“Magic squares” have fascinated people throughout history. The fact that numbers can be arranged in such a way as to add up to the same total in myriad ways is impressive. Since people believe that magic squares must take plenty of calculating and re-calculating, this feat is made more impressive when you quickly generate a custom magic square for them!
Prerequisites:
Link SystemMajor System
(Click here for more tips on this feat from The Magic Cafe)
Getting the Number
You need to get a number from 21 to 100. This method will work with numbers beyond 100, but the resulting magic square may give a clue as to the method. If you are working for a gentleman who is obviously over 21, you could ask him his age (never try this with a lady!). If this doesn't work, simply ask for a number this way: “I need a number that's not too large and not too small. Keep it between, say, 20 and 100.” Should some wise guy say 20, you can gently remind him that you said “BETWEEN 20 and 100.” Giving the range this way seems fair, while still offering a large range of possibilities to choose fromCreating the Magic Square
There's two parts to the method. You memorize 12 digits in a pattern, and apply a simple formula to fill in the other four digits. The digits should be memorized in the following arrangement:8 11 BL 1
BL 2 7 12
3 BL 9 6
10 5 4 BL
The “BL” in the above diagram denotes a space that will be left open until the formula is applied. The “Peg” and “Link” methods will be used to keep this arrangement is easily memorized. The following system will help you to remember:
The first row is 8, 11, then a blank, then a 1. This is remembered as “faded tie”. Note that the space between the words denotes the location of the blank space. Next, “faded tie” is linked to “nicotine” (2712). To help you remember that the space is in the first position of the row, remember “a spot of nicotine”. The “spot” helps you remember the empty space. Now link “spot of nicotine” to “my beach” (3 96). Once again, note that the space between words denotes the location of the blank space. Finally, link “my beach” to “dazzler” (1054).
When writing in the initial memorized numbers, don't just go across each row filling them in. Place 1 or 2 digits of each row, and then go on to the next row. Next, go back and place the remaining memorized digits into the square. This way, it looks as if you are randomly placing numbers in the grid, and makes it look more impressive.
Once the memorized numbers are written in, the remaining blank spaces a filled via a simple formula. Take the number your are given, and subtract 21 from it. To make this easier, simply subtract 10, subtract 10 again, and then subtract 1. This number then goes in the blank space in the second row. The other blanks are filled clockwise with each space being filled with a number one greater than the last.
For example, you are given the number 45. You write the memorized numbers down (as above), leaving blanks in the appropriate spots. You then mentally think: 45-21=45-10-10-1=35-10-1=25-1=24. The 24 is then placed in the second row in place of the blank (previously placed numbers in grey):
8 11 BL 1
24 2 7 12
3 BL 9 6
10 5 4 BL
The remaining blanks are then filled in clockwise (first row, then fourth row, then third row), each with a number 1 higher than the one you previously placed. In the “45” example, the number 25, 26 and 27 are put in as follows (previously placed numbers in grey):
8 11 25 1
24 2 7 12
3 27 9 6
10 5 4 26
The total can be found by adding up four numbers in 28 different ways:
Columns (4 ways):
8 11 25 1
24 2 7 12
3 27 9 6
10 5 4 26
Rows (4 ways):
8 11 25 1
24 2 7 12
3 27 9 6
10 5 4 26
Diagonals (2 ways):
8 11 25 1
24 2 7 12
3 27 9 6
10 5 4 26
Four corners (1 way):
8 11 25 1
24 2 7 12
3 27 9 6
10 5 4 26
Four center squares (1 way):
8 11 25 1
24 2 7 12
3 27 9 6
10 5 4 26
Pan diagonals (2 ways):
8 11 25 1
24 2 7 12
3 27 9 6
10 5 4 26
Four corners of any 3x3 square (4 ways):
8 11 25 1 8 11 25 1
24 2 7 12 24 2 7 12
3 27 9 6 3 27 9 6
10 5 4 26 10 5 4 26
Four corners of any 2x2 square that includes a pair of numbers in the top or bottom row (6 ways):
8 11 25 1 8 11 25 1 8 11 25 1
24 2 7 12 24 2 7 12 24 2 7 12
3 27 9 6 3 27 9 6 3 27 9 6
10 5 4 26 10 5 4 26 10 5 4 26
Four “wrap-around squares” (4 ways):
8 11 25 1 8 11 25 1
24 2 7 12 24 2 7 12
3 27 9 6 3 27 9 6
10 5 4 26 10 5 4 26
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