# Trappist-1

## Introduction

Trappist-1 (also called "Chess on an Infinite Plane with Huygens Option") is a chess variant played on a chessboard of infinite size. The game includes two huygens for each color. Huygens can jump 5, 7, 11 and other prime numbers of squares in orthogonal directions (i.e. 5, 7, 11, 13, 17,...). Since it jumps in prime numbers, other jumpers such as the knight and hawk, need to make an inefficient maneuver when pursuing a huygens, causing wasted moves.## Setup

## Pieces

Black and White each have the following pieces: 1 king, 1 queen, 2 chancellors, 2 rooks, 4 bishops, 4 knights, 2 guards, 2 hawks, 2 huygens, and 26 pawns.**Chancellor**(C) - Moves and captures as rook + knight.

**Hawk**(Ha) - Leaps exactly 2 or 3 squares in any orthogonal or diagonal direction. The leaping move means it can jump over other pieces.

**Guard**(G) - Moves and captures the same as a king but is not affected by check.

**Huygens**(Hu) - Huygens jump 5, 7, 11 13, and other prime numbers of squares in orthogonal directions.

**Pawns**play the same and promote at the same rank as in classical chess. (Using the board coordinates shown in the diagram, white pawns promote at rank 16, and black pawns promote at rank 9). Pawns can promote to chancellor, hawk, huygens, or guard, in addition to queen, rook, bishop, or knight. Pawns may capture en passant with the same rules as in classical chess.

## Rules

**There is no castling.**

**There is no fifty-move rule.**Draws can only occur from stalemate, threefold repetition, agreement, or a proven case of insufficient material to force checkmate.

**All other rules are the same as in classical (FIDE) chess.**

**The Chessboard:**

**1. Board for OTB Play:**

**2. Diagram for Online Play:**

**Ranks**are numbered just as in classical chess; ranks 16 and higher are deeper into black's side; ranks 9 and less are deeper into white's side.

**Files**visible in the initial diagram are labeled a - x. From white's view, they continue to the right y and z, and then aa,ab,ac, and so on. The file immediately to the left of "a" is "phi" ("φ"). Files further to the left are -a,-b,-c, and so on to -z, and then -aa, -ab, -ac, and so on. For convenience, the "φ" file can be written "0". (The zero file = "φ" = "0")

## Notes

A diagram with the huygen's moves on a 50 x 50 grid can be seen here:**Mathematical note of Interest:**It may be mathematically impossible to devise an algorithm to "solve" Trappist-1. The huygens jumps prime numbers of squares, and the complete set of prime numbers is unknown (and no method to compute it), thereby placing Trappist-1 into a category of unsolvable games.

**Fergus Duniho**for making Diagram Designer available, and also the abstract piece collection. Also thanks to

**Kevin Pacey**for helping with Diagram Designer.

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By V. Reinhart.

Web page created: 2017-02-28. Web page last updated: 2017-02-28