Guessing the sum of numbers on the chips. Effective trick and its solution

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Guessing the sum of numbers on the chips. Focus secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

To demonstrate, you need to have 6 chips with numbers on both sides. The figure shows one side of the chips, on the bottom - the corresponding reverse side. Please note that the numbers in the top row are written in bold lines; in the bottom row; the numbers are more subtle.

Focus Guessing the sum of the numbers on the chips

The magician asks the viewer to shuffle the chips between the palms, and then arrange them on the table in two rows of three chips each. While the demonstrator is standing with his back turned, the spectator turns over three chips, without telling which ones. Then the person showing asks to turn over a few more chips.

After this, the spectator takes any chip he wishes, turns it over and covers it with something (for example, a playing card or a coin - as long as the number is not visible). He repeats the same thing with two more chips. Now there are three chips on the table open and three closed.

At this moment, the person showing turns to the audience and calls the sum of the three covered numbers.

Focus secret:

Before turning away from the table, the magician takes a quick look at the chips and remembers the location of those with bold numbers facing up. After the spectator turns over three random tiles, the shower asks him to turn over a few more tiles. He says: “Please turn over the second chip in the first row and the third chip in the bottom row.” These chips must be the ones whose position he remembered (i.e., which were initially located in the places occupied by the chips facing the bold numbers upward).

The spectator now turns over the three chips, covering each of them with a card. The demonstrator turns to the audience and makes the following calculations in his head: he notices the number of chips facing up in bold numbers (it will be zero, one, two or three), and multiplies this number by 10. He adds 15 to the resulting product. From this sum he subtracts the sum of three open numbers. The remainder will be equal to the sum of the top numbers on the three chips covered with cards.

Focus Guessing the sum of the numbers on the chips

The sum of the thin numbers is 15, and the difference between the bold and thin numbers on each chip is 5. Therefore, if at the beginning of the experiment there were k chips with bold numbers, then the total sum of all the numbers revealed to the audience was 15 + 5k. Let's assume that the spectator has turned over i chips with bold numbers and j chips with thin ones. The demonstrator asks to turn back these i chips and k - i more chips remaining with bold numbers, as a result, the total amount will be 15 + 5k + 5j - 5(k - i) = 15 + 5(i + j) = 30, and the number chips with bold numbers turns out to be equal to i + j = 3. Further, let the viewer turn over and close p chips with bold numbers and q with thin numbers. As a result, the total sum of digits on six chips will be 30 - 5p + 5q = 30 - 5p + 5(3 - p) = 45-10p = 10(3 - p)+15, which gives the calculation scheme.

You can simplify the counting if you do not force the spectator to turn over the covered counters; then the sum of the digits of the covered chips is obtained by subtracting the sum of the digits of the open chips from 30.

Author: M.Gardner

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