How much fruit does the farmer have?

The man at the farmer's market thinks he is a mathematician. He likes


to arrange his fruit in nice rows. However, when he lays his fruit in rows of 3 he has one left over. When he lays them in rows of 5 he also has one left over. Remarkably he also has one left over when he arranges them in rows of 7 and 9. 11 seems to be the magic number, for, in rows of 11 there is no fruit left over.

How much fruit does the farmer have?
3*5*7*9+1


=946
Reply:Since 9 is 3², LCM of 3, 5, 7, 9 will be (5 * 7 * 9) = 315.





To be divisible by 11, this means that


(315n + 1) mod 11 = 0


From n = 1 To 11, one of them will be a solution.





315(3) + 1 = 946 which is also divisible by 11.





Hence the farmers has 946 fruits.