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Counting Factors

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Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

Red Card Blue Card

Age 11 to 14 Short Challenge Level:

Sally has 5 red cards, numbered 1, 2, 3, 4 and 5, and 4 blue cards, numbered 3, 4, 5 and 6.

Can you find a way in which Sally can line the cards up so that the colours alternate, and so that the number on each red card is a factor of every number next to it?




This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.