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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.

More Magic Potting Sheds

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

You may like to start by having a go at the Magic Potting Sheds problem.

It may be useful to keep a record of your trials.

Try working backwards from the number of plants in the last garden (remembering that you must always have whole numbers of plants in the gardens and shed).

Describing the different stages algebraically may be helpful.