Marketing

The word marketing has lots of definitions, but to say in a simple word it means that marketing is the process of making profit by delivering the proper right product or the service to the consumer in right time. Marketing is all about giving right products to the consumers according to their needs. The proper  link building service marketing includes proper research, putting all product together, labeling it with a reasonable price, packing that has a effective appeal to the consumers, promoting it and finally distributing the product. The most important things required for the marketing is the research and proper plan. One should properly analyse depth of the industry and properly execute the plan.

Mummification Story

Mummification in ancient Egypt was a very long and expensive process. From start to finish, it took about seventy days to embalm a body. Since the Egyptians believed that mummification was essential for passage to the afterlife, people were mummified and buried as well as they could possibly afford. High-ranking officials, priests and other nobles who had served the pharaoh and his queen had fairly elaborate burials. The pharaohs, who were believed to become gods when they died, had the most magnificent burials of all. In the case of a royal or noble burial, the embalmers set up workshops near the tomb of the mummy.
The art of Egyptian mummification consisted of many steps. First, the body was washed and ritually purified. The next step was to remove the deceased person's inner organs. A slit was cut into the left side of the body so that the embalmers could remove the intestines, the liver, the stomach and the lungs. Each of these organs was embalmed using natron, which served to dry out the organs and discourage bacteria from decaying the tissues.
The organs were then individually wrapped using long strips of linen and placed in canopic jars. The lids of these jars were fashioned after the four sons of Horus, who were each entrusted with protecting a particular organ.

Here are some canopic jars with lids depicting the four sons of Horus: Qebehsenuef, the falcon head -- intestines Duamutef, the jackal head -- stomach Hapy, the baboon head -- lungs Imsety, the human head -- liver

After the removal of the inner organs, the body cavity was stuffed with natron. The brain was then removed through the nose using long hooks. Since the ancient Egyptians considered the brain unimportant, it was probably thrown away.
The body was then placed on a slanted embalming table and completely covered with natron. This allowed fluids to drip away as the body slowly dried out. This part of the process took about forty days, after which the natron was removed, inside and out, to reveal a dried, shrunken body. After another cleaning, the body was rubbed with unguents to aid in preserving the mummy's skin. The head and body cavity were stuffed with packing.
The mummy was then prepared for bandaging. First, the embalming cut in the side of the body was sewn up and covered with a patching depicting the protective eye of Horus. The body was adorned with gold, jewels and protective amulets. Fingers and toes were covered with protective gold caps and individually wrapped with long, narrow strips of linen. Arms and legs were also wrapped, then the entire body was wrapped to a depth of about twenty layers. The embalmers used resin to glue the layers of wrappings together. The wrapped head was covered with a mummy mask. Finally, the last layer of bandages went on and was given one last coating of resin. The mummy was the ready for burial.

Once the mummy was finally prepared, it was time for the funeral. The mummy and its canopic jars were transported by sled from the embalming tent to the tomb. People were hired to demonstrate their grief by crying and throwing dust on their hair. At the site of the tomb, religious ceremonies were held to prepare the dead for the afterlife. In particular, the Opening of the Mouth ceremony was believed to allow the mummy to see, hear, eat and drink in the spirit world.

How To Count Cards In Black Jack

CARD COUNTING 101

What is Card Counting?
Let’s start out with what counting is and, more importantly, isn’t. Card counting is a means of tracking the relationship between the high-value cards (good for the player) and the low-value cards, which are good for the dealer. When people ask me what I "do" (except at the tables) I tell them I’m a "Statistical Probability Analyst."
Why are the low-value cards good for the dealer? Well, the dealer has to follow rigid rules regarding hitting. She must hit if she has less than 17. The most important card in the deck for the dealer is the lowly-appearing five, as this will make at least 17 out of any stiff hand. Card counting allows us to know when there are more high cards than low left in the deck(s), and we raise our bet accordingly, because we now have an advantage over the house.
How large is this advantage? On certain individual hands this can be as high as three or four percent, but overall we hold about a one percent advantage, depending upon the game and rules. Counting does not give us an automatic winning edge on every hand - far from that. This isn’t the movies, and we aren’t Rainman. We will win, on average, about 44% of all hands played. When the count is high the dealer has just as good a chance to get good hands as we do. However, the dealer can’t split or double, and only gets even money on blackjack - this constitutes our basic edge. Many times in high counts our 20 will lose to the dealer’s blackjack (or push her 20) but over the long run we’ll win with that ~1% edge.
The long run is defined as beginning after about 400 or 500 hours of play. This will give us some 50,000 hands, a number large enough that it can have some statistical meaning. An analogy: if we flip a coin ten times it would not be too unusual for tails to come up, say seven times. However, if we flip that same coin 50,000 times it’s much more likely that tails will come up very close to its expectation of 50% - maybe the number would be .4997. So it is with blackjack - the more hands we play the closer to the statistical curve we get, the closer to our mathematical expectation.

