A **one person game** is a sequence of moves following certain rules satisfying

- there are finitely many moves at each stage,
- there is a finite sequence of moves which yields a solution,
- there are no chance or random moves,
- there is complete information about each move,
- each move depends only on the present position, not on the existence or non-existence of a certain previous move (such as chess, where castling is made illegal if the king has been moved previously).

A ** permutation puzzle **is a one person game (solitaire) with the following five properties listed below. Before listing the properties, we define the **puzzle position** to be the set of all possible legal moves. The five properties of a permutation puzzle are:

- for some n > 1 depending only on the puzzle’s construction, each move of the puzzle corresponds to a unique permutation of the numbers in T = {1, 2, …, n},
- if the permutation of T in (1) corresponds to more than one puzzle move then the the two positions reached by those two respective moves must be indistinguishable,
- each move, say M, must be “invertible” in the sense that there must exist another move, say M
^{-1}, which restores the puzzle to the position it was at before M was performed,
- if M
_{1} is a move corresponding to a permutation f_{1 }of T and if M_{2} is a move corresponding to a permutation f_{2 }of T then M_{1}*M_{2} (the move M_{1} followed by the move M_{2}) is either
- not a legal move, or
- corresponds to the permutation f
_{1}*f_{2}.

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