You are a biochemist, working with a 12-slot centrifuge. This is a gadget that has 12 equally spaced slots around a central axis, in which you can place chemical samples you want centrifuged. When the machine is turned on, the samples whirl around the central axis and do their thing.
To ensure that the samples are evenly mixed, they must be distributed in the 12 slots such that the centrifuge is balanced evenly. For example, if you wanted to mix 4 samples, you could place them in slots 12, 3, 6 and 9 (assuming the slots are numbered from 1 to 12 like a clock).
Problem: Can you use the centrifuge to mix 5 samples?