NIM
Posted by admin | Filed under Allgemein
Das klassische Nim-Spiel besteht aus drei Haufen oder Reihen mit 3, 4 und 5 Streichhölzern. Die beiden Spieler müssen abwechselnd aus einem der Haufen mindestens ein Streichholz wegnehmen. Wer das letzte nimmt, hat gewonnen. An Stelle von Streichhölzern kann man Steinchen, Münzen oder beliebige andere Gegenstände verwenden. Bezüglich der Anzahl Haufen und Gegenstände existieren zahlreiche Varianten. Es gibt auch die Regel, dass der Spieler, der den letzten Gegenstand nimmt, verliert.
Geschichte
Die Herkunft des Spiels ist ungewiss. Vergleichbare Spiele sind in China bereits in alter Zeit belegt. In Europa sind Varianten des Spiels seit Anfang des 16. Jahrhunderts bezeugt. Auch die Etymologie des Namens ist unsicher. Eine mögliche Erklärung ist die Herleitung vom altenglischen oder germanischen nim (”nimm!”).
Mathematik
Die Theorie des Nim-Spiels geht auf den Harvard-Mathematikprofessor Charles Leonard Bouton zurück (1902). Seine Lösung für eine beliebige Anzahl von Haufen und Gegenständen beruht auf der binären Darstellung der ganzen Zahlen. Man schreibt die Anzahl von Gegenständen in jedem Haufen als Summe von Zweierpotenzen. Die Situation ist für einen Spieler dann günstig, wenn er aus einem Haufen so viele Gegenstände wegnehmen kann, dass nach dem Zug im Gesamten keine Zweierpotenz in einer ungeraden Anzahl vorkommt. Andernfalls ist die Situation ungünstig. Daraus ergibt sich für jede Anfangssituation die Lösung des Spiels. Bei der klassischen Spielvariante gewinnt mit der richtigen Strategie immer der erste Spieler.
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