MR 2002b:05012 
Csákány, Bé\c la(H-SZEG); Juhász, Rozália(H-SZEG) 
The solitaire army reinspected. 
Math. Mag. 73 (2000), no. 5, 354--362.


0786.90109
Duncan, John; Hayes, Donald
Triangular solitaire. (English)
[J] J. Recreational Math. 23, No.1, 26-37 (1991). [ISSN 0022-412X]

The classical version of solitaire is surely well-known; a thorough account is now available
in a book of {\it J. D. Beasley} [`The ins and outs of peg solitaire', Oxford Univ. Press
(1985)]. {\it N. G. de Bruijn} [J. Recreational Mathematics 5, No. 2, 133-137 (1972)] gave
a delightful argument to provide a necessary condition for a solution to the standard game;
his argument using invariants with values in the field of four elements has become a
feature in some first courses in abstract algebra, and will reappear here in slightly modified
form. In his final chapter, Beasley gives a brief account of triangular solitaire, which is
played on a triangular board with an equilateral triangle grid of holes. He notes that ``little
appears to have been on it..., Perhaps readers will be tempted.'' In fact, the first author
originally encountered triangular solitaire in roadside cafes in Scotland (set out on the
tables for the amusement of customers) and has used it in teaching problem-solving. {\it I.
R. Hentzel} [ibid. 6, No. 4, 280-283 (1973)] developed a variant of de Bruijn's argument for
triangular solitaire; we give a more direct analogue of de Bruijn's argument by employing
skew coordinates. In the spirit of Beasley's book we consider more general problems
related to triangular solitaire; in particular, we solve completely the army problem by an
elaboration of Conway's ``golden pagoda'' argument [explained in Beasley's book].

MSC 2000: 
       *91A46 Combinatorial games

Keywords: triangular solitaire; skew coordinates; skew coordinates