Sumplete is Hard, Even with Two Different Numbers

TL;DR

This paper proves that determining the solvability of Sumplete puzzles remains NP-complete even when the grid contains only two distinct numbers, highlighting the puzzle's computational complexity.

Contribution

The paper establishes the NP-completeness of Sumplete puzzles with only two different numbers, extending understanding of its computational difficulty.

Findings

Sumplete is NP-complete with two numbers in the grid.

Deciding Sumplete solvability is computationally hard.

Complexity persists even under simplified conditions.

Abstract

Sumplete is a logic puzzle famous for being developed by ChatGPT. The puzzle consists of a rectangular grid, with each cell containing a number. The player has to cross out some numbers such that the sum of uncrossed numbers in each row and column is equal to a given integer assigned to that row or column. In this paper, we prove that deciding solvability of a given Sumplete puzzle is NP-complete, even if the grid contains only two different numbers.