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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.

Ones Only

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.