Mathematics of a Sudo-Kurve

TL;DR

This paper explores the mathematical properties of Sudo-Kurve, a Sudoku variant with bent rows and columns, introducing Sudo-Cube and analyzing solution counts, symmetry, clues, and symbol placements.

Contribution

It introduces Sudo-Cube as an equivalent variant of Sudo-Kurve and provides mathematical analysis of solution counts, symmetry, and clues needed.

Findings

Total number of solution grids analyzed

Minimum clues required for unique solutions

Number of symbol placement configurations

Abstract

We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.