new puzzle challenge

[Claudio L.]

(03-30-2015 03:19 AM)Paul Dale Wrote:  Just off the top of my head, there are five rotations of that position, plus the reflections and rotations.

The problem isn't as difficult as 19! There are a lot of short cuts a search can make. My initial thought is only ten locations need to be searched, the rest are determined by these ten numbers without choice.


Pauli

There's 19 unknowns, and unless I'm mistaken we can write 15 linearly independent equations, so there's only 4 independent variables, not 10 I think.
The first one can take 19 values, the second one only 18 possible values, the third one 17, and the last one 16.
The maximum number of solutions to try by brute force then would be 19*18*17*16 = 93024, I'd say its manageable. Most of those solutions will end with some of the dependent variables with values outside the range of the problem. Sorting the equations from the simplest (w/3 elements) to the more complex would allow for faster testing, or even a matrix multiplication could yield all dependent variables at once, then the code only has to test if they all fall in the 1-19 range to discard the solution.
Brute force doesn't look so bad, I think it's doable.