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16
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15
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13
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The magic square with a hole
Here are a few from this site. Any magic square with integers 0-15 will work, considering the 0 as a hole. I've chosen four with the 0 in the inner four cells just to be sure it meets your criteria. ...
- 9,733
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Are there any sets of 9 numbers that can form two essentially distinct magic squares?
Note that any two magic squares with the same numbers must have the same row/column sum. The middle number must be 1/3 of the sum (because the sum of the four lines passing through the center is the ...
- 33.6k
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Number of magic squares with magic constant 0?
Take the example square below:
-3 2 1
4 0 -4
-1 -2 3
To generate a new square, simply multiply each element of this square by any positive integer. As there ...
- 7,319
12
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Can you fill $3 \times 3$ magic square?
There are two ways to do this: the algebraic way and the 'clever' way.
The algebraic way
The clever way
- 145k
10
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Not-Quite-Sufficiently-Advanced-Technology Square
I was able to find one of the solutions using "paper and pencil". I stopped searching for more solutions after that. It is certainly very very time consuming.
In my explanation I name rows as A,B,C,...
- 1,305
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Create a magic square of 4-digit numbers
Building on the strategy of Omega Krypton, this is one possibility which also gets the diagonals to sum to the magic total
First of all, construct four single digit magic squares...
Then concatenate ...
- 133k
9
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Magic square 4x4 that sum to 38
Here's how I would go about it:
Firstly, we want to split the numbers in two groups, each having 8 numbers with a total of 76. We are going to use one of the groups for the diagonals, and the other ...
- 75.8k
9
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8
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No ordinary magic square part 2. How many solutions are there?
According to the simple-minded 7-line Python program I just wrote, there are exactly
There is at least a 25% chance that I didn't make any stupid blunders.
Here's the code:
...
- 117k
8
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8
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7
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No ordinary magic square part 2. How many solutions are there?
My Python code to iterate the solutions and their respective $8$ sums:
Counting them:
Some more information:
- 21.1k
7
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Unsolved Mysteries: Magic Square of Squares
Copied entirely from http://mathpages.com/home/kmath417.htm
This is not a solution; it is just a MathJAXed version of the link provided.
Magic Square of Squares
It's an open question whether there ...
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Magic square using consecutive odd numbers -5 through 11
Take the standard $3 \times 3$ square, double each entry and subtract $7$. That is the linear transformation that takes $1$ to $-5$ and $9$ to $11$
$$\begin {array}{c c c} 9&-5&5\\-1&3&...
- 7,366
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Put numbers to a star-shaped puzzle
This does it:
There may be other solutions beyond symmetry ...now to write some code
new code for all valid solutions up to symmetry
previous slow, non-symmetry "naive" search
- 21.1k
7
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How big can a witchcraft square be?
As @2012rcampion said, this is only possible when $n$ is even: The sum of all row and column sums of a witchcraft square is the sum of $2n$ consecutive natural numbers, and if $n$ is odd, this sum ...
- 2,684
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7
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It cannot be done. I think
Using only basic operators (+ - * / ^)
There are 16 solutions that, like yours, are missing the center column:
There are 64 boards total that are missing any one row, column, or diagonal.
Here is the ...
- 10.4k
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Place the numbers 1-7 in the squares so that each row and columns adds up to the same total
The same 56 solutions but with logical reasoning instead of bruteforcing:
- 11.3k
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How to solve 3x3 Magic Squares with negative values when only 2 values are given?
Turns out you don't have enough information -- but you could put anything you wanted in any other cell!
As shown by Joe Z in this answer, all 3×3 magic squares can be expressed as:
$$\begin{array}{|c|...
- 145k
6
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An Antimagic Square
For any such magic square the sum of all rows, columns and diagonals:
$$\sum_{x=0}^7{x}=28$$
Now each number is counted at least twice, once for the row and once for the column.
Furthermore each ...
- 5,886
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An Antimagic Square
The unique solutions (ignoring rotations and flips) are:
Found through the method of full exhaustion.
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What type of magic square is this?
The given square $X$ results from the following classical magic square (which arranges the number $1,2,\ldots,25$ in a $5\times5$ square so that every row, every column, and each of the two main ...
- 45.4k
6
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Magic square with equal sums on rows, columns and diagonals
The answer is:
Right So, here's an image
Here's a description of the working:
- 15.1k
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Magic square 4x4 that sum to 38
One thing to consider is that there are only 4 odd numbers in the puzzle: 7, 7, 11, 13.
Which means every row/column/diagonal that has one of those four numbers must have exactly two of them (you can'...
- 406
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