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## 'Product Sudoku' printed from http://nrich.maths.org/

##### By Henry Kwok

### The Basic Rules of "Product Sudoku"

Like the conventional Sudoku, this Sudoku variant consists of a grid of nine rows and nine columns subdivided into nine $3 \times 3$ subgrids. Like the Sudoku Classic, it has two basic rules:

1. Each column, each row, and each box ($3 \times 3$ subgrid) must have the numbers 1 to 9.

2. No column, row or box can have two squares with the same number.

The puzzle can be solved with the help of the numbers in the top parts of certain squares. These numbers are the products of the digits in all the squares horizontally and vertically adjacent to the square.

### A Short Demonstration

The square in the top left corner of this Sudoku contains the number 20. 20 is the product of the digits in the two adjacent squares, which therefore must contain the digits 4 and 5. The 5 cannot go in the cell below the top left hand corner because 5 is not a factor of 96 (the product shown in the third cell down on the left hand side of the puzzle). Therefore 5 must be entered into the
cell to the right of the cell containing 20 and 4 in the cell below.

A printable version of the problem can be found

here.