#2 SIDED PEG SOLITAIRE FULL#

We consider the standard single vacancy complement problem (SVCP), where we attempt to play from a full board minus a single man to the complementary position where only the initially vacant hole contains a single man (Figure 1 shows the starting position for the (0,0) complement problem). This notation is much bulkier than the standard notation for the English board, but we can use it on any board without having to redo the notation, and it is also very easy to remember.Īny generalized cross board can easily be shown to be a null-class board, meaning that any position and its complement are in the same fundamental class (ref). In the case of multiple jumps we can use the compact notation (0,0)RU for the two moves (0,0)R, (2,0)U. We shall use Cartesian coordinates to identify all board locations, with (0,0) always the center of the cross (the unoccupied hole in Figure 1).Ī move shall be represented with the starting coordinate of the move followed by a direction U,D,L,R for up, down, left and right.įor example the 4 moves available in Figure 1 are (2,0)L, (0,2)D, (-2,0)R and (0,-2)U. We consider the standard peg solitaire problem, where the legal moves are those where a man is jumped over another to an empty hole, the man jumped over being removed from the board. These two boards have square symmetry, but the generic generalized cross board has no symmetries at all. Note that the standard English board is the special case (2,2,2,2), and Wiegleb's board is the special case (3,3,3,3) (ref).

We shall denote a particular cross board by the four-tuple ( n 1, n 2, n 3, n 4). The arm length can be any non-negative integer (i.e. BellĪ Generalized Cross Board consists of a 3x3 center square of holes with four 'arms' attached to it of length n 1, n 2, n 3 and n 4 and width three (see figure 1). Peg Solitaire on Generalized Cross Boards Peg Solitaire on Generalized Cross Boards by George I.

2 sided peg solitaire