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The legendary Xmas quiz

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 At the school concert there were mince pies for everyone.  One huge tray I saw if the pies were divided into 2 equal piles there would have been one left over.  But if the same pies were put into 3 equal piles, there would have been one left over.  To my surprise, 4 equal piles gave a remainder of 1, five piles had one left over, and the pies when shared into six piles also had one mince pie left over.

What was the smallest number of mince pies there could have been on the tray?  I have just moved to Chesterton, and need to get my hair cut.

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