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On the Game of Moksha-Patam

Aninda Kumar Nanda, Amit Kumar Misra

Abstract

The game of Moksha-Patam, often known as `Chutes and Ladders', is a widely played indoor game worldwide. While studies have been conducted regarding the nature of an individual board, the possibilities that open up when we change the positions of the chutes and the ladders on a board are mostly unventured. In this article, we classify and study the different possible types of Moksha-Patam Boards, introduce a naming convention for them and establish a count for the boards that can be constructed adhering to some basic assumptions of the game.

On the Game of Moksha-Patam

Abstract

The game of Moksha-Patam, often known as `Chutes and Ladders', is a widely played indoor game worldwide. While studies have been conducted regarding the nature of an individual board, the possibilities that open up when we change the positions of the chutes and the ladders on a board are mostly unventured. In this article, we classify and study the different possible types of Moksha-Patam Boards, introduce a naming convention for them and establish a count for the boards that can be constructed adhering to some basic assumptions of the game.

Paper Structure

This paper contains 7 sections, 29 equations, 3 figures.

Figures (3)

  • Figure 3: A Few Moksha-Patam Boards.
  • Figure 4: One-step Transition Probability Matrix of the $14(G_0)$ Board.
  • Figure 5: An algorithm to identify the winnability of Moksha-Patam boards.

Theorems & Definitions (16)

  • Definition 1.1: Entrance
  • Definition 1.2: Non-entrance Cell
  • Definition 1.3: Exit
  • Definition 1.4: Non-exit Cell
  • Definition 1.5: Non-component Cell
  • Definition 1.6: Chute-Barrier
  • proof
  • proof
  • proof
  • proof
  • ...and 6 more