# Questions tagged [magic-square]

A puzzle related to magic squares: grids of integers where all rows, columns, and diagonals have the same sum.

72 questions
Filter by
Sorted by
Tagged with
3k 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 ...
7k 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 $3 \times 3$...
1k views

### 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 ...
765 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 ...
1k 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 ...
3k views

### 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 ...
448 views

### 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. ...
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 ...
12k 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 ...
715 views

### Put numbers to a star-shaped puzzle

For users who can not see picture, see description below ...
7k 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 ...
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 ...
411 views

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 ...
4k views

### 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 ...
446k views

433 views

...
799 views

### 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
156 views

### Can you fill $3 \times 3$ magic square?

In the magic square Each number in the matrix is unique and natural. Each row, column and the two diagonals add up to the same number (the magic constant). Can you fill in the missing numbers? \...
168 views

51k views

### Fill number in missing?

Given options are: A. 13 B. 42 C. 18 D. 30