Becoming a Counter

STEP ONE: Basic Strategy

First and foremost we must learn Basic Strategy. In this age of the computer there is very little argument on what constitutes valid Basic Strategy - virtually every book on the market explains this foundation. Basic Strategy (BS) must be so firmly ingrained that we never have to think about it. Every possible decision must be automatic, reflexive. How do we accomplish this? We read and study BS, then we run hands at the kitchen table with the book open for reference until we no longer need the reference material. Then we practice some more. This cannot be stressed enough - unless we have a solid foundation with perfect BS we will never succeed in counting. We practice until BS is firmly embedded in our subconscious. After totally mastering Basic we will then have to be aware of not seeming to be automatic in play. The typical player at the tables hems and haws over decisions - we should appear to do the same at times. The average person should accomplish learning Basic in about 20 dedicated hours.

STEP TWO: Learning to Count

Now we begin counting. There are many systems available and they fall into two general categories: balanced and unbalanced. Unbalanced counts, like the KO (Knock Out) system were designed to eliminate true count conversion (see Step Three). Generally speaking, the easier a system is to use the less effective it is; sometimes the difference amounts to splitting hairs, but there is a difference. We are going to use High-Low for this example as it is a simple balanced count, and is perhaps the most widely used system. High-Low falls somewhere in the middle of the pack for playing efficiency. We would suggest using this as your counting method at first - switching to a more complicated system should not be hard once High-Low is mastered, and stepping down, as it were, to a simpler count will be very easy.
In High-Low the 2-6 are valued at +1, and the 10s and Aces are counted as -1. Note that there are the same amount in each group: 2,3,4,5,6 and 10,J,Q,K,A. The 7,8,9 are neutral in this count and our eye should be trained to not even see these for counting purposes, for they have no bearing on the count. If the low cards are good for the dealer why are they counted as plus value? Because when we see that low card come out the ratio of high to low cards remaining has changed slightly in our favor.
We start with a deck of cards, flipping them over one at a time and keeping the running count. If they come out 8,K,3,3,6,2,7,A we would count 0,-1, 0, +1, +2, +3, +3, +2. At the end of the deck we should come out at "0". We won’t, at least in the beginning. Keep practicing until you do come out even at the end, every time, and gradually build speed. Eventually we will want to approach 25 seconds running the deck down one card at a time while maintaining accuracy. This speed will guarantee that no dealer alive can spread cards faster than we can count.
When proficient at this try pulling a card out of the deck, face down. Set it aside. After running the deck "guess" what the remaining card is. Your validation will come when you say, "It has to be a ten or an ace," and then flipping it over to find yourself correct.
Next we’ll flip the cards two at a time. We often see this in "pitch" games, that is, hand-held single and double deck games. On a bust the dealer flips up the player’s two hole cards. It’s a good idea to learn to disregard "matching pairs" like Q, 5, as they cancel each other out. The less we have to deal with the better, and by not allowing our eye to register these "matched pairs" we will streamline our counting.
In actual play there are many individual styles of counting the cards. In a face-up shoe game some people advocate waiting until the second card is dealt to each hand and counting the hands as whole units, as often a hand will cancel itself out, i.e., 10-6, or two consecutive hands will: K,10 - 3,5. Other folks insist it’s easier to count the cards as each one comes out. Try both methods and find what works best for you. In a pitch game it’s a bit different. Count your cards and the dealer’s up card first, then all exposed cards from hits, splits, doubles, and busts as they happen. Next count the dealer’s hole card and subsequent hits. As the dealer exposes the remaining hole cards one hand at a time a quick glance should suffice to carry the count forward. Practice for the game you intend to play but don’t neglect the other - your favored game might not be playable because of crowds, bad rules, etc.
Speaking of rules in general, don’t play under bad conditions. If the only game in your area is a six-deck with two+ decks cut off - save up and go to where the games are better. Normally this would automatically mean Las Vegas, but over Super Bowl weekend there I observed a double deck game where a deck-and-a-quarter was cut off - a horrible stunt by the management. At another place that normally had a good single deck game they were dealing three hands in heads-up play, when five and sometimes six is the norm. I overheard some dealer-talk about juicing the games for the Super Bowl crowd. The point is to shop for good penetration and to walk when it’s not there. Penetration is a key element in winning. For a good picture of this read Chapter Six of Blackjack Attack.
We should be able to master the above two drills in about 20 hours of dedicated practice; as always, your mileage may vary.

