Day Fifteen/Night Fifteen

Here is a puzzle for you: You hold in your hands an array of five colorful squares – black, blue, silver/white, red and yellow – and five connector cables in the same colors. You need to connect each square to another using a cable of a different color than any of the two squares it touches. When all connected, the five squares should form a circle. What do you do?

Now do the same exercise, this time with only four squares and four cables in the same colors as the squares; your goal is to form a square out of squares at the end. Now do the same with three — a triangle out of squares. Now two — a straight line out of squares. At which point can we no longer avoid squares and connectors of the same color touching? What does this say about the connections that…