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A
Different
Type Of Magic Square
Thanks Martin G How to
astonish the
brightest mathematician
Procedure:Write your prediction without showing the participants. Place it in front of you. Ask all paricipants to: Pick any number in the square. Place a "Happy Face" on this number. Cross out all other numbers in the same row and in the same column. Now pick a second number and place a "Happy Face" on this number. Cross out all other numbers in the same row and in the same column. Now pick a third number and place a "Happy Face" on this number. Cross out all other numbers in the same row and in the same column. Now pick a fourth number and place a "Happy Face" on this number. Cross out all other numbers in the same row and in the same column. Place the last "Happy Face" on the one uncovered number. Ask participants to uncover the "Happy Faces" and then to add the numbers. Their total will be 57. Show your prediction. Click here to obtain PDF templates. Explain the trick: The "Magic Square" is an addition table, arranged in a tricky way. The table is generated by two sets of numbers: 12, 1, 4, 18, 0 and 7, 0, 4, 9, 2. The sum of all these numbers is 57. (12+1+4=+18+0+7+0+4+9+2 = 57) You can see at once how the numbers in the cells are determined by writing the first set of numbers horizontally above the top row of the square, and the second set vertically beside the first column. The number in the first cell (top row, first column) is the sum of 12 and 7, and so on through the square. It is now easy to see the underlying principle of the trick.  Each number in the square represents the sum of a pair of numbers in the two generating sets. That particular pair is eliminated when a "Happy Face" is placed on the number. The procedure forces each "Happy Face" to be in a different row and column. Notice that the five "Happy Faces" cover the sums of five different pairs of the ten generating numbers. This is the same as the sum of all ten numbers. Follow-up: Ask participants to construct a “magic square" of this type by using the template. The "Magic Square" can be as large as they like and with any combinations of numbers they choose. |