STEP THREE: Converting to True Count

This "running" count must be converted to a "true" count to be effective for betting and playing decisions. To do this we divide the running count by the amount of decks left unseen. For instance, in a double deck game after the first hand we have a running count of +4. Since there are virtually two full decks remaining we divide the count by 2, yielding a true of +2.
In multiple-deck games we’ll have to keep an eye on the discard tray to accurately estimate how many decks are remaining. So with two decks gone we’d have four left (in a 6D game); dividing the above +4 by four decks gives us a true of +1. One trick here: practice glancing at the discard tray just before the completion of the hand, and see what your divisor is going to be for the next hand. This will give you extra time to compute the true while the dealer is making payoffs and picking up cards.
In single deck with a quarter-deck dealt we have three-fourths left. To divide with fractions we invert and multiply, so we would multiply the running count by the inverse 4/3. That same +4 count would now be multiplied by the 4 (=16), then divided by the 3 (=5.33). One thing about single deck: the true is always more than the running count, both positive and negative, as we always have less than a full deck remaining. While we can get lazy for betting purposes and use the running count as the true count here in single deck, when it comes to Basic Strategy deviations (playing decisions) we need to have an accurate true count. This is fully covered in the recommended reading.
Now we start dealing hands. Deal one hand to yourself, one for the dealer. Go as slow as you need to keep the count accurately. Keep score with poker chips or the like. Although you will never see this in casino play, deal down to the last six or eight cards. After the last hand run the remaining cards out to check your count. When you can deal, play all hands correctly, count, convert to true count, pay off hands, and check the remaining deck for the count (and are correct on the count) in under two minutes with this single deck you are well on the way. Once speed has been gained consider switching from the kitchen table to a good software package, like Casino Verite by Norm Wattenberg. Programs like this will automatically track your play from session to session, providing valuable input on your progress. This will perhaps be the longest stretch in building our game, taking maybe 60 more hours of practice.

STEP FOUR: Overcoming Casino Distractions

Our next step is to start dealing two, then three hands, playing all of them as above and keeping an accurate count. Take your time and build to this point. Now we’ve arrived! Well, no... we haven’t. Casinos offer much in the way of distraction, so we must account for that, too. Cocktail waitresses will be interrupting every 2.875 minutes, dealers get chatty, players get obnoxious, slot bells are ringing, the craps table goes berserk, etc.
Begin with a radio playing nearby and continue dealing out multiple hands, playing and paying, until you are exactly on the count every time. Then add a television along with the radio. If you happen to have a couple of small children nearby this is even better. Each individual will differ in the ability to overcome these distractions, but 20 hours of practice should do it. When none of the above disrupts your counting ability and accuracy we’re ready for the next step: talking.
You will invariably need to talk and interact with other people at the table in the casino. You don’t want to appear to be an individual locked deeply in concentration with furrowed brow, staring at the cards. So, with the radio and TV going have a friend or (hopefully supportive) spouse deal to you. Carry on normal small talk. Look around. Be loose at the table. You’ll get this in real life, so practice it: "So, where you from?" and "Are you in town on business?" and so on. You will need to be able to think and respond while keeping the count without looking like you’re doing so.
People develop very individualistic methods for "holding" the count while carrying on an in-depth conversation - others are fortunate enough to be able to put the count in an area of the brain where they can retrieve it instantly. Some folks place x number of fingertips on their thigh under the table, some employ knuckle joints on top of the table, some use chips to indicate the count. However you accomplish it, you must remember the count! Perhaps another 20 hours will gain this goal with the friend dealing multiple hands to you in the above scenario. In building our game we cannot practice too much; the results will be readily apparent at the tables if we don’t.

