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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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0answers
68 views

-4 to 3 magic square [on hold]

Write the numbers -4 ,-3 ,-2,-1,0,1,2,3 in correct place value so that each of the square adds up to 0 Please solve this question, because I have tried this this question many times without success. ...
10
votes
4answers
370 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
149 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
214 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
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2answers
504 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
213 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
156 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
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1answer
118 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
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5answers
748 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
276 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
368 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
981 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
2k 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
285 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
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6answers
38k views

Fill number in missing?

Given options are: A. 13 B. 42 C. 18 D. 30
1
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0answers
50 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
815 views

Magic square with equal sums on rows, columns and diagonals

. Transcription: ...
5
votes
1answer
383 views
8
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1answer
267 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
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2answers
219 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
142 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
635 views

Put numbers to a star-shaped puzzle

For users who can not see picture, see description below ...
7
votes
5answers
513 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
752 views

Magic Square using numbers 4-12 [duplicate]

I have to make a magic square using number 4-12.
6
votes
2answers
834 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
756 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
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
3k 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
839 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
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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
664 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
289 views

What type of magic square is this?

What type of magic square is this?
7
votes
1answer
981 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 ...
20
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
957 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
737 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
439 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
24k 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
6k 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 $3 \times 3$...
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votes
1answer
114 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
190 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
272 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
276 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 ...