A man buys 52 coconuts, but some are lost on his way home. If he evenly divides the amount of coconuts he has left among four people, 3 coconuts are left. If he divides the coconuts among three people, 2 remain. And if he divides the coconuts among five people, he's left with 2 coconuts. How many coconuts did he lose on his way home?

He lost 5 coconuts.

Step-by-step explanation:

When he divides the number left among 3 and 5 people the remainder is 2 in each case so the number that each person gets must be 15 or a multiple of 15.

So if x is the number left when he reaches home, then:

2 = x mod 3 and

2 = x mod 5

where x = 15 + 2 = 17 or 30 + 2 = 32 or 45 + 2 = 47.

But we also must satisfy 3 = x mod 4

If x = 17:

17 mod 4 = 1 so its not 17.

32 mod 4 = 0 so it's not 32.

47 mod 4 = 3 so x = 47.

Therefore the number he lost = 52 - 47 = 5.