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.
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