Question

The integers from 1 to 1000 are written in order around a circle. Starting at 1, every fifteenth number is marked (that is 1, 16, 31, etc.). This process is continued until a number is reached which has already been marked. If the number of marked numbers is A, then find A/50.

Answer 1

In the first round all integers, which leave remainder 1 when divided by 15, will be marked; last number of this category is 991. Next number will be 91 + 15 - 1000 = 6. That means in second round all integers, which leave remainder 6 when divided by 15, will be marked.

In short, numbers of the form 5k + 1 will be marked. Therefore,

A = 200 and A/50 = 4