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Repeaters

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.

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Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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Skeleton

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

Multiples Sudoku

Age 11 to 14 Challenge Level:

Why do this problem?

This is no ordinary Sudoku because it requires mathematical knowledge in addition to logical thinking. This problem offers an engaging context in which to apply knowledge of factors and multiples.
 

Possible approach

These printable resource may be useful: Multiples Sudoku
                                                           Multiples Sudoku Journey
 

If your students do not know the rules of Sudoku then set aside a little time for them to become familiar with the 'standard' Sudoku.

Work together with the class filling in a few cells to make sure everyone understands the rules.

Then hand out the sheets and invite students to work in pairs, emphasising that they must convince each other of their suggestions before anything gets added onto their papers.
 

Key questions

Some clues have lots of possibilities and some have few. Which are which?
Which are the most helpful clues to begin?
 

Possible extension

Students may wish to work on the similar but more challenging tasks Diagonal Product Sudoku and Product Sudoku.

For more on Factors and Multiples, see Gabriel's Problem or the Factors, Multiples and Primes Short Problems collection.

Possible support

Provide students with this possible journey through Multiples Sudoku and suggest they try to retrace the route.

For other Factors and Multiples problems that might help to prepare your students for this task, see Dozens, the Factors and Multiples Game, and the Factors, Multiples and Primes Short Problems collection.