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# A box contains many candies. If 3 candies are taken away, the rest can be shared evenly among...

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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 9, 2020

$$x\equiv 3\pmod{7}, x\equiv 6\pmod{8}, x\equiv 2\pmod{5}$$. You can either list or use CRT from here. You should get 262.