Questions tagged [magic-square]
A puzzle related to magic squares: grids of integers where all rows, columns, and diagonals have the same sum.
95
questions
1
vote
2
answers
279
views
modified 3x3 panmagic squares
This is a modified 3x3 panmagic squares.
The square is divided into 2 triangles.
Numbers 1 to 9 is arranged to upper triangles.
Numbers 10 to 18 is arranged to lower triangles.
All rows, all columns, ...
- 17.8k
4
votes
2
answers
203
views
modify a magic square - part II
This is a 4x4 magic square of multiplication,
in which product of each row, column, and diagonal are equal.
$\begin{bmatrix}2 & 15 & 50 & 18\\ 9& 30& 4& 25\\ 20& 5& 45&...
- 17.8k
8
votes
5
answers
2k
views
Modify a magic square
This is a 3x3 magic square of summation,
in which sums of each row, column, and diagonal are equal.
$$\begin{array}{c|c|c}
4&9&2\\\hline
3&5&7\\\hline
8&1&6
\end{array}$$
Now ...
- 17.8k
12
votes
1
answer
733
views
Put numbers to a star-shaped puzzle
For users who can not see picture, see description below
...
- 17.8k
7
votes
5
answers
692
views
Arrange the numbers in a 4x4 table
Put these numbers:
2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 45, 50, 75
in a 4x4 square table so the products of all numbers in any given row, column and diagonal are equal.
Note : There are ...
- 17.8k
-3
votes
1
answer
1k
views
6
votes
2
answers
985
views
No ordinary magic square part 2. How many solutions are there?
Same rules as last time except this time count or calculate the number of possible solutions!
No ordinary magic square
Place 1-9 in the squares below in a manner such that none of the columns, rows or ...
- 372
7
votes
5
answers
1k
views
No ordinary magic square
Instead of placing every number from 1-9 in the square below such that each column, row and long diagonal has the same sum, do the opposite!
Place 1-9 in the squares below in a manner such that none ...
- 372
-5
votes
2
answers
924
views
Magic square using consecutive odd numbers -5 through 11
Using consecutive odd numbers from negative five to eleven, make a 3x3 magic square
- 13
1
vote
3
answers
5k
views
Sum of numbers in any row, column or diagonal is 50
In the following grid;
Sum of numbers in any row is equal to 50.
Sum of numbers in any column is equal to 50.
Sum of numbers in any diagonal is equal to 50.
Numbers in any two cells cannot be equal ...
0
votes
2
answers
6k
views
Number of magic squares with magic constant 0?
How can we determine the number of magic squares with magic constant 0?
- 17
6
votes
3
answers
986
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 $0, 1, 2, 3, 4, 5, 6, 7$...
- 8,914
36
votes
3
answers
4k
views
Unsolved Mysteries: Magic Square of Squares
This is the first in what will hopefully be a series of Unsolved Mysteries posts.
Note that this puzzle has no known solution, nor any proof that a solution is impossible. We will see how ...
- 25.7k
6
votes
1
answer
695
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 ...
user88
9
votes
5
answers
8k
views
Complete the magic square!
So, my math teacher gave us a magic math square with
the 9 in the bottom right corner,
the 7 in the left column middle row, and
the 1 in the middle column top row.
She said she would give whoever ...
3
votes
1
answer
373
views
8
votes
1
answer
1k
views
The magic square with a hole
Alice loves magic squares. She has a 4x4 square, where she can put a number in each cell. But alas! Some evil person has poked a hole in her square. Alice is really really sad because she can't make a ...
- 4,010
20
votes
3
answers
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 ...
- 32.1k
12
votes
2
answers
13k
views
Magic square using numbers 0,2,3,4,5,6,7,8,10
I have to make a 3x3 magic square using the numbers 0-10 without 1 and 9. I have tried various things but am not good at this. The sums of each row, column, and diagonal have to be equal; I added all ...
- 129
8
votes
2
answers
1k
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 ...
- 116k
1
vote
4
answers
5k
views
Fill 3x3 magic square with distinct numbers 1..60 summing up to 69
I have to fill a whole 3x3 grid in such a way that the sum of each row, column, and main diagonal is 69. I couldn't find any logic to fill it up. I have to use distinct numbers from 1 to 60 for this. ...
