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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2answers
84 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?
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1answer
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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 ...
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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 ...
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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 ...
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6answers
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Fill number in missing?

Given options are: A. 13 B. 42 C. 18 D. 30
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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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4answers
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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 ...
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2answers
168 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 ...
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1answer
317 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 ...
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2answers
511 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?
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3answers
226 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 ...
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5answers
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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 ...
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5answers
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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 ...
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1answer
161 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
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5answers
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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 ...
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1answer
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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 ...
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3answers
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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 ...
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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 ...
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1answer
292 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 ...
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1answer
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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.
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3answers
539 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 ...
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4answers
1k 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, ...
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1answer
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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 ...
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1answer
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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? ...
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6answers
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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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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 ...
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1answer
297 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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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
853 views

Magic square with equal sums on rows, columns and diagonals

. Transcription: ...
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5answers
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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 ...
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4answers
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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. ...
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1answer
414 views
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4answers
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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: $$\begin{array}{ccc} 6 &...
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1answer
272 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 ...
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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, ...
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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&...
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1answer
677 views

Put numbers to a star-shaped puzzle

For users who can not see picture, see description below ...
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5answers
550 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
798 views

Magic Square using numbers 4-12 [duplicate]

I have to make a magic square using number 4-12.
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5answers
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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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2answers
838 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 ...
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2answers
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Magic square using consecutive odd numbers -5 through 11

Using consecutive odd numbers from negative five to eleven, make a 3x3 magic square
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3answers
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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 ...
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2answers
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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?
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2answers
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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 ...
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3answers
859 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 $0, 1, 2, 3, 4, 5, 6, 7$...
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1answer
668 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 ...
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1answer
305 views

What type of magic square is this?

What type of magic square is this?
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2answers
284 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 ...
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3answers
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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 ...