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Tom has a collection of more than 24 coins. When he puts the coins in piles of 6, there are 3 coins remaining. When he puts the coins in piles of 8, there are 7 coins remaining. How many coins remain when he puts the coins in piles of 24?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.