Baron Munchhausen Redeems Himself: Bounds for a Coin-Weighing Puzzle

TL;DR

This paper analyzes a coin-weighing puzzle from the Moscow Math Olympiad, generalizes it, and establishes an improved upper bound showing that logarithmically-many weighings are sufficient to solve it.

Contribution

It introduces a generalized version of the coin-weighing puzzle and derives a tighter upper bound on the number of weighings needed, improving upon trivial bounds.

Findings

Logarithmic number of weighings suffices

Derived an upper bound better than trivial bounds

Generalized the original puzzle to more coins

Abstract

We investigate a coin-weighing puzzle that appeared in the Moscow Math Olympiad in 1991. We generalize the puzzle by varying the number of participating coins, and deduce an upper bound on the number of weighings needed to solve the puzzle that is noticeably better than the trivial upper bound. In particular, we show that logarithmically-many weighings on a balance suffice.