Baron Munchhausen's Sequence

TL;DR

This paper analyzes a coin-weighing puzzle from a math Olympiad, generalizes it for any number of coins, and proves that the objective can be achieved in at most two weighings regardless of coin count.

Contribution

It introduces a generalized version of the coin-weighing puzzle and provides a complete solution showing the objective is achievable in no more than two weighings.

Findings

The puzzle can be solved in at most two weighings for any number of coins.

The analysis methods differ from classical coin-weighing puzzles.

A complete solution to the generalized puzzle is provided.

Abstract

We investigate a coin-weighing puzzle that appeared in the all-Russian math Olympiad in 2000. We liked the puzzle because the methods of analysis differ from classical coin-weighing puzzles. We generalize the puzzle by varying the number of participating coins, and deduce a complete solution, perhaps surprisingly, the objective can be achieved in no more than two weighings regardless of the number of coins involved.