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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.

This problem is taken from the UKMT Mathematical Challenges.