Calendar prediction. Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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Calendar prediction. Focus Secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

On some sheet of a monthly report card, the viewer puts sixteen numbers in a square. The magician, after a cursory glance at the outlined figure, writes down the prediction. The spectator then selects four numbers in this square, apparently arbitrary, but subject to the following rule. The first number chosen (circled) is completely arbitrary. Then all the numbers that are in the same line and in the same column as the number just circled are crossed out.

For the second number, the spectator may circle any number that is not crossed out. After that, he crosses out all the numbers that ended up in the same line and in the same column with the second circled number. The third number is also selected, and the corresponding row and column are crossed out.

As a result of these operations, a single number will remain uncrossed out. His viewer also circles. If we now take the sum of the four numbers we have noted, then it will turn out to be exactly equal to the predicted number.

The sum of the numbers chosen one at a time from each row and each column of the square is equal to the sum of the numbers on the diagonal. This latter is the sum of four members of an arithmetic progression (with a difference of 8) and is equal, by virtue of a well-known formula, to twice the sum of the first and last members)

Focus secret:

The demonstrator notices two numbers located on two diagonally opposite corners of the square. It doesn't matter which of the two possible pairs it will be. To get the answer, you need to add these two numbers and double the amount found.

A simpler trick, based on the same principle and not requiring a time sheet, can be demonstrated like this. Draw a square grid of 16 cells like a chessboard and renumber the cells from 1 to 16 in natural order. If now the spectator is asked to choose four numbers by means of the process described above and add them up, then in all cases he will receive the same amount, namely 34.

This principle can be demonstrated on squares with any number of cells.

Author: M.Gardner

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