STEP FIVE: The Act

Now we’re set! Well, close anyway. Now we need an act. Why? Well, we want to use everything we can to distract the house from seeing our bets going up and down with the count. We want to look like the "gamblers" at our table. Study them, emulate their language, their superstitions, their body language. Develop your act and make it real. Assume your persona when leaving your room, not at the table. You’re a nut-and-bolt salesman from Topeka in town on business and wanting to get a little action at the tables; you happen to be a tourist from LA there to blow off some stream, take in a few shows. The point is you don’t want to be caught flat-footed when someone asks you a question: "I, uh, well, duh...I’m here, ah, I’m here... on... business - Yeah! That’s it!" The importance of our cover act is directly proportional to the size of our wagering unit: the higher the unit the more cover needed.
Never reveal that you know anything about blackjack other than something like, "I used to do pretty good at the VFW Casino Night. Of course, my friend Bob was dealing..." (if something like this fits your act).
Dress to fit your act. Would a tourist be in a three-piece suit? An attorney at a convention might, but not a guy from Encino who dragged the wife and kids out for a few days of gambling and sight-seeing.
You’ll know you’re on course when you can do everything we’ve talked about so far while speaking to a pit boss about good restaurants.

STEP SIX: Bet Spreads

Watch your bet range, or spread. While everything mathematical tells us to jump our bet from, oh, $5 to $100 this is the surest way to get unwanted attention in the least and outright barring at the extreme. To survive we must unfortunately limit our spreads; the pits are not stupid - they basically know how counting works.
In pitch games this usually means spreading about 1-5 units; in shoe games we will get away with much larger spreads, say 1-8 or even two hands at 6 each. Generally counters step their bets up with the count: 1 unit at negative or 0, then incrementally up with the count. Read books like Stanford Wong’s Professional Blackjack and Don Schlesinger’s Blackjack Attack for more input in this area. In fact read everything you can find from these two authors as well as Snyder, Uston, and other accepted experts. Read, then read some more.
At this point it would be prudent to take it slow, and play at the lowest tables you can find. Fine-tune your game and act. There are still one-dollar tables in Nevada. Read the suggested authors - bankroll is very important. Even spreading 1 to 5 in silver a counter needs a bankroll in the hundreds. Never play under-financed - it’s self-defeating. Wild swings happen all the time in this game, and we don’t win consistently - the proficient counter wins in the long run.

SUMMARY

Following the above practice recommendations we have something in the neighborhood of 140 learning hours called for; your mileage may vary dramatically from this number. If that’s spread out - an hour an evening, several hours each on weekend days - we should be ready for the tables in a few months. Do yourself a favor - don’t rush the process and play before you’re ready. You could get lucky, but that blackjack devil might just decide to bite you in the butt, and believe me his teeth are sharp. A note: once learned, counting stays with you. At most you’ll need brush-up practice if it’s been a while.
Most people do not have the time, desire, or energy to do what it takes to become an expert card counter. Card counting is not rocket science, but it does takes work. A lot of work. If you follow through you will be part of a very small fraternity/sorority, more knowledgeable than perhaps 98% of the people sitting on either side of those tables. Is it worth all the effort? In a word, yes.

