Mathematical_Recreations-Kraitchik-2e

Mathematical Recreations
Triple hopscotch is played on the 24 vertices of a board
such as that shown in Figure 160. Each player has 9 pieces,
and these, as in simple hopscotch,
l"- I / are placed on the board alternately
I'-. ,/
by the players, and are then moved
alternately in the same fashion.
- - :-~
Whenever a player gets three pieces in
line he may remove anyone of his
,/
"- opponent's pieces. The first player
V I
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to be reduced to two pieces is the
FIGURE 160. Triple loser. In one variation of the game a
Hopscotch Board. player who has been reduced to three
pieces may move them to any empty vertices without having
to follow the lines. In another variation there are no diagonal
lines.
13. TRICOLOR. This game is a modification of lasca,
played on an hexagonal array of hexagonal cells colored
white, red, and black so that no two cells which meet along
an edge have the same color. (In Figure 161 shading denotes
red cells; the black and white cells are obvious. We
shall use the numbering of this figure.) As in lasca, the game
is played with stacks of one or more pieces, but the stacks
are free to move in anyone of the three or six directions
leading out from a cell.
The range of a stack - that is, the maximum number of
cells it can traverse in anyone direction in a single moveis
determined by the number of pieces in the stack: 1 cell
for a single piece, 2 cells for a stack of two pieces, and 3 cells
for any larger stack.
The combat strength of a stack depends upon both the number
of pieces in the stack and the color of the cell on which
it rests. Taking the strength of a single piece on a white cell
as the unit, the strength of a stack of two pieces on a white
cell is 2 units, that of any larger stack on a white cell is 3