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A blue-red Hackenbush girl, introduced in the book Winning Ways for your Mathematical Plays. In the original folklore version of Hackenbush, any player is allowed to cut any edge: as this is an impartial game it is comparatively straightforward to give a complete analysis using the Sprague–Grundy theorem.
The game was received positively, with PC World describing the game as "amusing", although noting that the game can "eat up a lot of time if you're not careful." [3] Lifehacker praised the game as a "nice stress reliever for adults", but similarly mentioned "the potential to be the biggest productivity killer of all time."
In the mathematical theory of automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to be the Mellin transform of a modular form. More generally a converse theorem states that a representation of an algebraic group over the adeles is automorphic whenever the L-functions of various twists of it are well-behaved.
For example, the four-vertex theorem was proved in 1912, but its converse was proved only in 1997. [3] In practice, when determining the converse of a mathematical theorem, aspects of the antecedent may be taken as establishing context. That is, the converse of "Given P, if Q then R" will be "Given P, if R then Q".
The converse of the theorem is not true in general. A holomorphic function need not possess an antiderivative on its domain, unless one imposes additional assumptions. The converse does hold e.g. if the domain is simply connected; this is Cauchy's integral theorem, stating that the line integral of a holomorphic function along a closed curve is ...
As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation.
Playing with both these variations makes the game quite difficult, but a very skilled player will still be able to win at least two games out of three. Devil's Grip is a broadly related game with similar game-play to Calculation, using two-decks stripped of the Aces, [9] and playing cards to a 3x8 grid where cards increase by three in rank. [10 ...
Nielsen–Schreier theorem (free groups) Niven's theorem (number theory) No-broadcasting theorem (quantum information theory) No-cloning theorem (quantum computation) No-communication theorem (quantum information theory) No-deleting theorem (quantum information theory) No free lunch in search and optimization (computational complexity theory)