Mathematical_Recreations-Kraitchik-2e

Games 313
one tries to construct squares of 4, 9, or 16 pieces whose
boundaries will have the same colors as the pattern piece.
Some of the many possibilities are illustrated in the sketches
of Figure 174.
7. THE 16 BICOLORED PIECES. This game, similar to
tetrachrome, is also due to Chicandard. The pieces are
painted with two colors chosen from among eight, and the
two colored regions are separated by a diagonal line. The
TYPE 1 TYPE 2
FIGURE 174.
Tetrachrome.
squares formed from these pieces may be required to satisfy
various requirements, such as using a certain number of
colors (4, 5, 6, 7, or 8) in each row and column. In Figure
175 are a number of such designs.
8. FROGS AND TOADS. On 2n + 1 cells in a straight line
are placed n frogs and n toads, with one cell between them.
A frog may move one cell toward the toads to an empty cell,
or may leap over either a frog or a toad to an empty cell;
similarly for a toad.
The object of the game is to interchange
the frogs and toads by such moves. The moves need
not alternate. Here are the solutions for n = 2, 3, and 4.
In general, n(n + 2) steps are needed.