Redraw the figure so that each of the seven circles is big enough to hold a penny. The problem is to shade each of the shaded circles. However, there’s a catch. Here’s the rules that you have to follow.
Starting with any circle, count clockwise three circles and shade the third circle. Continue in this way, each time beginning at an empty circle and counting clockwise three circles and then shading.
As there are seven circles, the students where able to change the problem from counting over three spaces to counting over n spaces. They where able to figure out that multiples of seven will not work and that 10 is congruent to 3 modulo 7.