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

Inclusion Exclusion

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Since this problem can be tackled in a variety of ways it can lead to useful discussions on the merits of different strategies.

If students disagree about the correct answer they can be challenged to develop convincing arguments that justify their conclusions.