Chess Is Hard Even for a Single Player

Authors N.R. Aravind, Neeldhara Misra, Harshil Mittal

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Author Details

N.R. Aravind
  • Department of Computer Science and Engineering, Indian Institute of Technology, Hydrebad, India
Neeldhara Misra
  • Department of Computer Science and Engineering, Indian Institute of Technology, Gandhinagar, India
Harshil Mittal
  • Department of Computer Science and Engineering, Indian Institute of Technology, Gandhinagar, India


The authors would like to thank the anonymous reviewers of FUN 2022 for their useful feedback.

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N.R. Aravind, Neeldhara Misra, and Harshil Mittal. Chess Is Hard Even for a Single Player. In 11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We introduce a generalization of "Solo Chess", a single-player variant of the game that can be played on The standard version of the game is played on a regular 8 × 8 chessboard by a single player, with only white pieces, using the following rules: every move must capture a piece, no piece may capture more than 2 times, and if there is a King on the board, it must be the final piece. The goal is to clear the board, i.e, make a sequence of captures after which only one piece is left. We generalize this game to unbounded boards with n pieces, each of which have a given number of captures that they are permitted to make. We show that Generalized Solo Chess is NP-complete, even when it is played by only rooks that have at most two captures remaining. It also turns out to be NP-complete even when every piece is a queen with exactly two captures remaining in the initial configuration. In contrast, we show that solvable instances of Generalized Solo Chess can be completely characterized when the game is: a) played by rooks on a one-dimensional board, and b) played by pawns with two captures left on a 2D board. Inspired by Generalized Solo Chess, we also introduce the Graph Capture Game, which involves clearing a graph of tokens via captures along edges. This game subsumes Generalized Solo Chess played by knights. We show that the Graph Capture Game is NP-complete for undirected graphs and DAGs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Theory of computation → Design and analysis of algorithms
  • chess
  • strategy
  • board games
  • NP-complete


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