Enumerating 3D-Sudoku Solutions over Cubic Prefractal Objects

抄録

We consider three-dimensional extensions of the Sudoku puzzle over prefractal objects. The prefractal objects we use are 2nd-level cubic approximations of two 3D fractals. Both objects are composed of 81 cubic pieces and they have 9 × 9-grid appearances in three orthogonal directions. On each object, our problem is to assign a digit to each of the 81 pieces so that it has a Sudoku solution pattern in each of the three 9 × 9-grid appearances. In this paper, we present an algorithm for enumerating such assignments and show the results.