possible amount or degree', random means easy mathematically. There are 16!/2 15 puzzles, a little over 10 trillion, of which the number that are hard to solve is counted in the hundred thousands. Therefore a randomly chosen puzzle is easy. --Nigel Galloway (talk) 10:36, 6 October 2017 (UTC)--Nigel Galloway (talk) 10:36, 6 October 2017 (UTC)

## Extra credit for non-random puzzles

We could offer extra credit for solving hard puzzles:

``` 2  1  3  4
5  6  7  8
9 10 11 12
13 14 15  0
```

and

```  0 12  9 13
15 11 10 14
3  7  2  5
4  8  6  1
```

--Nigel Galloway (talk) 13:08, 6 October 2017 (UTC)