# Mathematics Magic And Mystery By Martin Gardner Pdf

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This is one of the better tricks of its kind, because the effect of reversing the digits isn't obvious to most people at first The middle digit is always 9, while the first and last digits of any such multiple add up to 9. Thus, a new table must be provided each time. Several online implementation do this quite effectively, with nice graphics. Using a pocket calculator, another spectator multiplies that number by some secret 3-digit number which he chooses freely and keeps for himself.

## Mathematics, magic and mystery

This is one of the better tricks of its kind, because the effect of reversing the digits isn't obvious to most people at first The middle digit is always 9, while the first and last digits of any such multiple add up to 9. Thus, a new table must be provided each time. Several online implementation do this quite effectively, with nice graphics. Using a pocket calculator, another spectator multiplies that number by some secret 3-digit number which he chooses freely and keeps for himself.

The result is a 6 or 7-digit number. The spectator withholds one of those digits and reveals all the others in a random order. The magician then reveals the withheld digit! The result is therefore a multiple of 9 and the sum of its digits is a multiple of 9. When all the digits but one are revealed, the last one is thus known modulo 9. This does reveal it unless it's either a zero or a nine. Many variants of this trick can be devised based on any obscure process which produces a multiple of 9.

Here is one:. Ask a spectator to pick any 4-digit number and to consider the number obtained by reading it backwards. Let the spectator secretly subtract the lesser number from the larger one, add 54 and multiply the result by a 3-digit number freely chosen by the spectator Count ostensibly on your fingers how many digits you are given to make sure you're only missing one.

The following effect can be repeated as many times as needed to convince the spectators that you can read their minds with perfect accuracy as they pick one of three choices. Put three cards face-up on the table. Flip the three cards over. Now face the table again and instruct the spectators to switch cards as many times as they wish in front of your eyes. Before you flip the cards and turn around, remember which card is in the middle. When you face the table again, focus of the card which is now in the middle and keep track of its position as spectators move cards around.

Otherwise, the chosen card can be neither the one you had memorized nor the one you're now seeing. It's the third card. Regardless of the details of that show, it should be clear that a magician can only make predictions about outcomes which do not depend on the choices of his many spectators.

However, surprisingly many people want to believe in some irrational explanation. The teacher tells the class that a crowd can be driven to think about the same thing; very few people will escape the mental picture shared by all others Each student in the class is asked to think about a small number and is then instructed to perform the following operations silently. The teacher then announces to a puzzled classroom that their collective thinking must have gone wrong, since " there are no grey elephants in Denmark " The 4!

However, since we may choose what card is offered for guessing, we have an additional choice among 5. The resulting possible courses of action are more than enough to convey the relevant information. Here's one practical way to do so:. We offer the hidden card up for "guessing". The order in which the remaining 3 cards are presented can be used to reveal this count, as there are 6 possible permutations of 3 given cards.

Using some agreed-upon ordering of the cards in a deck, we hold a high card H , a medium card M and a low card L. Some arbitrary code is used, like:. This trick is credited to Dr. William Fitch Cheney, Jr. It was used in a job interview and subsequently appeared on the rec. In , Robert Orenstein implemented Vesterman's encoding for online play at www. For many years, that page was apologizing for having "temporarily" shut down its terse interactive features, since Mathematical Intelligencer 24 1 Winter Here's one way to present the effect:.

If we use a regular deck of cards, we either remove the face cards or attribute to them the same value 1 as aces. All told, only a few cards are thus singled out as special. The majority are not You may play this version online with a computer which honestly shuffles the deck.

Allow yourself to be baffled a few times before reading on Well, the explanation is simply statistical. You are instructed to pick any word in the first red section of the text. Then, skip as many words as there are letters in your chosen word. For example, if you picked the fourth word "Course" you have to skip 6 words "of human Events, it becomes necessary" to end up on the word "for" Iterate the same process, by skipping as many words as there are letters in the successive words you land on.

What's the first word you encounter in the last green section? The sequence would continue with the words: descent , that , causes. The "magic" is based on the Kruskal principle discussed above The words that do work have been underlined for you. This includes the first 17 words of that yellow section. Since all words of the red section have less than 17 letters, that solid chunk of underlined words can't be jumped over and, therefore, all paths starting in the red section will ultimately lead to the word "God" in the green section.

Actually, any word up to the word "Station" is a valid beginning of a sequence which ends up on the word "God". One trick is to have a spectator cut the deck. Here they are:. For example:. This is just a straight consequence of binary numeration.

Each card actually shows all the numbers which have a "1" in their respective binary representations at a given position. Each card shows the 54 numbers which have a nonzero digit at a specific ternary position. This is a classic no-brainer. Ask what pile the chosen card belongs to and collate the cards so the chosen pile is in the middle. Deal and collate again in the same way.

