Uncovering the Mystery of Magic Squares

In summary, a magician at an exposition quickly worked out a magic square with a sum of 47, using an audience member's number between 41 and 100. The square was constructed with the sum of 47 in all horizontal lines, vertical lines, and 2x2 squares. There are links to instructions for constructing similar squares, but it is unclear how to adapt them for other sums. One theory is that the magician had a handful of these squares and could quickly recall and add the numbers. Another theory is that it is much easier to do with a sum of 48. The conversation ends with a request for more information on finding squares for other sums.
  • #1
Magic Square


Don't know, which forum, so i put it to general...

Yesterday i saw something like an magician on an exposition, showing some math to angle for attention.

He asked the audience to give him a number between 41 and 100. So he got the 47.

He worked out a magic square _very_ quickly.

It was that one:
4 18 14 11
15 10 5 17
9 12 20 6
19 7 8 13

You see, that the horizontal lines, the vertical lines, and all possible 2x2 - squares have the sum of 47...

How did the magician do that?

I've found some links here:

But i don't know how to adapt the instructions for constructing an squad with doubly even order to other sums of the lines, etc ..

Can someone please help me?
It would be great :-)

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  • #2
Could he just have a handful of these such squares (I have no idea how he found them originally) and then just be adding on squares of all ones? Then all you would need is one for 41,42,43,44 and you'ld have the squares for 41 and up. You already have the square for 43 now right?
3 17 13 10
14 9 4 16
8 11 19 5
18 6 7 12
If you rehearse enough I imagine you can recall and add the numbers as fast as you can write them. Just a guess... no idea how you find the other 3 squares
  • #3
snoble said:
Then all you would need is one for 41,42,43,44 and you'ld have the squares for 41 and up. You already have the square for 43 now right?

Yes that's an interesting idea...

45 = 41 + 4*1
46 = 42 + 4*1
47 = 43 + 4*1
48 = 44 + 4*1
49 = 41 + 4*2
100 = 44 + 4*14

He said that it would be much easier to do with 48.
Does that fit?

thanks for your answer!

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  • #4
any suggestions how he found these squares for 41, 42, ... ?

Or does someone of you know the other squares?


What is a magic square?

A magic square is a grid of numbers where the sum of each row, column, and diagonal is the same. This sum is called the "magic constant" and is determined by the size of the grid. Magic squares have been studied and used for centuries, with the earliest known example dating back to 650 BC.

How do you create a magic square?

There are various methods for creating a magic square, but the most common way is to start with the number 1 in the middle of the top row, then fill in the numbers in a specific pattern based on the size of the grid. For example, in a 3x3 magic square, the numbers are filled in a specific pattern: 1, 8, 3, 6, 4, 9, 2, 7, 5. Other methods involve using mathematical algorithms or constructing the square using specific rules and patterns.

What is the significance of magic squares?

Magic squares have intrigued and fascinated mathematicians, scientists, and philosophers for centuries. They have been associated with mystical and supernatural powers, and have also been used for divination and fortune-telling. In modern times, magic squares have been used in puzzles, games, and even in encryption algorithms for computer security.

Are there different types of magic squares?

Yes, there are many different types of magic squares, including odd, even, pandiagonal, and bordered magic squares. Odd magic squares have an odd number of rows and columns, while even magic squares have an even number of rows and columns. Pandiagonal magic squares have the additional property that the broken diagonals also add up to the magic constant. Bordered magic squares contain a border of numbers around the main magic square, creating additional patterns and symmetries.

What are some applications of magic squares?

Besides their use in puzzles and games, magic squares have been used in various fields such as mathematics, computer science, and art. They have also been used in ancient Chinese medicine as a diagnostic tool. In recent years, magic squares have been studied for their potential use in coding and cryptography, as well as in the design of computer algorithms and artificial intelligence.

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