For description of the problem see Threaded Pins

How many pieces of thread will be needed in general ? i.e; given number of pins N and clockwise gap G, Express the number of Threads needed T, as a function of N & G.

Source : ” Thinking Mathematically ” by John Mason et.al

PS: This problem is related to “rotation of array” problem where you are asked to rotate the array by a given amount using only O(1) extra space. For example, rotating array containing 3, 5, 9, 14, 1, 2, 11 by 3 positions will yield 14, 1, 2, 11, 3, 5, 9.

PPS : I highly recommend “Thinking Mathematically” for kids, it helps to develop good practices which aid in solving problems.