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

Magic Potting Sheds

Age 11 to 14 Challenge Level:

For another problem that builds on the ideas in this problem, students can be directed to More Magic Potting Sheds

Full details of a tried and tested classroom approach to this problem can be found in the Notes to More Magic Potting Sheds

This activity offers students the opportunity to explore a new environment and challenges them to use some deductive reasoning. The problem can be tackled on paper but access to the interactivity will speed up the process of exploring different possibilities.
It is important to have paper available for students to record the results of the different trials.