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 separated. The slots on the centrifuge are numbered 1 through 12 clockwise (and clock-like).
12 1
11 2
10 3
°
9 4
8 5
7 6
When the machine is turned on, the samples whirl around the central axis and do their thing. To ensure that the centrifuge runs smoothly, the samples must be distributed in the 12 slots such that it is balanced evenly.
Can you use the centrifuge to run 5 samples?
For example, if you have four samples, they may be placed in slots 1, 4, 7, and 10 to balance the centrifuge.
... who used to do lots of lab work before academic duties called me away from the bench:
The dummy tube solution was always the favourite one ... it took far less thinking about ;)
Also - at speeds offering less than about 10,000 g we would regularly take a chance with a non-balanced set up if we were centrifuging for a short amount of time.