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Phutball Draws

Sucharit Sarkar

Abstract

In this short note, we exhibit a draw in the game of Philosopher's Phutball. We construct a position on a 12 x 10 Phutball board from where either player has a drawing strategy, and then generalize it to an m x n board with m-2 >= n >= 10.

Phutball Draws

Abstract

In this short note, we exhibit a draw in the game of Philosopher's Phutball. We construct a position on a 12 x 10 Phutball board from where either player has a drawing strategy, and then generalize it to an m x n board with m-2 >= n >= 10.

Paper Structure

This paper contains 2 theorems, 2 equations, 5 figures.

Key Result

Theorem 1

There are drawn configurations in Phutball played on a $12\times 10$ board.

Figures (5)

  • Figure 1: An illustrative Phutball position.
  • Figure 2: Shots, tackles, and jots.
  • Figure 3: A drawn position in Phutball.
  • Figure 4: Half of the forced sequence of moves in the draw.
  • Figure 5: A drawn position in Phutball on the standard pitch.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Corollary 2
  • proof