Cyclic number

If you multiply the number 142857 by any integer from two to six, you get a number that will be made up of the same digits, only with their circular permutation. Therefore the number 142857 is called cyclic. On this property of this number, this focus is based.
Choose from the deck 5 red cards with numerical values ​​2, 3, 4, 5, 6 and give them to any of the spectators. Take yourself 6 cards of a black suit and arrange them so that their numerical values ​​are figures of 142857. After that you and the spectator shuffle each of your cards, in fact you should only pretend that you're shuffling cards, you need to keep the order of your cards. The kind of shuffling of cards can create a simple double shifting of cards from one side to the other side. After shuffling the cards, you lay out cards on the table in a row, face up, so that the number 142857 is formed. The viewer takes one of his cards and puts it face up under your cards. Then the viewer should multiply our number by the numerical value of the card that he chose. While the viewer multiplies, you collect your cards and put the first card on the left to the next one, and then to the next one and so on. Cards are taken 1 time, and then you have to put them stacked on the table in a closed form. As soon as the viewer finishes the multiplication, you take your stack of cards and again spread them from left to right with the face up. The six-digit number that will be obtained will coincide with the multiplication result that the viewer received. The secret meaning of this trick is that you collect the cards of a black suit, without violating their order in which they were laid out. Suppose the viewer multiplies our number by 6. In this case, the product must end with a deuce, because 6 times multiplied by 7 will be 42. If the deck is removed in such a way that the deuce is at the bottom, then after opening the cards it will be the last card and the viewer's response will coincide with The number represented by cards.