Bleach

Ichigo Kurosaki is a teenager gifted with the ability to see spirits. His life is drastically changed by the sudden appearance of a Soul Reaper—one who governs the flow of souls between the human world and the afterlife—named Rukia Kuchiki, who arrives in search of a Hollow, a dangerous lost soul. When Rukia is severely wounded defending Ichigo from the Hollow, she attempts to transfer half of her reiatsu (霊圧, literally, "spiritual pressure") energy to Ichigo so that he can defeat the Hollow. However, Ichigo takes almost all of her energy, transforming into a Soul Reaper and allowing him to defeat the Hollow with ease. With her powers diminished, Rukia is left stranded in the human world until she can recover her strength. In the meantime, Ichigo must take over Rukia's role as a Soul Reaper, battling Hollows and guiding souls to the afterlife realm known as the Soul Society (尸魂界 (ソウル·ソサエティ), Sōru Sosaeti).
As time passes and Rukia has yet to return to the Soul Society, her Soul Reaper superiors learn about her whereabouts and actions and sentence her to death for performing the illegal act of transferring her powers. Although he is unable to stop Rukia's departure to the Soul Society, Ichigo resolves to rescue her with the aid of several of his spiritually aware classmates, Orihime Inoue, Yasutora Sado, and Uryū Ishida, and the ex-Soul Reapers Yoruichi Shihōin and Kisuke Urahara. Once at the Soul Society, Ichigo and company battle against the elites of the Soul Reaper military and strive to reach Rukia before her execution. It is revealed that Rukia's execution and Ichigo's rescue attempt both had been manipulated by a high-ranking Soul Reaper, Sōsuke Aizen, who was previously believed to have been murdered, as part of a far-reaching plot to take control of the Soul Society. Aizen betrays his fellow Soul Reapers and allies himself with the strongest of the Hollows, the Espadas, whom he enhances. Aizen thus becomes the main antagonist of the series, and the Soul Reapers form an alliance with Ichigo.
At this point, Bleach chronicles the war between the Soul Reapers, the Espadas, and Aizen. After each of the involved's eventual defeats, Ichigo undergoes intense training with his father Isshin who turns out to be a former Soul Reaper to become strong enough to battle Aizen alone. As Aizen is weakened by his battle with Ichigo, a spell that Urahara had previously hidden within him activates and seals him, thus ending the conflict and leaving the Soul Society to imprison him. As a result of using all of his Soul Reaper powers to defeat Aizen, Ichigo loses them and becomes an ordinary human once again.
Seventeen months later, Ichigo meets "Xcution", a group of humans possessing Fullbring powers based on Hollows and want Ichigo to absorb them. Ichigo starts training to regain his Soul Reaper powers by first developing his own Fullbring following the appearance of Shūkurō Tsukishima, the former leader of Xcution who is targeting his friends. After developing his Fullbring, Ichigo is betrayed by Xcution's current leader Kūgo Ginjō, a former Substitute Soul Reaper who had his memories rewritten to act as Tsukishima's enemy and help Ichigo gain powers to steal them. With help from Soul Society, Ichigo regains his Soul Reapers powers and starts fighting Ginjō's group alongside Soul Society's forces. The Soul Society forces end victorious with Ichigo killing Ginjō and Byakuya presumably killing Tsukishima.
Following these events, A group of Quincies called the "Vandenreich" declare war on the Soul Society. Ichigo once again ventures to Hueco Mundo, which has also been invaded by The "Vandenreich", while at the same time, The captains in the Soul Society battle a powerful group in the "Vandenreich" army known as the "Stern Ritter".

Egyptian Book Of Dead

The Book of the Dead is the common name for the ancient Egyptian funerary texts known as The Book of Coming [or Going] Forth By Day. The name "Book of the Dead" was the invention of the German Egyptologist Karl Richard Lepsius, who published a selection of some texts in 1842.

Religion guided every aspect of Egyptian life. Egyptian religion was based on polytheism, or the worship of many deities. The Egyptians had as many as 2000 gods and goddesses each representing characteristics of a specific earthly force, combined with a heavenly power. Often gods and goddesses were represented as part human and part animal.

