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最神奇的数学魔术

发布日期:2010-05-19

        你相信心灵感应魔术存在吗?在一次表演上,魔术师杰克兄弟两人为大家表演了扑克牌的心灵感应。首先老杰克先上场,拿出一副扑克牌,在现场任意找了一位观众,让他抽出五张牌,老杰克用眼睛迅速扫了一下五张牌,分别是红桃4,梅花6,方片A, 黑桃5和方片9,然后选出方片9交给观众,让观众将牌翻过去,自己将剩下的四张牌正面朝上一一摆放到桌面上,而刚刚发生的这一切,站在远处的小杰克完全无法看清楚。之后,老杰克对这位观众说,“刚才我给你的这张牌是什么,只有你和我知道,但是我和我的弟弟小杰克在心理上有一种神秘的感应力量,他也可以猜得到这张牌是什么,下面就请小杰克走过来”。小杰克走到放着扑克牌的桌子前,双手合拢放到胸前,沉思几秒钟,迅速说出了老杰克给观众的牌是方片9。

放在桌面上的四张牌:


拿走的方片9:


        这个魔术从八十年代开始在美国流行,很多观众看完魔术后第一反应是老杰克和小杰克之间一定发生了某种信息交流,比如手势、身体语言,可是用一两个动作同时表示出一张牌的花色和大小并不是易事。其实这个魔术是一个纯粹的数学游戏,最初由美国麻省理工学院一位数学博士发明。为了增加魔术的趣味性,一些魔术师在表演这个魔术时,两个表演搭档身处两个城市甚至身处两个国家,通过电话、电子邮件通知自己的猜测,不过无论表演的方式如何改变,有一点是不变的,小杰克必须知道或看到五张牌中剩下的四张牌。

        既然魔术的玄机在在这四张牌上,那么老杰克是如何通过这四张牌告诉小杰克第五张牌的花色和大小的呢?有人会想到排列组合,四张不同的扑克牌一共有4*3*2*1=24种排列方式,是不是因为这个?可是一副扑克牌(除去大小王52张),拿掉4张后,还剩40多张,24种排列方式也表示不了40多种可能性,而且每次抽出的五张牌中,还可能出现同样的数字,同样的花色,兄弟两人事先也不知道观众到底会抽出哪五张牌,接着想下去,真让人头疼。

        实际上,这个魔术不是一个简单的排列组合,要经过几个步骤,第一步靠的是老杰克。大家都知道,扑克牌只有四种花色,如果抽出五张牌,其中至少有两张牌是一种花色的,(相当于把5个苹果放到四个箱子里,至少会有一个箱子里有两个或以上的苹果),上面的五张牌中方片A和方片9就属于一个花色,老杰克给观众的牌不是任意给的,一定是两个相同花色牌中的一个,之后他把剩下的四张牌放到桌子上时,要保证第一张牌(方片A)和观众手中的牌(方片9)是一个花色,这样小杰克看到方片A之后,就可以推断出那张牌的花色也是方片。有人会说,如果总是把和要猜的牌一样花色的牌放在第一个位置,会不会被人察觉到,其实兄弟两可以事先约定好放在第几个位置,未必一定是第一个。

        知道了花色以后,老杰克又是怎样用红桃4,黑桃5和梅花6告诉小杰克那张牌的数字是9的呢?剩下的这三张牌可能都是6,也可能都是梅花,但是有一点是确定的,来源于同一副扑克的这三张牌是互不相同的,魔术发明者的智慧正在于此。老杰克和小杰克首先要制定一个比较任意两张牌谁大谁小的“规则”,例如在扑克52张牌中红桃的牌最大,黑桃的牌其次,然后是梅花、方片,同样花色的牌,K最大,A最小。这样,任意三张牌中,都会有一个“大牌”,一个“中等牌”和一个“小牌”。在摆放这三张牌时,有大中小、大小中、小大中、小中大、中大小,中小大六种摆放顺序,上面图中显然属于“大中小”方式。

        这六种排列方式可以分别代表1、2、3、4、5、6六个数字,可是扑克牌一共有从A到K十三个数字,六个数字无论如何也表示不了十三个数字呀!很多聪明的观众在自己思考这个魔术的原理时,或许也可以猜得出之前的所有秘密,但是最后一步却把他们难住了,这也正是这个魔术的画龙点睛之笔。

        在魔术的第一步,一个和被藏起来的牌花色一样的牌被用来指示花色,但是它的角色其实还没有说完。老杰克拿出了方片9给观众,但是没有拿方片A给观众,这也是有原因的。我们可以在上图这个13张牌排成的环中找到9和A,然后逆时针从9数到A,要数8次;如果从A数到9,只需要数5次。剩下的“大中小”三张牌可以表示5,却表示不了8,所以老杰克把9给了观众,而当小杰克看到了A和5的信息后,在自己的脑海里从A逆时针数5下得到最后的答案9。

        在整个魔术的过程中,老杰克和小杰克更像是完成了一次秘密通信,在表演开始前,两个人先要制定好这几条“通信协议”,之后有老杰克用那四张亮着的牌为藏在观众手中的牌进行加密,之后小杰克按照自己已经知道的规则进行解密,“感应”到那张牌的花色和数目。

