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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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11 votes
5 answers
639k views

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 ...
Freya's user avatar
  • 129
14 votes
2 answers
1k views

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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14 votes
2 answers
22k 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 ...
Kevin's user avatar
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11 votes
6 answers
4k views

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 ...
warspyking's user avatar
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6 votes
3 answers
1k 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 ...
Bass's user avatar
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3 votes
1 answer
1k 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 ...
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2 votes
2 answers
273 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 ...
Uvc's user avatar
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-5 votes
2 answers
935 views

Magic square using consecutive odd numbers -5 through 11

Using consecutive odd numbers from negative five to eleven, make a 3x3 magic square
katherine's user avatar
36 votes
3 answers
4k 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 ...
GentlePurpleRain's user avatar
22 votes
6 answers
9k 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 $3 \times 3$...
LaBird's user avatar
  • 670
15 votes
4 answers
2k views

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 ...
John Bupit's user avatar
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12 votes
2 answers
13k 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 ...
tyler's user avatar
  • 129
8 votes
3 answers
2k 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 ...
LaBird's user avatar
  • 670
8 votes
1 answer
1k 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 ...
Rohcana's user avatar
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7 votes
5 answers
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 ...
Greg Hastings's user avatar
6 votes
2 answers
994 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 or ...
Greg Hastings's user avatar
6 votes
2 answers
533 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?
Lucy's user avatar
  • 79
5 votes
1 answer
665 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 ...
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4 votes
2 answers
2k views

Are there any sudoku puzzles combined with magic squares? [duplicate]

As everyone knows, in Sudoku the sum of each row and column is 45. So all Sudoku solutions are some kind of magic square. My question is: Has anyone seen a Sudoku puzzle combined with the magic square ...
Rafe's user avatar
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3 votes
1 answer
324 views

Smallest 3x3 Magic Square of different square sums

Consider the follow magic square highlighted in yellow. The sum of its rows and columns are in green and the sum of the diagonals in red. All of its sums are a square number with the sum of the whole ...
Maff's user avatar
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2 votes
1 answer
242 views

Sets of tetrominoes forming a magic square

Is it possible to place $n$ sets of five free tetrominoes on a $K \times K$ square grid, such that: No two tetrominoes overlap. Tetrominoes can be rotated or flipped. Every row, column and two main ...
Dmitry Kamenetsky's user avatar
-2 votes
1 answer
242 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 ...
Daniella's user avatar
  • 127
-5 votes
1 answer
743 views

How Many Undefined Magic Constants are there?

Magic Square: An nxn square where every horizontal,vertical, and diagonal line all add up to the same number. Magic Constant: The number which every line with a magic square adds up to So most magic ...
warspyking's user avatar
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