They considered animals such as the bull, the cat, and the crocodile to be holy. Their two chief gods were Amon-Ra and Osiris. Amon-Ra was believed to be the sun god and the lord of the universe. Osiris was the god of the underworld and was the god that made a peaceful afterlife possible. The Egyptian "Book of the Dead" contains the major ideas and beliefs in the ancient Egyptian religion. Because their religion stressed an afterlife, Egyptians devoted much time and energy into preparing for their journey to the "next world." The text was initially carved on the exterior of the deceased person's sarcophagus, but was later written on papyrus now known as scrolls and buried inside the sarcophagus with the deceased, presumably so that it would be both portable and close at hand. Other texts often accompanied the primary texts including the hypocephalus (meaning 'under the head') which was a primer version of the full text. Books of the Dead constituted as a collection of spells, charms, passwords, numbers and magical formulas for the use of the deceased in the afterlife. This described many of the basic tenets of Egyptian mythology. They were intended to guide the dead through the various trials that they would encounter before reaching the underworld. Knowledge of the appropriate spells was considered essential to achieving happiness after death. Spells or enchantments vary in distinctive ways between the texts of differing "mummies" or sarcophagi, depending on the prominence and other class factors of the deceased. Books of the Dead were usually illustrated with pictures showing the tests to which the deceased would be subjected. The most important was the weighing of the heart of the dead person against Ma'at, or Truth (carried out by Anubis). The heart of the dead was weighed against a feather, and if the heart was not weighed down with sin (if it was lighter than the feather) he was allowed to go on. The god Thoth would record the results and the monster Ammit would wait nearby to eat the heart should it prove unworthy. The earliest known versions date from the 16th century BC during the 18th Dynasty (ca. 1580 BC–1350 BC). It partly incorporated two previous collections of Egyptian religious literature, known as the Coffin Texts (ca. 2000 BC) and the Pyramid Texts (ca. 2600 BC-2300 BC), both of which were eventually superseded by the Book of the Dead. The text was often individualized for the deceased person - so no two copies contain the same text - however, "book" versions are generally categorized into four main divisions – the Heliopolitan version, which was edited by the priests of the college of Annu (used from the 5th to the 11th dynasty and on walls of tombs until about 200); the Theban version, which contained hieroglyphics only (20th to the 28th dynasty); a hieroglyphic and hieratic character version, closely related to the Theban version, which had no fixed order of chapters (used mainly in the 20th dynasty); and the Saite version which has strict order (used after the 26th dynasty). It is notable, that the Book of the Dead for Scribe Ani, the Papyrus of Ani, was originally 78 Ft, and was separated into 37 sheets at appropriate chapter and topical divisions.

Tower Of Hanoi Solution

Tower Of Hanoi

According to the legend of the Tower of Hanoi (originally the "Tower of Brahma" in a temple in the Indian city of Benares), the temple priests are to transfer a tower consisting of 64 fragile disks of gold from one part of the temple to another, one disk at a time. The disks are arranged in order, no two of them the same size, with the largest on the bottom and the smallest on top. Because of their fragility, a larger disk may never be placed on a smaller one, and there is only one intermediate location where disks can be temporarily placed. It is said that before the priests complete their task the temple will crumble into dust and the world will vanish in a clap of thunder.
Does this make mathematical sense?

In the classic math problem, there are three posts. Disks of different sizes (call the number of disks "n") are placed on the lefthand post, arranged by size with the smallest on top. You are to transfer all the disks to the righthand post in the fewest possible moves, without ever placing a larger disk on a smaller one. One move is considered to be moving one disk from one post to another post.

How many moves will it take to transfer n disks from the left post to the right post?

Let's look for a pattern in the number of steps it takes to move just one, two, or three disks. We'll number the disks starting with disk 1 on the bottom.
1 disk: 1 move

Move 1: move disk 1 to post C
    

2 disks: 3 moves
Move 1: move disk 2 to post B
Move 2: move disk 1 to post C
Move 3: move disk 2 to post C
    

3 disks: 7 moves
Move 1: move disk 3 to post C
Move 2: move disk 2 to post B
Move 3: move disk 3 to post B
Move 4: move disk 1 to post C
Move 5: move disk 3 to post A
Move 6: move disk 2 to post C
Move 7: move disk 3 to post C
    

Can you work through the moves for transferring 4 disks? It should take you 15 moves. How about 5 disks? 6 disks? Do you see a pattern?

