Brilli the ant placed the numbers 1,2,…,n in order clockwise around a circle. She can create an infinite sequence A={aj}∞j=0 of integers by letting a0=k∈{1,2,…,n} and constructing ai+1 from ai by taking the integer that is ai positions clockwise in the circle from ai. For a set of sequences S={A0,A1,…,Am}, we say that S covers the circle if each number on the circle occurs an infinite number of times in the sequences of S.

Question

Brilli the ant placed the numbers 1,2,…,n in order clockwise around a circle. She can create an infinite sequence A={aj}∞j=0 of integers by letting a0=k∈{1,2,…,n} and constructing ai+1 from ai by taking the integer that is ai positions clockwise in the circle from ai. For a set of sequences S={A0,A1,…,Am}, we say that S covers the circle if each number on the circle occurs an infinite number of times in the sequences of S.

We define the Circle Cover Number of n to be the minimum size of a set S that covers the circle with entries {1,2,…,n}. Determine how many integers from 1 to 100 have Circle Cover Number equal to 2.

Details and assumptions
It is possible for the Circle Cover Number of n to be infinite, if there is no finite set S which covers the circle.

Answer 1

One manufacturer needs to calculate the net price of an order with a list price of $300 and a trade discount series of 12/9/5. Use the net decimal equivalent to find the net price.