Solving KenKen puzzles — by not playing

John R. Gerlach
2010 Pharmaceutical Programming  
Solving Kenken puzzles requires more than making sure that numbers are used only once in a row and column of a matrix. Unlike Sudoku puzzles that can use any symbol and have sub-matrices, Kenken puzzles require actual integers and have contiguous cells, called cages. And, unlike a sub-matrix that contains a unique collection of numbers or symbols, Kenken puzzles have cages that must contain natural numbers representing a total as a function of its assigned arithmetic operation. For example,
more » ... ider a 4x4 Kenken puzzle having a cage containing 3 cells whose total is 11 as a function of simple addition. One possible set of 3 numbers would be: 4+3+4=11. The objective is to complete the grid using numbers ranging from 1 to N that satisfies both cage arithmetic and row / column uniqueness. Depending on the size of the NxN grid, the number (and size) of the cages, as well as the arithmetic operations used, a Kenken puzzle offers a formidable challenge for logic puzzle fans. However, rather than play the game of considering numerous possible sets ranging from two integers, for subtraction and division, to N-digits, for addition and multiplication, this paper proposes a SAS solution that obtains the viable sets for each cage straight-away and solves the puzzle by identifying the only appropriate collection of cage-specific sets.
doi:10.1179/175709310x12847352884285 fatcat:wzl3gcw6yfdnzmu7uy2yugk2h4