19 votes
Accepted

Modify a magic square

How about: Check: An answer which is not of this form is:
elias's user avatar
  • 9,610
16 votes

Modify a magic square

My Shot: Reasoning. Second try. And maybe the simplest function
Marius's user avatar
  • 18.1k
15 votes

I'm trying to create a magic square

You need to:
JMP's user avatar
  • 35.6k
13 votes

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 ...
frodoskywalker's user avatar
12 votes
Accepted

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
Deusovi's user avatar
  • 146k
10 votes
Accepted

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,...
ppgdev's user avatar
  • 1,315
10 votes
Accepted

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 ...
hexomino's user avatar
  • 136k
10 votes

sums and differences in consecutive grid

Very nice puzzle! @WeatherVane beat me to the answer but thought I'd post with some logical deductions: Logic on how to solve:
Beastly Gerbil's user avatar
9 votes
Accepted

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 ...
Bass's user avatar
  • 77.4k
9 votes
Accepted

A riddle that has been killing me the whole day

The answer is: The formula is: Examples:
nishuba's user avatar
  • 477
8 votes
Accepted

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: ...
Gareth McCaughan's user avatar
8 votes
Accepted

Perfect magic 4x4 square

Solution: Notes:
loopy walt's user avatar
  • 21.4k
8 votes
Accepted

Four 3x3 semimagic squares in a 5x5 grid

user1502040's user avatar
7 votes
Accepted

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
Jonathan Allan's user avatar
7 votes

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:
Jonathan Allan's user avatar
7 votes

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&...
Ross Millikan's user avatar
7 votes
Accepted

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 ...
Anon's user avatar
  • 2,684
7 votes
Accepted

Magic-preserving Permutations on a 4x4 Magic Square

Jaap Scherphuis's user avatar
7 votes
Accepted

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 ...
DenverCoder1's user avatar
  • 10.5k
7 votes

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:
trolley813's user avatar
  • 11.3k
7 votes

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|...
Deusovi's user avatar
  • 146k
6 votes

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:
Sid's user avatar
  • 15.2k
6 votes

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'...
Adam S.'s user avatar
  • 406
6 votes
Accepted

Create a 3x3 Magic Square that uses integers from -10 to -2

Excited Raichu's user avatar
6 votes
Accepted

How to fill $4320$ multiplicative semi-magic square?

Here's one way to do it Strategy
hexomino's user avatar
  • 136k
6 votes
Accepted

Fill in a 4x4 multiplicative magic square

Again the short answer is with the example of The analysis and most of the heuristic from my 5x5 solution works here as well, but I introduced a little more heuristic which was unused in 5x5. First, ...
Bubbler's user avatar
  • 14.1k
6 votes
Accepted

Sum in Magic star puzzle

Assuming "sector beams" are the five kite-shaped things joined in the centre one solution would be
loopy walt's user avatar
  • 21.4k
6 votes
Accepted

Near Magic Squares with the First 25 Primes

I'll get things started with You can achieve
RobPratt's user avatar
  • 13.7k
6 votes

sums and differences in consecutive grid

My solution:
Weather Vane's user avatar
  • 14.4k
5 votes
Accepted

Find the missing numbers in the magic square

I think this was not very difficult.
Seyed's user avatar
  • 2,234

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