        这个五张纸牌的魔术曾经被很多人誉为“最精彩的数学魔术”,让很多人领略到了神秘的数学中的乐趣。

        Do you believe in telepathy magic exist? In a performance, the Magic Jack, two brothers as we performed a poker telepathy. First of all, the first play old Jack, come up with a deck of cards, any look at the scene of a viewer, let him out five cards, old Jack eyes quickly scanned about five cards, namely, 4 of hearts, plum 6 side pieces A, spades 5 and 9 square pieces, and then select side piece 9 to the audience, the audience will turn over cards that he will be remaining four cards face up one by one placed to the desktop, and just All this happened, stood a small distance can not look at Jack completely. , The old Jack the audience said, "I give you what this card is only you and I know, but me and my little brother Jack in the psychological sense there is a mysterious force, he can guess What are this card, and asked the following small Jack came. " Jack went to a small table playing cards stood before, his hands folded into his chest and thought a few seconds, quickly out of the old Jack to the audience's card is 9 square pieces. 


        The magic in the United States since the eighties pop, a lot of viewers watching the old magic after the first reaction is between Jack and Little Jack must have taken place in some kind of exchange of information, such as gestures, body language, but also said that with one or two movements out the color and size of a card is not easy. In fact, this magic is a purely mathematical game, originally developed by a mathematics Ph.D. Massachusetts Institute of Technology invented. In order to increase the Magic's interesting, some of the magician the magic, the two partners live performances and even the two cities are in two countries, by telephone, e-mail notification own speculation, but no matter how to change the way performance, One thing is constant, small Jack must know or see the five cards in the remaining four cards.

        Since the magic of the mystery in the four cards on this, then how old Jack is told by the four licensed small-Jack and the fifth card of the suit the size of it? Some people may think of permutations and combinations, four different cards, a total of 4 * 3 * 2 * 1 = 24 arrangement, it is because of this? But a deck of cards (remove the size of the King 52), remove four, the remaining 40 sheets, 24 said the arrangement can not be more than 40 kinds of possibilities, but each time the five cards, it is also possible The same figure, the same color, two brothers in the end the audience will not know in advance which of five cards out, and then want to go, really a headache.

        In fact, the magic is not a simple permutation and combination, to go through several steps, first by the old Jack. We all know that poker only four colors, and if out of five cards, of which at least two cards is a suit, (the equivalent of four to five apples into a box, at least there will be a box two or more of the apple), above 5 cards the Chinese film A and the side piece 9 on the part of a suit, old Jack is not a license to any given audience, and must have two identical cards in a suit, then he The remaining four cards on the table, we must ensure that the first card (side pieces A) and the audience in the hands of the card (side pieces 9) is a flower, to see such a small square piece Jack A, one can infer The suit goes on is out of square pieces license. Some people would say, and to guess if always the same suit cards on the first position the license, will be aware, in fact, the two brothers can be good on the first of several pre-agreed location, not necessarily the first .

        After that the colors, the old Jack is how to use Hearts 4 Spades 5 and 6, told a small plum Jack goes on the license number is 9 then? The remaining three cards that may have been 6, but also may have been plum, but one thing is certain, from this same deputy poker three cards is a separate, magic inventor's wisdom lies. Old Jack and Little Jack first to compare any two cards to develop a big who who is small, "rules", for example, poker 52 cards in the hearts of the cards the most, followed by spades in the card, then plum blossom, square film, the same suits of cards, K maximum, A Min. Thus, any three cards in, there will be a "big", a "middle card" and a "small card." In placing the three cards, there are large, medium, size medium and small sized, small Zhongshan University, in size, small and medium display large order of six, the above figure is clearly the "medium and small" approach.

        This arrangement could represent the six 1,2,3,4,5,6 six figures, but the cards from A to K, a total of 13 numbers, six numbers in any case that can not be 13 numbers ah ! A lot of smart thinking in his audience the principles of this magic, perhaps you can guess all the secrets before, but the last step confused them stumped, and this is precisely the magic of finishing touch the pen.

        The first step in magic, and the hidden cards of a suit the cards are used to indicate the same color, but its role really has not finished. Jack took out the old square piece 9 to the audience, but did not get side-chip A to the audience, this is a reason. We can in the figure the 13 cards arranged in a ring found in 9 and A, then the number of counter-clockwise from 9 to A, to the number 8; if the number from A to 9, only a few 5. Rest of the "medium and small", said three signs of 5, but that can not be 8, so the old Jack to 9 to the audience, and when Little Jack saw A and 5 of the information, in their minds from A counterclockwise Number 5, 9, under the final answer.

        In the course of the magic, the old Jack and Little Jack is more like a secret communication to complete, before the start of the show, two of these articles should first formulate the "communication protocols", after a four lit with that old Jack The license for the possession of the cards in the hands of the audience is encrypted, then a small Jack already know the rules of their own to decrypt, "response" to the color and number of licenses goes on.

        The five cards of magic has been a lot of people as "the most brilliant mathematical magic," so many people to experience the mystery of mathematics in the fun.