Question

A boy with a collection of marble realise that if he makes a group of 5 or 6 marbles at a time there are always 2 marbles left. Can you explain why the boy cannot have a prime number of marbles.

Answer 1

Number of marbles is 5n+2 or 6m+2 ,i.e., a multiple of 5 or 6 plus 2 marbles. Hence number of marbles must be a multiple 5x6 or 30 plus even number 2. Hence number of marbles cannot be a prime number