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Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Adding All Nine

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!

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GOT IT Now

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Missing Multipliers

Stage: 3 Challenge Level: Challenge Level:1

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?
 
This text is usually replaced by the Flash movie.

 
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:

A 6 by 6 grid, using multipliers up to 15

An 8 by 8 grid, using multipliers up to 18

A 10 by 10 grid, using multipliers up to 20

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