Groupe d’études et de recherche en analyse des décisions

# Ordering 15 Marbles with a Three-Way Scale

## Charles Audet

Consider a scale that accepts three marbles of different weights. The scale only ranks the marbles, by indicating the heaviest, the lightest and the middle one of the three. What is the least number of weighings necessary to rank 15 different marbles from heaviest to lightest? This paper proposes a strategy that requires at most 20 weighings.

, 13 pages