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## 'Missing Multipliers' printed from http://nrich.maths.org/

The multiplication square below has had all its headings and answers hidden. All of the headings are numbers between 2 and 12, and no heading appears twice horizontally or vertically.

By revealing some of the answers, can you work out what the headings must be?

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What is the smallest number of answers you need to reveal in order to work out the missing headers?

Can you describe a strategy that allows you to complete the Level 3 challenge most of the time?

Can you suggest any reasons why your strategy might not always work?

Once you have a strategy for completing Level 3, here are some more Missing Multiplier challenges you might like to try:

You might also like to try some challenges which include negative numbers.

A 4 by 4 grid, using multipliers from -4 to +4
A 6 by 6 grid, using multipliers from -6 to +6
*If you enjoyed this problem you may also enjoy Gabriel's Problem*