Saw the following puzzle on HN and thought I would repost here. It can be solved using Simplex, but I was wondering if there is a more elegant solution, or if someone can prove NP-completeness.
Each dot below represents the position of a laser. Indicate the direction that the laser should fire by replacing the dot with ^, v, <, or >. Each grid position i,j should be hit by exactly grid[i][j] lasers. In the example below, grid position 0,0 should be hit by exactly grid[0][0] = 2 lasers.
A laser goes through everything in its path including other guns (without destroying those guns).
2 2 3 . 1 . 2 2 3
1 . 2 1 1 . 1 . 2
2 3 . 1 . 2 . 4 .
. 3 . 2 2 . 2 3 4
1 . 2 . 2 3 2 . .
2 3 . 3 . 3 2 2 .
3 . 2 4 2 . 2 . 2
1 1 . . 1 3 . 2 .
. 2 1 . 2 . 1 . 3