A. Recursive pattern

From the moves necessary to transfer one, two, and three disks, we can find a recursive pattern - a pattern that uses information from one step to find the next step - for moving n disks from post A to post C:
First, transfer n-1 disks from post A to post B. The number of moves will be the same as those needed to transfer n-1 disks from post A to post C. Call this number M moves. [As you can see above, with three disks it takes 3 moves to transfer two disks (n-1) from post A to post C.]
Next, transfer disk 1 to post C [1 move].
Finally, transfer the remaining n-1 disks from post B to post C. [Again, the number of moves will be the same as those needed to transfer n-1 disks from post A to post C, or M moves.]
Therefore the number of moves needed to transfer n disks from post A to post C is 2M+1, where M is the number of moves needed to transfer n-1 disks from post A to post C.
Unfortunately, if we want to know how many moves it will take to transfer 100 disks from post A to post B, we will first have to find the moves it takes to transfer 99 disks, 98 disks, and so on. Therefore the recursive pattern will not be much help in finding the time it would take to transfer all the disks.

However, the recursive pattern can help us generate more numbers to find an explicit (non-recursive) pattern. Here's how to find the number of moves needed to transfer larger numbers of disks from post A to post C, remembering that M = the number of moves needed to transfer n-1 disks from post A to post C:

for 1 disk it takes 1 move to transfer 1 disk from post A to post C;
for 2 disks, it will take 3 moves:    2M + 1 = 2(1)  + 1 =  3
for 3 disks, it will take 7 moves:    2M + 1 = 2(3)  + 1 =  7
for 4 disks, it will take 15 moves:   2M + 1 = 2(7)  + 1 = 15
for 5 disks, it will take 31 moves:   2M + 1 = 2(15) + 1 = 31
for 6 disks... ?

B. Explicit Pattern

Number of Disks         Number of Moves
        1                          1
        2                          3
        3                          7
        4                         15
        5                         31
    Powers of two help reveal the pattern:
Number of Disks (n)     Number of Moves
        1                 2^1 - 1 = 2 - 1 = 1
        2                 2^2 - 1 = 4 - 1 = 3
        3                 2^3 - 1 = 8 - 1 = 7
        4                 2^4 - 1 = 16 - 1 = 15
        5                 2^5 - 1 = 32 - 1 = 31
So the formula for finding the number of steps it takes to transfer n disks from post A to post B is: 2^n - 1.
From this formula you can see that even if it only takes the monks one second to make each move, it will be 2^64 - 1 seconds before the world will end. This is 590,000,000,000 years (that's 590 billion years) - far, far longer than some scientists estimate the solar system will last. That's a really long time!

Schrodinger's Cat

Schrodinger's Cat

Schrödinger's cat is a famous illustration of the principle in quantum theory of superposition, proposed by Erwin Schrödinger in 1935. Schrödinger's cat serves to demonstrate the apparent conflict between what quantum theory tells us is true about the nature and behavior of matter on the microscopic level and what we observe to be true about the nature and behavior of matter on the macroscopic level -- everything visible to the unaided human eye.

Here's Schrödinger's (theoretical) experiment: We place a living cat into a steel chamber, along with a device containing a vial of hydrocyanic acid. There is, in the chamber, a very small amount of hydrocyanic acid, a radioactive substance. If even a single atom of the substance decays during the test period, a relay mechanism will trip a hammer, which will, in turn, break the vial and kill the cat.

The observer cannot know whether or not an atom of the substance has decayed, and consequently, cannot know whether the vial has been broken, the hydrocyanic acid released, and the cat killed. Since we cannot know, according to quantum law, the cat is both dead and alive, in what is called a superposition of states. It is only when we break open the box and learn the condition of the cat that the superposition is lost, and the cat becomes one or the other (dead or alive). This situation is sometimes called quantum indeterminacy or the observer's paradox: the observation or measurement itself affects an outcome, so that the outcome as such does not exist unless the measurement is made. (That is, there is no single outcome unless it is observed.)

We know that superposition actually occurs at the subatomic level, because there are observable effects of interference, in which a single particle is demonstrated to be in multiple locations simultaneously. What that fact implies about the nature of reality on the observable level (cats, for example, as opposed to electrons) is one of the stickiest areas of quantum physics. Schrödinger himself is rumored to have said, later in life, that he wished he had never met that cat.