# Questions tagged [magic-square]

A puzzle related to magic squares: grids of integers where all rows, columns, and diagonals have the same sum.

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### Number of magic squares with magic constant 0?

How can we determine the number of magic squares with magic constant 0?
360 views

### Magic Penteract!

(Don't worry, this is the last magic square themes question I'll be posting (as far as I know), so I picked a challenging one!) First off, let's define what a magic square is; A magic square is an ...
903 views

### An Antimagic Square

You are to place the numbers $1$, $2$, $3$, $4$ and five zeros in a $3 \times 3$ grid. Do this in such a way so that the column, row, and two diagonal sums form the sequence $0, 1, 2, 3, 4, 5, 6, 7$...
680 views

### Are there any sets of 9 numbers that can form two essentially distinct magic squares?

It's known that the numbers 1 to 9 can only form eight different magic squares, which are all rotations and reflections of each other. Is there any set of 9 distinct numbers that can form two ...
297 views

### Warped magic squares

A $3\times3$ grid contains altogether six squares that are formed by its nine entries: there are five squares whose sides are parallel to the sides of the grid (four small ones and a big one), and ...
1k views

### The 5040 Square

Fill a $4\times4$ grid with positive integers so that: Every cell has a different integer The product of the numbers in each row is $5040$, and similarly for the columns Source: This was an NPR ...
997 views

### The magic of the primes

A mathematician, a physicist, and an engineer found themselves caught in an ancient anecdote. Lacking a chemist to brew them an anecdote antidote, they fell to arguing over which of them was to be the ...
770 views

### Magic Square Mixups [Challenge]

This kind of puzzle is different than your normal magic square puzzles. Here are 3, in increasing difficulty. Some numbers have been switched, and you have to find them and swap them around to make ...
1k views

### Magic square with the position of 8 fixed

A magic square (of order 3) is a 3x3 matrix consisting of distinct numbers from 1 to 9, where the numbers in each row, column and diagonal add up to 15. For example, the following would be a magic ...
1k views

### What is the fewest number of filled-in squares required to uniquely define a magic square?

The magic square is a well-known grid of the numbers from 1 to 9 in which every row, column, and diagonal adds up to 15: 4 9 2 3 5 7 8 1 6 But it is also ...
469 views

### Magic cutting squares with given sum

You meet a guy on the road. The following conversation follows: He: Let's play a game. Give me any natural number from $3$ to $10$. I'll call this number the grid size You: Okay, $4$. (...
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### How do I solve these 3x3 magic squares? [duplicate]

I'm doing 3x3 magic squares. Here are the squares I'm working on: | | 5 | | | | | | | 8 | | | The values must be between 3 and 12, and each line ...
132 views

### Not Regular This Time

We can say that an $n$-by-$n$ square is regular provided that: Each of the integers from $0$ to $n^2 ā 1$ appears in exactly one cell, and each cell contains only one integer (so that the square is ...
2k views

### 3x3 āMagic Squareā of Prime Numbers — Part II

Glad to know the previous puzzle, which was the first puzzle I posted in Puzzling, was warmly welcomed (Thank you!), and an optimal solution was found. Inspired by the comments there, here is the ...
250 views

### Create a 4-by-4 regular square

We can say that an $n$-by-$n$ square is regular provided that: Each of the integers from $0$ to $n^2 ā 1$ appears in exactly one cell, and each cell contains only one integer (so that the square is ...
651 views

### How Many Undefined Magic Constants are there?

Magic Square: An nxn square where every horizontal,vertical, and diagonal line all add up to the same number. Magic Constant: The number which every line with a magic square adds up to So most magic ...
7k views

### Magic Squares in Sudoku Grids

A 3x3 magic square is a 3x3 grid containing the numbers 1-9 once each, and in which every row, column, and diagonal sums to 15: 294 753 618 And I presume we all ...
308 views

### Magic Matrices?

Can you determine any number of magic squares, that when treated as matrices, can be applied mathematical operations to return a new magic-matrix? You cannot use the same matrix twice! The answer ...