拈的取數問題研究

拈是一種流傳久遠的遊戲，人類樂衷於各種遊戲的原因，無非是獲得勝利時的快樂，或者是可得到一大筆的獎賞。因此，如果能找出遊戲的致勝關鍵，是非常迷人的一個課題。哈佛大學數學系副教授查理士．理昂納德．包頓(Chales Leonard Bouton)，曾以拈為主題，做一番深入的研究分析，在至少取1子的規則下，找出所有致勝的數型。但拈是可任意改變規則的遊戲，而在不同的規則之下，當然致勝的數型必然不同。我們研究的主題內容，是根據三種不同的規則，找出致勝的數型；首先將最少取子數規定為2，再進一步擴大成一般的自然數，接著限制最多取子數，最後綜合前兩種規則，將取子數設定在任意兩自然數之間。當然，規則愈複雜，要找出致勝的數型，其困難度自然加大，尤其最後一個主題，我們只有在特定的條件下得到結論，所以仍有很大的探討空間。

關鍵字

最多限制；最少限制

並列摘要

Nim is one kind of the tradittonal games.The reason for Human addict to each kind of games is nothing but gaining the joy when they win, or obtaining a big reward.Therefore, discovering the key to win the game is an enchanting topic. The Associate Professor of Math Department in Harvard University Chales Leonard Bouton ,once took Nim as the subject and made a thorough research and analysis.Under the rule of taking at least one ,he discovered all numbers types to win. But,Nim is the game which we could chang the rule. Under the different rules,the number types are inevitably different.The main content we study is to discover the number types which result in wining the game baed on three kind of different rules.First,the taken number is stipulated to at least two.Then,we expand the number type to that of the general natural number.Further,we limit the most taken numbers.Finally,we synthesize the first two kind of rules. The taken number is hypothesized between two random naturalnumers. Certainly,if the rule is more complex,it must be more difficult to discover the number types which people could win.Especially in the last subject,we only obtain the conclusion under the specific condition.Therefore,the subject is worth discussed thoroughly.

並列關鍵字

Nim is one kind of the tradittonal games

參考文獻

17. A.M. Yaglom and I.M. Yaglom,Challenging Mathematical Problems with Elementary Solutions, vol. 1 and 2, translated into English by James McCawley, Jr.

1.拈及其變形遊戲