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Summer Maths Puzzles - Thursday 22 August - Sweet Enough

Sweet Enough

A group of 5 children are discussing how they should divide up the ridiculously large amount sweets that they were given at Halloween.

  • One of the children suggests that they could share them equally between themselves but then there would be 3 left over.
  • Another of the children suggests that they could share them equally with the rest of their football team (ie between 11 children) but they realise that there would still be 6 sweets left over.
  • Observing that there were almost as many sweets as there are days in the year, their parents decided that they should share them equally between all of their class (ie 31 children) and give the remaining 17 sweets to their teacher. 


  1. How many sweets were there altogether?
  2. In the end, how many sweets did they each get?


p.s.  Any answer is wonderful but we'd love it if you used the Chinese Remainder Theorem to solve this one :)


Please email your answers to deputy-director[at][dot]uk and remember to include your name (or the name of the group that you solved the puzzle with) so that we can publish it on our website if you are one of the first few to successfully solve the problem.  

Answers to all puzzles will be published at the end of the month. 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons