How many cards are transferred? Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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How many cards are transferred? Focus Secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

The magician removes a pack of 13 cards several times and passes them to the viewer. Then he turns his back to the audience and asks to shift one at a time any number of cards - from one to thirty inclusive - from the bottom of the pack up.

The artist turns to face the audience, takes the pack, fanning it face down, and without hesitation pulls out the card. The card is opened, and everyone sees that its numerical value is equal to the number of transferred cards. This trick can be repeated as many times as you like.

Focus secret:

To demonstrate this trick, 13 cards are specially chosen so that for each integer from 1 to 13 there is one card with the corresponding numerical value. They are arranged in descending order of numerical value, starting with the king and ending with the ace. The demonstrator removes the pack several times and passes it to the spectator, imperceptibly looking at the bottom card. Let's say it was four. After the cards have been transferred, the showman counts four cards from the top and reveals the last one. Its numerical value will indicate the number of transferred cards.

After a series of withdrawals, the arrangement of cards in a 13-card deck with the initial arrangement (top) 13, 12, 11, ... 3, 2, 1 (bottom) will be replaced by the following: (top) k-1, k-2, ... , 2, 1, 13, 12, ..., k (bottom), where 1?k?13. There are k-13 cards above card 1, and card 13 itself is the kth card from the top.

Then, as a result of the transfer of one card from the bottom of the deck to the top, card 1 will lie on top in the k-th place, as a result of the transfer of two cards, card 2, etc.; Thus, if, as a result of the removal, the card is transferred from the bottom to the top, let's say, m cards, then the card m will lie in the kth place from the top, which is required.

Author: M.Gardner

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Gastronomic preferences of cats 02.11.2015

Where did we and animals get the ability to distinguish between different tastes? It would be reasonable to assume that different taste buds help to find more suitable food, differentiated taste sensitivity allows you to more accurately determine the quality of food, to distinguish more nutritious from less nutritious and more harmful from less harmful. For example, thanks to the feeling of sweet, you can understand where there are more carbohydrates, which, as you know, contain a lot of available energy. On the other hand, a bitter taste can indicate toxins, which are especially common in plants.

In accordance with this hypothesis, one would expect that the presence or absence of certain taste receptors depends on the diet of one or another animal species. If we take cats that do not feel sweet, then everything is true here: the gene responsible for the "sweet" receptor broke down during evolution, and there was no need to fix it, because felines eat almost exclusively meat, and sensitivity to carbohydrates for them, shall we say, irrelevant. (In the same way, many other carnivorous animals, such as sea lions and spotted hyenas, do not feel the sweet taste.) It would seem that the same could be expected from the "bitter" receptors, because dangerous substances with such a taste, as we said usually of vegetable origin. But no - as researchers from the Monell Center write in their article in PLoS ONE, ordinary domestic cats have as many as 12 genes encoding receptor proteins for bitter taste.

But maybe not all of them work? Weiwei Lei and colleagues tested these genes for functionality in cell culture - it turned out that cells that were supplied with cat receptor proteins reacted to the corresponding substances (a total of 25 bitter molecules were used, in different combinations). So it was possible to find out that 7 out of 12 genes work quite well, that is, they encode a protein that can bind at least one bitter substance. As for the other five, they just haven't been tested yet; it is possible that all the "bitter" genes work in cats in general.

The same was repeated with several more species: with a dog, a polar bear, a giant panda and a ferret. Bottom line: a dog has 15 "bitter" receptor genes, a ferret has 14, a panda has 16, and a polar bear has 13. Their diet is different and one would expect that panda, which eats bamboo, and dogs, which can be called omnivores, there will be more receptors for bitter substances. But the expectations were not met. That is, taste genes, on which sensitivity to bitter taste depends, were affected by some other selection factors, and not just the need to feel unpleasant vegetable bitterness.

Cats are known to be very picky eaters. Is it possible to blame this feature of theirs on the abundance of bitter receptors? Maybe you can, but let's not forget that a person has more than 30 of them. However, here we can recall another recent work published in BMC Neuroscience. The authors compared two feline "bitter" receptors with human ones and found that one of the feline receptors was ten times less sensitive to the bitter phenylthiourea molecule and not at all to 6-n-propylthiouracil. (Though there are many people who don't taste the bitter taste of phenylthiourea.)

Another receptor in cats, like in humans, reacted to aloin (which is found in aloe plants) and denatonium (it is added to various household chemicals so that children and pets do not eat them), but feline protein reacted weaker to aloin, and on denatonium - stronger. At the same time, feline receptors did not respond to saccharin, which has a bitter aftertaste for humans.

In other words, cats' taste sensations are qualitatively different from ours, and even leaving aside the question of the intensity of sensations, they can taste bitterness where none of us will feel it - because the cat's receptors simply “catch” other molecules. Only the whims of feline evolution can be blamed here, however, for those who have to deal with their gastronomic whims every day, this is not easier.

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