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Toads and Frogs
The combinatorial game Toads and Frogs is a partisan game invented by Richard Guy. This mathematical game was used as an introductory game in the book Winning Ways for your Mathematical Plays.
Known for its simplicity and the elegance of its rules, Toads-and-Frogs is useful to illustrate the main concepts of combinatorial game theory. In particular, it is not difficult to evaluate simple games involving only one toad and one frog, by constructing the game tree of the starting position. However, the general case of evaluating an arbitrary position is known to be NP-hard. There are some open conjectures on the value of some remarkable positions.
== Rules ==
Toads and Frogs is played on a 1 × ''n'' strip of squares. At any time, each square is either empty or occupied by a single toad or frog. Although the game may start at any configuration, it is customary to begin with toads occupying consecutive squares on the leftmost end and frogs occupying consecutive squares on the rightmost end of the strip.
On his turn, Left may move a toad one square to the right if it is empty. Alternatively, if a frog occupies the space immediately to a toad's right, and the space immediately right of the frog is empty, Left may move the toad into that empty space; such a move constitutes a "hop". Toads may not hop over more than one frog, nor are they allowed to hop over another toad. Analogous rules apply for Right: on a turn, he may move a frog left into a neighboring empty space, or hop a frog over a single toad into an empty square immediately to the toad's left. As usual, the first player to be unable to move on his turn loses.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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