Sources page biographical material

5.R.1.a. TRIANGULAR VERSION
The triangular version of the game has only recently been investigated. The triangular board is generally numbered as below.
1

2 3

4 5 6

7 8 9 10

11 12 13 14 15
Herbert M. Smith. US Patent 462,170 -- Puzzle. Filed: 13 Mar 1891; issued: 27 Oct 1891. 2pp + 1p diagrams. A board based on a triangular lattice.

Rohrbough. Puzzle Craft. 1932. Triangle Puzzle, p. 5 (= p. 6 in 1940s?). Remove peg 13 and leave last peg in hole 13.

Maxey Brooke. (Fun for the Money, Scribner's, 1963); reprinted as: Coin Games and Puzzles; Dover, 1973. All the following are on the 15 hole board.

Prob. 1: Triangular jump, pp. 10-11 & 75. Remove one man and jump to leave one man on the board. Says Wesley Edwards asserts there are just six solutions. He removes the middle man of an edge and leaves the last man there.

Prob. 2: Triangular jump, Ltd., pp. 12-13 & 75. Removes some of the possible jumps.

Prob. 3: Headless triangle, pp. 14 & 75. Remove a corner man and leave last man there.

M. Gardner. SA (Feb 1966) c= Carnival, 1975, chap. 2. Says a 15 hole version has been on sale as Ke Puzzle Game by S. S. Adams for some years. Addendum cites Brooke and Hentzel and says much unpublished work has been done.

Irvin Roy Hentzel. Triangular puzzle peg. JRM 6:4 (1973) 280-283. Gives basic theory for the triangular version. Cites Gardner.

[Henry] Joseph & Lenore Scott. Quiz Bizz. Puzzles for Everyone -- Vol. 6. Ace Books (Charter Communications), NY, 1975. Pennies for your thoughts, pp. 179-182. Remove a coin and solve. Hint says to remove the coin at 13 and that you should be able to have the last coin at 13. The solution has this property.

Alan G. Henney & Dagmar R. Henney. Computer oriented solutions. CM 4:8 (1978) 212 216. Considers the 'Canadian I. Q. Problem', which is the 15 hole board, but they also permit such jumps as 1 to 13, removing 5. They find solutions from each initial removal by random trial and error on a computer.

Putnam. Puzzle Fun. 1978. No. 15: Jumping coins, pp. 5 & 28. 15 hole version, remove peg 1 and leave last man there.

Benjamin L. Schwarz & Hayo Ahlburg. Triangular peg solitaire -- A new result. JRM 16:2 (1983-84) 97-101. General study of the 15 hole board showing that starting and ending with 5 is impossible.

J. D. Beasley. The Ins and Outs of Peg Solitaire. Op. cit. above, 1985. Pp. 229-232 discusses the triangular version, citing Smith, Gardner and Hentzel, saying that little has been published on it.

Irvin Roy Hentzel & Robert Roy Hentzel. Triangular puzzle peg. JRM 18:4 (1985-86) 253 256. Develops theory.

John Duncan & Donald Hayes. Triangular solitaire. JRM 23:1 (1991) 26-37. Extended analysis. Studies army advancement problem.

William A. Miller. Triangular peg solitaire on a microcomputer. JRM 23:2 (1991) 109-115 & 24:1 (1992) 11. Summarises and extends previous work. On the 10 hole triangular board, the classic problem has essentially a unique solution -- the removed man must be an edge man (e.g. 2) and the last man must be on the adjacent edge and a neighbour of the starting hole (i.e. 3 if one starts with 2). On the 15 hole board, the removed man can be anywhere and there are many solutions in each case.

Remove man from hole: 1 2 4 5

Number of solutions: 29760 14880 85258 1550

Considers the 'tree' formed by the first four rows and hole 13.