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A box contains many candies.
If 3 candies are taken away, the rest can be shared evenly among 7 people.
If 6 are taken away, the rest can be shared evenly among 8 people.
If 3 candies are added, then the box can be shared evenly among 5 people.
What is the smallest number of candies in the box?

 Sep 13, 2020
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Using CRT and MMI

C - 3 mod 7 = 0,

C - 6 mod 8 = 0, 

C+3  mod 5 = 0, solve for C

 

C =280n + 262, where n =0, 1, 2, 3.......etc.

The smallest number of candies in the box = 262

 Sep 13, 2020

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