# Finding a Unique Solution to Radon-Kaczmarz Puzzles

## TL;DR

This paper establishes an upper size bound for Radon-Kaczmarz puzzles, ensuring unique solvability for puzzles within that size, based on the slopes defining the clues.

## Contribution

It provides a new theoretical upper bound on puzzle size guaranteeing unique solutions for Radon-Kaczmarz puzzles.

## Key findings

- Upper bound for puzzle size ensuring uniqueness
- Applicable to puzzles with specific slope sets
- Enhances understanding of puzzle solvability constraints

## Abstract

Solving a Radon-Kaczmarz puzzle involves filling a square grid with positive integers, each between one and nine, satisfying certain clues coming from the sum of entries that lie on the same line in the square grid. Given a set of slopes (of a particular order) that define clues of Radon-Kaczmarz puzzles, we give an upper bound of the size such that any solvable Radon-Kaczmarz puzzle whose size is less than or equal to that is uniquely solvable.