# Kazimierz Chomicz Proposes Geometric Approach to Frobenius Problem with Four Variables

- Published: 2026-11-06 16:15 UTC
- Section: Science › Research
- Tags: Frobenius problem, coin problem, Chicken McNugget problem, Kazimierz Chomicz, discrete geometry, linear Diophantine equations, Frobenius number
- URL: https://realtech.media/news/rt-19d799d181c85dd716d66448_kazimierz_chomicz_proposes/

**The 18-year-old researcher mapped combinations to three-dimensional space, providing explicit formulas for specific sequences.**

![Kazimierz Chomicz Proposes Geometric Approach to Frobenius Problem with Four Variables](https://sgzwpqqelzmajkcubgkl.supabase.co/storage/v1/object/public/rt-media/2026/11/ff2dd82be51bf14c.jpg)
*Ruleroll, Wikimedia Commons, CC BY-SA 4.0*

Polish student Kazimierz Chomicz won first place at the European Union Contest for Young Scientists with a new geometric method for the Frobenius coin problem, spektrum.de reported. The work focuses on identifying the largest integer that cannot be expressed as a linear combination of given positive integers with non-negative integer coefficients [1]. While a closed-form formula exists for two generators and algorithms exist for three, cases with four or more generators lack general closed-form solutions [1].

Chomicz analyzed the problem for four distinct package sizes by transferring the algebraic problem into three-dimensional space [1]. In this framework, the smallest package size serves as a reference base, while coordinates $(x, y, z)$ define the frequencies of the remaining three generators [1]. Each combination is represented as a unit cube within a spatial lattice, converting the unbounded combinatorial search into a spatial structure [1].

## Spatial Reduction and Boundary Formulation

The method systematically eliminates regions of the lattice that do not provide minimal representations of integers [1]. Chomicz proved that the essential search space for any four generators reduces to a finite three-dimensional geometric body [1]. By bounding this volume, the algorithm discards infinite subsets of irrelevant combinations, isolating the boundary configurations where the Frobenius number occurs [1].

## Solutions for Specific Sequences

The approach yields closed-form solutions when the generators follow structured mathematical progressions [1]. Chomicz applied the geometric construction to sets of four consecutive squares and four consecutive triangular numbers, characterizing the resulting shapes precisely enough to derive explicit formulas for their Frobenius numbers [1]. The framework provides a systematic geometric foundation for evaluating multi-variable Frobenius problems [1].

## Sources

1. [spektrum.de](https://www.spektrum.de/news/algebra-18-jaehriger-macht-fortschritte-beim-chicken-nuggets-problem/2353042)

---

Source: RealTech, realtech.media — https://realtech.media/news/rt-19d799d181c85dd716d66448_kazimierz_chomicz_proposes/