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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1answer
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Fill in a 6x6 magic multiplicative magic square
Let's say you fill in a 6 by 6 square with the numbers 1, 2, ..., 36. Is there a way to fill it so that the product of the first row is equal to the product of the first column, the product of the ...
4
votes
1answer
391 views
Fill in a 4x4 multiplicative magic square
Suppose we have 4 by 4 grid with numbers 1, 2, .., 16. Can we fill the grid so that the product of the first row is equal to the product of the first column, the product of the second row is equal to ...
3
votes
1answer
199 views
Fill in a 5x5 multiplicative magic square
Let's say you fill in a 5 by 5 square with the numbers 1, 2, ..., 25. Is there a way to fill it so that the product of the first row is equal to the product of the first column, the product of the ...
2
votes
3answers
96 views
Form a magic square with assorted numbers
Arrange the following numbers in a way such that all rows, columns and the diagonals add up to the same number.
...
3
votes
3answers
448 views
How to solve 3x3 Magic Squares with negative values when only 2 values are given?
I'm prepping for this math contest and I've been given notice that the special question is a magic square
(this is Caribou Contest, they tell you on their website what the special question is a couple ...
1
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2answers
126 views
Does a systematic way to solve a magic square made up of domino pieces exist?
I've found this problem in an older book which goes by the name of Logical aptitude circa 2019. It doesn't list any other markings. The thing is no matter how I attempt to look into it, I'm trapped in ...
0
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0answers
62 views
Put the numbers 1 to 8 in the boxes so that all row sums are the same [duplicate]
I recently ran across this puzzle: Place the numbers 1, 2, 3, 4, 5, 6, 7, 8 in this grid
So that each row and column of 3 digits sum to the same number. I was able to find a number of solutions. ...
4
votes
1answer
182 views
Can you fill $3 \times 3$ magic square?
In the magic square
Each number in the matrix is unique and natural.
Each row, column and the two diagonals add up to the same number (the magic constant).
Can you fill in the missing numbers?
\...
6
votes
1answer
103 views
4x4 magic square consisting of consecutive composite numbers
Is it possible to create a fourth-order magic square consisting of consecutive composite numbers that don't form an arithmetic sequence? If possible, give an example . If not, provide a proof.
...
7
votes
3answers
456 views
Can you fill in the missing numbers in this unfriendly magic square?
An unfriendly magic square is a magic square whereby the difference between neighbouring numbers always is subject to a minimum, i.e.
Each number in the matrix is unique.
Each row, column and the two ...
4
votes
5answers
897 views
Place the numbers 1-7 in the squares so that each row and columns adds up to the same total
A F
B D E
C G
A+B+C = B+D+E = F+E+G
Numbers 1,2,3,4,5,6,7
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2answers
457 views
It cannot be done. I think
I have spent too much time on this question. I am convinced this cannot be done. Please prove me right (or wrong) and explain why.
Below is a 5x5 grid. Digits 1 through 9 go in the 9 yellow boxes.
...
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0answers
129 views
Set of numbers generated from multiplying across every row and column of a grid using numbers 1,…9 [duplicate]
Imagine we start with a 3 by 3 square using the numbers 1,...,9. We then multiply the numbers across each row and note their products as the set {x1, x2, x3}. We then multiply the numbers across each ...
0
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2answers
299 views
What is the objective function of the magic square? [closed]
If I wanted to describe it as a minimum problem, where I want to identify the minimum value of the constant for a certain matrix order, how should I do it?
6
votes
3answers
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Create a magic square of 4-digit numbers
Example:
4567 4567 4567
4567 4567 4567
4567 4567 4567
what is magic square? if you add up each diagonal, row and column of
above matrix it will sum upto 13701.
Above is a 3*3 ...
3
votes
2answers
195 views
Rearrange these 9 digits - combinatorics puzzle
4 3 2 7 1 9 6 5 8
Can you rearrange these 9 digits so that in all of the 8 directions the difference between one of the digits and the sum of the remaining two shall always be the same?
In the ...
2
votes
2answers
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Magical Knight Moves with Effortless Ease in his Magical Kingdom
Magical Knight knows every Square of his Magical Kingdom.
In many respects, he is like any other knight...Literary,Prime, Normal(makes same allowed chess moves).
He is people Knight . As he traverses ...
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votes
4answers
422 views
Not-Quite-Sufficiently-Advanced-Technology Square
This was given as an assignment to a group of sixth graders, who were told they could use calculators. Beyond that, no real assistance was provided. They were not working on it as a group, so ...
5
votes
2answers
183 views
How to fill $4320$ multiplicative semi-magic square?
How can we fill $4*4$ Matrix with distinct positive integers such that product of the entries in each row & column is equal to $4320$ ?
My Strategy:
$$4320=2^5 \times 3^3 \times 5$$
First I ...
3
votes
1answer
425 views
Albrecht Durer Inspired Magic Square
A magic square is an n-dimensional matrix in which each row, column, and main diagonal sums to the same 'magic number' (denoted by s). A normal magic square uses each of the numbers from 1 to n ...
6
votes
2answers
522 views
I'm trying to create a magic square
I'm having trouble trying to make a $3\times3$ magic square with magic number $12$ and I can't figure it out.
Can you please help me?
7
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3answers
239 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 ...
asked Feb 10 '19 at 14:31
Bernardo Recamán Santos
12.3k2 gold badges22 silver badges114 bronze badges
3
votes
1answer
183 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
192 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
773 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
340 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
782 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
2k 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
3k 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
323 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 ...
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6answers
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0answers
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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.
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1answer
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1answer
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1answer
281 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
243 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
178 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
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1answer
727 views
7
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5answers
590 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 ...
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1answer
893 views
6
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2answers
862 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 ...
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votes
2answers
870 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
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3answers
4k 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
4k views
Number of magic squares with magic constant 0?
How can we determine the number of magic squares with magic constant 0?
6
votes
3answers
915 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 $0, 1, 2, 3, 4, 5, 6, 7$...
29
votes
3answers
3k 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
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1answer
687 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
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5answers
7k 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 ...