- 21
7
votes
2
answers
816
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 ...
- 417
5
votes
3
answers
496
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, $4$.
(...
- 6,936
6
votes
4
answers
29k
views
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 ...
- 61
8
votes
3
answers
2k
views
3x3 “Magic Square” 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 ...
- 670
22
votes
6
answers
8k
views
3x3 "Magic Square" of Prime Numbers
During the thinking and analysis of some mathematical problems, I came up with this puzzle:
Just like any magic square, one has to fill in $9$ different numbers $P_1, P_2, \dots P_9$ to a $3 \times 3$...
- 670
-2
votes
1
answer
220
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 $n^2 − 1$ appears in exactly one cell, and each cell contains only one integer (so that the square is ...
- 127
2
votes
1
answer
367
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 $n^2 − 1$ appears in exactly one cell, and each cell contains only one integer (so that the square is ...
- 127
8
votes
1
answer
3k
views
9-by-9 filled, magic square
Construct a 9-by-9 filled, magic square using the integers from
0 to 80. The magic square should additionally have the property that when it is divided
into ninths according to the picture below, each ...
- 127
2
votes
2
answers
332
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 ...
- 45.4k
2
votes
2
answers
418
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 ...
- 14.4k
11
votes
6
answers
4k
views
The Quite Unusual Square
Imagine an $n \times n$ grid filled with the numbers 1, ..., $n$
where $n$ > 3 each number appearing n times, where each row, column, and diagonal all equal the same number. Can you fill grid like ...
- 14.4k
5
votes
1
answer
328
views
Magic Square with more Magic Squares inside it?
Is it possible to have an $n \times n$ magic square with a another magic square of $\frac n 4 \times \frac n 4$ magic square inside it? If so provide an example, if not prove if impossible.
Rules:
$...
- 14.4k
14
votes
2
answers
19k
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 ...
- 1,273
1
vote
2
answers
423
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 ...
- 14.4k
-5
votes
1
answer
734
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 ...
- 14.4k
12
votes
2
answers
4k
views
Does a magic rectangle exist?
My definition of a magic rectangle:
Any $m \times n$ rectangle where $m \ne n$ and all the numbers $1, 2, 3,\dots, mn$ fit into the rectangle. All horizontal lines, vertical lines, and diagonal ...
- 14.4k
5
votes
2
answers
6k
views
How to Determine a Magic Constant in a Magic Square?
A magic square consists of the numbers $1,2,\ldots,m^2$ placed into $m\times m$ square grid, so that every row, column, and both diagonals have the same sum. The magic constant of the square is this ...
- 14.4k
8
votes
1
answer
5k
views
Can you fill a 3x3 grid with these numbers so the products of the rows and columns are the same?
Is it possible to form a $3\mbox{x}3$ grid containing the set of numbers: $${1,2,4,8,16,32,64,128,256}$$
in such a way that the product of the numbers in every row, column and diagonal are the same? ...
- 14.4k
4
votes
2
answers
2k
views
Are there any sudoku puzzles combined with magic squares? [duplicate]
As everyone knows, in Sudoku the sum of each row and column is 45. So all Sudoku solutions are some kind of magic square. My question is:
Has anyone seen a Sudoku puzzle combined with the magic square ...
- 5,718
6
votes
3
answers
532
views
Magic back yards
My back yard forms a rectangular grid of squares except some of the squares are missing as they are covered by pipes or a small tree. The layout is as follows. A 'x' indicates a square that is free ...
- 7,050
10
votes
5
answers
614k
views
Puzzle of putting numbers 1-9 in 3x3 Grid to add up to 15
In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row, column and diagonal add up to 15.
I have only been able to come up with one solution:
6
1
8
7
5
3
2
9
4
...
- 119
15
votes
1
answer
4k
views
Elegant solution to the Magic Hexagon problem
The Magic Hexagon Problem
A magic hexagon of order $n$ is an arrangement of close-packed hexagons containing the numbers $1, 2, ..., H_{n-1}$, where $H_n$ is the $n^{th}$ hex number such that the ...
- 2,344
14
votes
2
answers
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 ...
user88
15
votes
4
answers
2k
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 ...
- 1,249