Questions tagged [magic-square]
A puzzle related to magic squares: grids of integers where all rows, columns, and diagonals have the same sum.
7
votes
3answers
175 views
A 4 x 4 Magic Square with Pairwise Relatively Prime Entries
Find a 4 x 4 magic square of positive integers such that any two of its entries are pairwise different and relatively prime, i.e., have no common divisor greater than 1.
What is the least that the ...
3
votes
1answer
140 views
This four-by-four Magic Square uses all the integers from -7 to 8. Complete the square. More Magic Squares!
This four-by-four Magic Square uses all the integers from -7 to 8. Complete the square.
This is what has been given so far:
-7 _ _ _
_ -2 _ +1
_ _ +3 _
+5 _ _ _
Please Help. Thank you
1
vote
1answer
87 views
Create a 3x3 Magic Square that uses integers from -10 to -2
I've never used this before but i'm having trouble with this.
Create a 3x3 Magic Square that uses integers from -10 to -2.
By the way, this is a weird magic square since diagonals don't need to ...
19
votes
5answers
718 views
A riddle that has been killing me the whole day
So I'm walking around in London and found the following number riddle. The rules say, that what ever pattern you find, must be true for the rows as well as the columns. The answer in level 1 is for ...
4
votes
1answer
268 views
A challenging Magic Square
Find a 3x3 Magic Square where each row, column and both diagonals result in positive number 9
You are allowed any of the 4 math operations : add, subtract, multiply or divide. NO OTHER OPERATIONS ...
5
votes
3answers
306 views
Magic-preserving Permutations on a 4x4 Magic Square
Messing around with some magic-square puzzles, I faced the problem of deciding whether some two magical squares are, in fact, the one and same square wearing a different hat. It seemed to me, that for ...
5
votes
4answers
760 views
Magic square 4x4 that sum to 38
I'm stuck with this math puzzle, tried many strategies but can't solve it. I have to fill a 4x4 magic square that sums up to 38 (row, column, and both diagonals) with these given numbers: 4, 6, 7, 7, ...
7
votes
1answer
1k views
Find the missing numbers in the magic square
The following is a magic square: each row, column and diagonal add to 34, all of the numbers 1 to 16 appear exactly once. Find the missing numbers.
2
votes
1answer
265 views
I am not sure if this is related to magic squares but is something that is unanswered in my mind since I was a kid
It is easy to make a matrix of squares, being the same up as down and and odd number of rows and columns from 9 - 25 - 81 etc and have have equal amounts for each row and column. My question is simply ...
2
votes
6answers
32k views
1
vote
0answers
48 views
Total number of squares + inside square [duplicate]
How to calculate total number of squares if n×n square box available.
Need to calculate 1×1, 2×2 up to n.
1
vote
1answer
774 views
5
votes
1answer
365 views
8
votes
1answer
265 views
How big can a witchcraft square be?
A witchcraft square is defined to be an $n\times n$ square of distinct natural numbers such that the row sums and column sums form a set of $2n$ consecutive natural numbers. For example,
5 11 14 ...
1
vote
2answers
215 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, ...
4
votes
2answers
137 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&...
8
votes
5answers
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 ...
12
votes
1answer
624 views
7
votes
5answers
475 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 ...
-3
votes
1answer
686 views
6
votes
2answers
831 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 ...
7
votes
5answers
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 ...
-5
votes
2answers
695 views
Magic square using consecutive odd numbers -5 through 11
Using consecutive odd numbers from negative five to eleven, make a 3x3 magic square
1
vote
3answers
3k 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
2answers
2k views
Number of magic squares with magic constant 0?
How can we determine the number of magic squares with magic constant 0?
5
votes
3answers
828 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 $0, 1, 2, 3, 4, 5, 6, 7$...
25
votes
3answers
2k 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 ...
6
votes
1answer
657 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 ...
8
votes
5answers
4k 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
1answer
270 views
7
votes
1answer
960 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 ...
19
votes
3answers
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 ...
12
votes
2answers
10k 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 ...
8
votes
2answers
940 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 ...
1
vote
4answers
3k 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. ...
7
votes
2answers
714 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 ...
3
votes
3answers
424 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
votes
4answers
22k 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 ...
7
votes
3answers
1k 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 ...
19
votes
6answers
5k 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 $3 \times 3$...
-2
votes
1answer
111 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 ...
2
votes
1answer
188 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 ...
8
votes
1answer
2k 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 ...
1
vote
2answers
264 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 ...
0
votes
2answers
271 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 ...
10
votes
5answers
3k 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 ...
5
votes
1answer
287 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:
$...
12
votes
2answers
2k 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
vote
2answers
336 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 ...
-5
votes
1answer
583 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 ...
