How to Share Candies
I have a bag of candies, and I want to divide it with my friends.
When I divide the candies with 11 persons, there are left 3 candies.
When I divide the candies with 8 persons, there are left 7 candies.
When I divide the candies with 7 persons, there are left 5 candies.
What is the minimum number of candies in the bag?
The answer is 47.
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1 solution
Since 7 , 8 , 1 1 are coprime, by the Chinese remainder theorem there is at most one solution between 1 and 7 ⋅ 8 ⋅ 1 1 . Moreover, 4 7 ≡ 3 ( m o d 1 1 ) , 7 ( m o d 8 ) and 5 ( m o d 7 ) . Therefore, the answer is 4 7 .