language ESSENCE 1.3.0 $ Problem Alien Tiles $ $ Problem details available at http://www.csplib.org/Problems/prob027/ $ $ Essence model by Andrew Martin $ $ Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/ given gridSize : int(1..) given colours : int(1..) letting dGridSize be domain int(1..gridSize) letting dColours be domain int(0..colours-1) $ colours moves is always equal to no moves find clickMatrix : matrix indexed by [dGridSize, dGridSize] of dColours maximising (sum i,j : dGridSize . clickMatrix[i][j]) such that $ no way of reaching same state faster exists forAll simplerClickMatrix : matrix indexed by [dGridSize, dGridSize] of dColours . $ ensure not faster (sum i,j : dGridSize . clickMatrix[i][j]) <= (sum i,j : dGridSize . simplerClickMatrix[i][j]) \/ $ ensure not same (for each tile, check if sum of clicks effecting it %colours same as other clickmatrix) exists x,y : dGridSize . ((sum index : dGridSize . clickMatrix[index][y] + clickMatrix[x][index]) - clickMatrix[x][y]) % colours != ((sum index : dGridSize . simplerClickMatrix[index][y] + simplerClickMatrix[x][index]) - simplerClickMatrix[x][y]) % colours