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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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Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

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Skeleton

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

Long Multiplication

Age 11 to 14 Challenge Level:

Catherine, Rachel & Fiona from The Mount School, York, Sonia from Madras College, and the KS3 Maths Club from Strabane Grammar School all solved this. Everyone used trial and improvement but soon realised that there could not be a 2 in the two original numbers. James of Hethersett High School, Norwich gave the best explanation of the method. The answer is 775 multiplied by 33.

7 7 5
x 3 3

2 3 2 5
2 3 2 5 0

2 5 5 7 5