Question

A coconut farm owner asked his uneducated labour to count the number of coconuts pluged
After some time when the owner came back and asked for number. Labour replyed
1. If it is kept as two no's then one is left alone
2. If it is kept as three no's then one is left alone
3.If it is kept as four no's then one is left alone
4.If it is kept as five no's then one is left alone
5.If it is kept as six no's then one is left alone
6.If it is kept as seven no's then none is left alone
Owner got the count.. can u guess

Answer 1

Let us imagine a number who is a multiple of all numbers ranging from 1 to 6 but not a multiple of 7.

LCM (1,2,3,4,5,6) = 60

So the random number we imagined can be concluded to be a multiple of 60.

Let the number be 60x.

The number we require is actually (60x + 1) since one coconut was always left behind when arranged in groups of 1,2,3,4,5,6 each.

But (60x + 1) is a multiple of 7 as well.

There are an infinite number of solutions to the given problem. The solutions form a line when represented graphically whose equation is

7y-60x = 1

The smallest solution is 301.