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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.

A magic square is an arrangement of distinct numbers (i.e. each number is used only once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number. An $n\times n$ magic square that contains the integers from 1 to $n^2$ is called a normal magic square.

Example: Up to rotations and reflections, there is only one $3\times 3$ magic square with entries 1,2,...,9 (which is also known under its Chinese name "Lo Shu"): 

   8  1  6   
   3  5  7  
   4  9  2
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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 square: The problem is to construct a magic…
John Bupit
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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 possible to create magic squares using other numbers: 24 87 45 73 52 31 59 17 80 It's also…
user88
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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 this? If so, show an example, and include as much…
warspyking
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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 3-by-3 subsquare is also magic.
Daniella
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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 magic square anymore. Won't you cheer poor Alice…
Rohcana
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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 matrix where each entry is the same number. You need to…
Sayed Mohd Ali
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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 multiple solutions, it is preferred to find the…
Jamal Senjaya
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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 the magic square valid again. The zeros are for…
Vincent Tang
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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. Clarification: In case someone is not sure what…
Pedja
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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 $0, 1, 2, 3, 4, 5, 6, 7$ in some order. I find such a square pleasing in…
Tyler Seacrest
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How do I solve these 3x3 magic squares?

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 must add to 21. Here's another one: | | 9 | | | | | 3 | | | | | For this…
user12319
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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: $n$ cannot be 4 Clarifications: A magic square is…
warspyking
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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. $\begin{bmatrix}2 & 15 & 50 & 18\\ 9& 30& 4& 25\\ 20& 5& 45& 6\\ 75& 12& 3& 10\end{bmatrix}$ Now modify the magic square by defining a…
Jamal Senjaya
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Magic square with equal sums on rows, columns and diagonals

. Transcription: In a given magic square, if the sum of number in each row and each column and both of the main diagonals are equal, then the value of x is: 1) 10 2) 12 3) 8 4) 15 Source:INTSO Grade 3
Sasi
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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 to each other. Only the numbers from 5 to 20 are…
Tharindu Sathischandra
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