Bulo

Opening Position

Alternate Names

Tac Tix, TacTix

No. of Players

Two

Equipment

A 4x4 square grid and sixteen counters (the uniformity of the counters' color is not important) are required for play.

History

This game was claimed to be invented in 1949 by the scientist/mathematician/poet Piet Hein (also known for his game Hex). However, due to the game's simplicity and resemblance to other games of the Nim family, it (or a very similar game) is likely to be much older than 1949. Hein may have conceived that the game could be played on a square grid larger than 4x4. The game is now considered to be in the public domain and it is easy to find folk art versions for sale made with wooden boards and marbles as well as internet and computer software applications to play it.

The first major publicity for the game was probably in Martin Gardner's Scientific American column in the February 1958 issue. The column and reader's responses were later re-printed in his first book collection of columns, "Hexaflexagons and other Mathematical Diversions; The First Scientific American Book of Mathematical Puzzles and Diversions."

Objective

The loser is the player who removes the last counter from the board, making their opponent the winner.

Play

Alternate turns entail the removal of up to four counters from the board. If more than one counter is removed, they must be connected in an orthogonal line.

Strategy

Bulo is a solved game and is always a second player win with perfect play.

Variations

This game can be expanded to any board size, and also to allow different shapes to be removed (like pentominoes or diagonal crosses).

Eatcake is a version of Bulo with any NxM board full of counters. The first player removes horizontal lines of connected counters, and the second player removed vertical lines of connected counters. The last player to move wins.

Bonus Nim, invented by Bill Taylor, is played on a 7x7 board (which is expandable to any rectangular board). Alternate turns entail a player removing any orthogonal connected line of counters of any size. There is a restriction for the first move, where the move must take less than half the maximum possible. Also, there is a bonus of four counters for making the final capture. Winner is whoever obtains most counters.

Tac Tex is a version played on any hexagonal board.

Bulo with the counters placed at the intersections of the board, rather than the cells.

Bulo boards may be larger and have some diagonal lines added along which counters may be removed.

Sources

  1. Pentagames. Compiled by Pentagram. 1990. Fireside, Simon & Schuster Inc. ISBN 0-671-72529-7.