If five submarines, sunk on the same day, all went down at the same spot where another had previously been sunk, how might they all lie at rest so that every one of the six U-boats should touch every other one? To simplify we will say, place six ordinary wooden matches so that every match shall touch every other match. No bending or breaking allowed.
It will be seen from the illustration that this puzzle is absurdly easy — when you know how to do it! And yet I have not the slightest doubt that many readers found it a hard nut to crack. It will be seen that every match undoubtedly touches every other match.
Related: Suppose we’re coloring a map and we decide that no two adjoining regions should have the same color. What’s the smallest number of colors we’ll need to be sure of doing the job? On a flat map the answer is famously four. But what if we extend the question to three dimensions and try to color regions in space? In that case we might need any number of colors, as shown in this “proof without words” by CMG Lee:
