# Integrated Product Sudoku

##### Stage: 3 and 4 Challenge Level:

by Henry Kwok

### Rules of Integrated Product Sudoku

Like the standard sudoku, this sudoku variant has two basic
rules:

- Each column, each row and each box (3$\times$3 subgrid) must
have the numbers 1 to 9.
- No column, row or box can have two squares with the same
number.

The puzzle can be solved with the help of small clue-numbers
which are either placed on the border lines between selected pairs
of neighbouring squares of the grid or placed after slash marks on
the intersections of border lines between two diagonally adjacent
squares.

Each small clue-number is the product of two digits in the two
squares that are horizontally or vertically or diagonally adjacent
to each other. The position of each pair of diagonally adjacent
squares is indicated by either two forward slash marks // or two
backward slash marks \\.

For example:

- the //36 on intersection of border lines between the diagonally
adjacent squares (6, 8) and (7, 7) means that possible pairs of
numbers in the squares are: 4 and 9 or 9 and 4 or 6 and 6.
- the \\6 on intersection of border lines between the diagonally
adjacent squares (6, 6) and (7, 7) means that possible pairs of
numbers in the squares are: 1 and 6, 6 and 1; 2 and 3, or 3 and
2.
- finally, the clue-number 8 on the border line betweeen the
squares (9, 1) and (9, 2) means that possible pairs of numbers for
these squares can be from the following combinations: 1 and 8, 8
and 1; 2 and 4, or 4 and 2.