1. Halma An Unsolved Puzzle

2. The Normal British Way… “The normal British way, to sit in separate families in separate rooms in separate houses, each person occupied with a book, a paper, or a game of halma…” – George Bernard Shaw, 1898

3. History Halma is the Greek word for jump or leap, which is the best description for the game invented by George Howard Monks in 1883 Played on a checkerboard, the game is a thrilling alternative to the game of checkers and frequently mistaken for its relative, Chinese Checkers

4. How to Play The players set up an area in the corner of the board called a yard and the objective of the game is to be the first one to take over the opponent's yard by filling it completely with all your pieces. Traditionally played on a 16x16 board, up to 4 players can partake

5. How to Play cont. In a simplified version of the game, the board has 8x8 dimensions and each player has 10 pieces. This variant is known as “Grasshopper” and played by 2 people

6. Piece Movement A piece can move a step in any direction, like the king in a game of chess. A piece can jump over pieces on the board (both their own and their opponents') in order to move, as long as there is an empty space to land in.

7. Piece Movement cont. Unlike with checkers, pieces cannot be "taken" or removed. A jump can continue as a chain for as long as the player desires and as long as there are empty spaces to accommodate the leaps and landings. Steps and jumps can't be tied together in a single move.

8. No Solution The game has been around for over a century, but has set strategy of optimal play and isn’t commonly known Instead, Halma has provided an abundance of smaller scale puzzles that might eventually lead to a solution of the full board game

9. Strategies One basic strategy to all such games is to establish a diagonal ladder where pieces are set up in a way that there is a space between each counter for every move to be a jump leading from one yard to the yard diagonally across from it. This allows for the majority of your pieces to have an open route out of the starting position. I have found it is wise to leave 2-3 pieces together in the starting position in order for there to always be a piece of your color nearby to jump over.

10. Quickest Way to Win? Work with your opponent rather than against them

11. References 1. Beasley, John D. "The Analysis of Puzzles." In The Mathematics of Games (Oxford: Oxford University Press, 1990.) 77-83 2. Bell, George I. "The Shortest Game of Chinese Checkers and Related Problems" ''Integers: Electronic Journal of Combinatorial Number Theory 9'' (2009) #G01. Accessed September 14, 2015. http://arxiv.org/pdf/0803.1245.pdfhttp://arxiv.org/pdf/0803.1245.pdf 3. Gardner, Martin 1971. "The Game of Halma" ''Wheels, Life and other Mathematical Amusements'', W H Freeman & Co, 1983, 115-123 4. Gardner, Martin 1968. "Bridge-it and other Games" ''New Mathematical Diversions'' MAA, 1995 210-218 5. Gardner, Martin 1971. "Mathematical Games" Scientific American 225, no.4: 104 Accessed September 14, 2015 http://www.nature.com/scientificamerican/journal/v225/n4/pdf/scientificamerican1071-104.pdf http://www.nature.com/scientificamerican/journal/v225/n4/pdf/scientificamerican1071-104.pdf 6. Schaeffer, Jonathan and Robert Lake "Solving the Game of Checkers." Vol. 29. of Games of No Chance: Combinatorial Games at MSRI, 1994, ed. Richard J. Nowakowski (Cambridge: Cambridge University Press, 1996.) 119-131. 7. Silva, Jorge Nuno. ''Board Games''. n.p.: Salem Press, Inc, 2012. Gale Virtual Reference Library Accessed September 14, 2015 http://go.galegroup.com/ps/i.do?id=GALE%7CCX4003100063&v=2.1&u=gett36723&it=r&p=GVRL &sw=w&asid=7c5fc962506c083878a250b45a4c538c 119-122