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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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Have You Got It?

Can you explain the strategy for winning this game with any target?

Find from Factors

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

If 21 and 35 are factors of the number, then 3, 5 and 7 must all be included amongst its prime factors. This means that the required number must be a multiple of 105 and, as the complete list of factors of 105 is 1, 3, 5, 7, 15, 21, 35 and 105, the answer is 105.

This problem is taken from the UKMT Mathematical Challenges.