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WFF 'N PROOF is a game of modern logic, developed to teach principles of symbolic logic. It was developed by Layman E. Allen in 1962 [ 1 ] [ 2 ] a former professor of Yale Law School and the University of Michigan .
A proof game is called a shortest proof game if no shorter solution exists. In this case the task is simply to construct a shortest possible game ending with the given position. When published, shortest proof games will normally present the solver with a diagram - which is the final position to be reached - and a caption such as "SPG in 9.0".
For the purposes of the Sprague–Grundy theorem, a game is a two-player sequential game of perfect information satisfying the ending condition (all games come to an end: there are no infinite lines of play) and the normal play condition (a player who cannot move loses).
The secretary problem demonstrates a scenario involving optimal stopping theory [1] [2] that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.
[1] [2] It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990: [3] Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats.
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The theorem follows by induction on the length of the game from these two lemmas. Lemma 1. If s = 0, then t ≠ 0 no matter what move is made. Proof: If there is no possible move, then the lemma is vacuously true (and the first player loses the normal play game by definition).