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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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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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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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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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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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 ...
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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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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 ...
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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 ...
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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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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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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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Put numbers to a star-shaped puzzle
For users who can not see picture, see description below
...
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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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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:
6
1
8
7
5
3
2
9
4
...
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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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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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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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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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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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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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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 ...
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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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Perfect magic 4x4 square
Can you fill a 4x4 grid with every number from 1 to 16, such that every row, every column and every 2x2 sub-grid of numbers sum to the same value?
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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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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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Can you reactivate a 4x4 Magic Square?
We've already removed the magic from a 3x3 magic square. Recently, one of our 4x4 magic squares was scrambled in an earthquake and I need your help to reactivate it's magic:
Objective
Your objective ...
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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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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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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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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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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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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 ...
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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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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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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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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 or ...
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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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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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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 ...
user88
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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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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.
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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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Magic square 4x4 that sum to 38 [closed]
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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Four 3x3 semimagic squares in a 5x5 grid
Can you place every number from 1 to 25 in a 5x5 grid such that it contains four 3x3 semimagic squares? A semimagic square is a square whose rows and columns all sum to the same number. This is ...
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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:
$...
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Near Magic Squares with the First 25 Primes
There are 25 primes smaller than 100. What is the closest to a 5 x 5 magic square I can construct with them? By "closest" I mean the one with the most columns, rows, and diagonals (12 in all)...
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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 ...
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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, $4$.
(...
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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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