Ice sliding games

Abstract

This paper deals with sliding games, which are a variant of the better known pushpush game. On a given structure (grid, torus...), a robot can move in a specific set of directions, and stops when it hits a block or boundary of the structure. The objective is to place the minimum number of blocks such that the robot can visit all the possible positions of the structure. In particular, we give the exact value of this number when playing on a rectangular grid and a torus. Other variants of this game are also considered, by constraining the robot to stop on each case, or by replacing blocks by walls.

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Notes

  1. 1.

    https://en.wikipedia.org/wiki/Ricochet_Robot.

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Corresponding author

Correspondence to Aline Parreau.

Additional information

This research is supported by the ANR-14-CE25-0006 project of the French National Research Agency.

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Dorbec, P., Duchêne, É., Fabbri, A. et al. Ice sliding games. Int J Game Theory 47, 487–508 (2018). https://doi.org/10.1007/s00182-017-0607-5

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Keywords

  • Combinatorial game theory
  • Graph theory
  • Sliding games