Alcuin's Propositiones de Civitatibus: the Earliest Packing Problems

TL;DR

This paper explores three ancient city packing problems from Alcuin's work, analyzing their solutions and comparing them to modern algorithms, highlighting their complexity and historical significance.

Contribution

It provides the earliest known packing problems from Alcuin and offers the best solutions known, bridging historical and modern computational approaches.

Findings

Problems are challenging for current packing algorithms.

Alcuin's solutions are analyzed and contextualized.

Best solutions to these ancient problems are documented.

Abstract

We consider three problems about cities from Alcuin's_Propositiones ad acuendos juvenes_. These problems can be considered as the earliest packing problems difficult also for modern state-of-the-art packing algorithms. We discuss the Alcuin's solutions and give the known (to the author) best solutions to these problems.