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# Multiples Sudoku

#### Rules of Multiples Sudoku

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### Adding All Nine

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Age 11 to 14

Challenge Level

*Multiples Sudoku printable worksheet*

By Henry Kwok

Like a conventional Sudoku, this Multiples Sudoku has two basic rules:

- Each column, row, and 3 x 3 subgrid must have the numbers 1 to 9.
- No column, row, or subgrid can have two cells with the same number.

The puzzle can be solved with the help of the numbers which are placed on the border lines between selected pairs of neighbouring cells.

These numbers are the product of the two digits in the cells to the left and right of the clue.

For example, where there is a 12 on the line between two neighbouring cells, the cells must contain 2 and 6, or 6 and 2, or 3 and 4, or 4 and 3.

*You may be interested in the other problems in our Playful Puzzling Feature.*

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.