The official rules:
- The digits 1 through 9 appear in each row and each column exactly once.
- Digits in each shaded region must multiply to the indicated product.
- Squares with multiple colors contain a number that’s used in the product for adjacent regions of each of those colors.
- Remember: numbers can repeat within a shaded region if that doesn't violate the first rule.
- The board is a “toral board,” that is, cells at the end of one row are considered adjacent to those at the beginning of the same row; cells at the end of one column are considered adjacent to those at the beginning of the same column, and all corner cells are considered adjacent.