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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?


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

Tim from Gravesend Grammar School sent in this solution. Well done Tim.

Let the original number chosen be n.
The new six digit number formed is made by adding n to n shifted three digits to the left, ie 1000n, so the new number is 1000n + n, or 1001n. 1001=7*11*13, so 1001n will always have the factors 7, 11 and 13