ApSimon's Mint Problem with Three or More Weighings

TL;DR

This paper extends ApSimon's mint problem to three or more weighings, providing numerical solutions for identifying mints with genuine or secondary coins efficiently.

Contribution

It generalizes the original problem to multiple weighings and offers numerical results for optimal mint identification strategies.

Findings

Numerical solutions for three or more weighings.

Optimized strategies for mint identification.

Reduced total coin count for verification.

Abstract

ApSimon considered the problem of deciding by a process of two weighings on which of a known number of mints emit either coins of a known genuine weight or emit coins of a different secondary but unknown weight. The combinatorial problem consists of finding two sets of coin numbers to be loaded on the tray for each of the weighings, and then to minimize the total count of coins to be drawn from all mints for these two weighings. This work yields numerical results for the generalized problem which allows three or more weighings to settle which of the mints produce either sort of coins.