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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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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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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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 ...
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5answers
753 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 ...
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4answers
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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 ...
15
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1answer
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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 ...
13
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2answers
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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 ...
12
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2answers
11k 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 ...
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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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2answers
3k 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 ...
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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 ...
10
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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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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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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 ...
8
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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 ...
8
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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? ...
8
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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 ...
8
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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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2answers
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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 ...
8
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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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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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2answers
751 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 ...
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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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3answers
540 views

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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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 ...
7
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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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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
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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 ...
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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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4answers
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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 ...
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3answers
506 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 ...
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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 ...
6
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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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4answers
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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, ...
5
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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 $0, 1, 2, 3, 4, 5, 6, 7$...
5
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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 ...
5
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1answer
298 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: $...
5
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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
413 views

Interesting 3x3 table, with some unique prime numbers

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2answers
158 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 ...
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2answers
152 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&...
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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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2answers
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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 ...
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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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1answer
305 views

What type of magic square is this?

What type of magic square is this?
3
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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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3answers
460 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, $4$. (...
3
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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
206 views

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 ...
2
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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 ...