Deal one last time. The chosen card will be in the middle of the selected row. Reveal it in whatever dramatic way you like One method of eliminating half the cards in a face-down deck is to flip-over every other card, starting with the topmost one, to form two piles and get rid of the face-up pile The first elimination gets rid of the odd-numbered cards and reverses the order of the even-numbered ones:.

There are also two "false cuts" to give an impression of randomness. Add those two products together. There are two ways to do the interweaving.

So, only the case where the top pack is larger need be considered. All told, the only case where the faro shuffling of an odd number of cards does not reduce trivially to the shuffling of an even number of cards is the following one:. In such a shuffle, there's a pair of adjacent cards from the middle of the pack which remain adjacent at the bottom of the pack after the shuffle. It's much less regular than the other type of faro shuffling. Yet, some patterns appear:.

Put all the discs on the table, flip some of them over, shuffle them. Ask your spectators to do the same. The same basic situation repeats after a whole number of slices have been so obtained. The other 11 cards are then exposed.

Then, you do just that! Also, the first 11 cards allow you to determine the correct suit and leave a choice of only two values. This speed-flourish enhances the effect's impact. This trick works by relating the number of cards in several piles to the values of their top cards. Here's one:. If you deal out the number of cards indicated by that top card for two piles, each of them will have consumed a total of 14 cards. So, if you have removed 10 cards from your hand at the outset, there's a total of 14 cards left.

Counting them reveals the value of the pile's top card. The secret is to assign a unique number to each card an know what the total for the whole deck is. Mentally keep the running total of all the cards which have been shown. When only one card remains, its number is obtained by subtracting that total from the known total for the whole deck. The formula behind that calculation was discovered by Gauss when he was seven years old.

## Mathematics, Magic and Mystery

With an OverDrive account, you can save your favorite libraries for at-a-glance information about availability. Find out more about OverDrive accounts. Dover Recreational Math. Martin Gardner. Dover Publications. Why do card tricks work?

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## The Magic of Manhattan

Martin Gardner October 21, —May 22, [1] [2] was an American writer. He had many interests, so he wrote about many topics. He wrote about mathematics , magic , literature , philosophy , skepticism , and religion.

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By Martin Gardner. Like many another hybrid subject matter, mathematical magic is often viewed with a double disdain. Mathematicians are inclined to regard it as trivial play, magicians to dismiss it as dull magic. Its practitioners, to rephrase an epigram about biophysicists, are apt to bore their mathematical friends with talk of magic, their magic friends with talk of mathematics, and each other with talk of politics.

### Martin Gardner

После этого сюда полезут все, кому не лень. Каждый бит информации АНБ станет общественным достоянием. Фонтейн внимательно изучал ВР, глаза его горели. Бринкерхофф слабо вскрикнул: - Этот червь откроет наш банк данных всему миру. - Для Танкадо это детская забава, - бросил Джабба.

Мы должны пойти на. - Слишком поздно, - сказал Стратмор. Он глубоко вздохнул. - Сегодня утром Энсея Танкадо нашли мертвым в городе Севилья, в Испании.

Он уверяет, что в шифровалке полный порядок. Сказал, что ТРАНСТЕКСТ работает в обычном темпе. Что у нас неверные данные. Джабба нахмурил свой несоразмерно выпуклый лоб. - В чем же тогда проблема.

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В процессе форматирования стирается память машины - информация, программное обеспечение, вирусы, одним словом - все, и в большинстве случаев переформатирование означает потерю тысяч файлов, многих лет труда. Но ТРАНСТЕКСТ не был обычным компьютером - его можно было отформатировать практически без потерь. Машины параллельной обработки сконструированы для того, чтобы думать, а не запоминать. В ТРАНСТЕКСТЕ практически ничего не складировалось, взломанные шифры немедленно отсылались в главный банк данных АНБ, чтобы… Сьюзан стало плохо. Моментально прозрев и прижав руку ко рту, она вскрикнула: - Главный банк данных. Стратмор, глядя в темноту, произнес бесцветным голосом, видимо, уже все поняв: - Да, Сьюзан.

Сьюзан смотрела на него с сомнением.

Халохот продолжал двигаться. Расстояние между ним и Беккером быстро сокращалось. Он нащупал в кармане пиджака пистолет. До сих пор Дэвиду Беккеру необыкновенно везло, и не следует и дальше искушать судьбу. Пиджак защитного цвета от него отделяли теперь уже только десять человек.

Понятия не имею. КОМИНТ засек лишь исходящую почту. В данный момент мы ничего не знаем про Северную Дакоту, кроме анонимного адреса. - Возможно, это приманка, - предположила Сьюзан.