The Centrifuge

A centrifuge has 12 locations for test tubes, located evenly in a circle (let them be referenced as the hour locations on a clock.) Prior to spinning the tubes, the centrifuge must be evenly balanced about its center. Assuming all test tubes weigh the same amount, what numbers of test tubes (from 1 to 12) can be spun without needing to add dummy tubes to balance out the weight? For example, you can't spin 1 tube alone, but can you spin 5 tubes?

Source: rec.puzzles. Used as Ken's Puzzle of the Day 6/6/94.

Mail to Ken