## How Many Mangoes?

From a basket of mangoes when counted in twos there was one extra,

counted in threes there were two extra,

counted in fours there were three extra,

counted in fives there were four extra,

counted in sixes there were five extra,

but counted in sevens there were no extras.

At least how many mangoes were there in the basket?

119. The number has to be evenly divisible by seven for there to be no extras when counting in sevens, and it has to be odd in order for there to be one extra when counting by twos. It also can’t be evenly divisible by three through six. 119 is the first odd multiple of 7 that satisfies the requirements.

2 Comments on "How Many Mangoes?"vats says

August 25, 2014 @ 12:37

119

RamÃ³n says

April 17, 2015 @ 19:17

Alternatively:

n is a multiple of 7, and 1 short of a multiple of 3 or 4 or 5 or 6

Division by 6 takes care of division by 3, so n+1 = 4 x 5 x 6 x K

(where K will ensure it’s a multiple of 7)

So n = 119*K, and 119 is divisible by 7, so K = 1 and n = 119

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