HMMT November 2014 U23
- Guts
- Answer
Seven little children sit in a circle. The teacher distributes pieces of candy to the children in such a way that the following conditions hold.
- Every little child gets at least one piece of candy.
- No two little children have the same number of pieces of candy.
- The numbers of candy pieces given to any two adjacent little children have a common factor other than 1.
- There is no prime dividing every little child's number of candy pieces.
What is the smallest number of pieces of candy that the teacher must have ready for the little children?
Dataset text NuminaMath olympiads. Quoted with source.
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