# Questions tagged [magic-square]

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

95 questions
Filter by
Sorted by
Tagged with
95 views

### A multiplicative magic square

How can you transform a given magic square into a square where all the lines are invariant under multiplication?
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 ...
1 vote
189 views

### How Many Magic Hexagons that use repeated digits?

There exists only 1 normal magic hexagon that uses non repeating consecutive digits for 1 to 19. If We allow digits to repeat we can create something like this hexagon that is made up using ...
269 views

### Magic Hexagon 0 + 1 to 9 twice

Consider the following image. Within the grid the are a total of 19 cells. We have one cell for zero leaving 18 cells. Shading nine cells we create 2 sets of the digits 1 to 9. With one set being on ...
286 views

### 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 ...
162 views

### Smallest Magic Hexagon Using Repeat Digits

Consider this image below. Its a magic hexagon using repeated digits to create a magic sum of 10. All rows columns and diagonals, meaning the cells in any straight line through the hexagon in any ...
109 views

### Digital Digits Magic Square 3x3 that can be rotated 180 degrees

In the below image we have a magic square of a size 3x3. The magic number for all its rows, columns and both diagonals is 165. Rotate the grid 180 degrees and all sums still have the magic number 165. ...
227 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 ...
512 views

### 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)...
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 ...
3k views

### 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, ...
241 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 ...
204 views

### L tetrominoes forming an 8x8 magic square

This is a puzzle from Rodolfo Kurchan. Can you place 10 L-shaped tetrominoes on a 8x8 grid, such that: No two tetrominoes overlap. Tetrominoes can be rotated and flipped. Every row and column ...
442 views

### Sum in Magic star puzzle

I have the following problem: Place the first 11 natural numbers in the circles so that the sum of the four numbers at the tops of each of the five sectors-beams of the star equals 25. I came up with ...
1 vote
126 views

### A Magic Square (or is it?)

Sorry for taking so long but I've come up with a puzzle that I'm not sure is solvable but maybe you can help me with it? Okay, at least a hundred of us know the traditional magic square right? You ...
415 views

### Magic Matrices?

Can you determine any number of magic squares, that when treated as matrices, can be applied mathematical operations to return a new magic-matrix? You cannot use the same matrix twice! The answer ...
669 views

### 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 ...
1 vote
5k views

### Fill 3x3 magic square with distinct numbers 1..60 summing up to 69

I have to fill a whole 3x3 grid in such a way that the sum of each row, column, and main diagonal is 69. I couldn't find any logic to fill it up. I have to use distinct numbers from 1 to 60 for this. ...
985 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 ...
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 ...
178 views

### combinations of a strange magic square

The following question has been described to me by my math teacher: The diagram below is to be filled in so that each white square contains a different whole number from 1 to 12 (inclusive) and the ...
777 views

### 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?
1 vote
231 views

### Fill in a 6x6 magic multiplicative magic square

Let's say you fill in a 6 by 6 square with the numbers 1, 2, ..., 36. 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 ...
605 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 ...
728 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 ...
612k 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 ...
139 views

### Form a magic square with assorted numbers

Arrange the following numbers in a way such that all rows, columns and the diagonals add up to the same number. ...
743 views

### How to solve 3x3 Magic Squares with negative values when only 2 values are given?

I'm prepping for this math contest and I've been given notice that the special question is a magic square (this is Caribou Contest, they tell you on their website what the special question is a couple ...
1 vote
358 views

### Does a systematic way to solve a magic square made up of domino pieces exist?

I've found this problem in an older book which goes by the name of Logical aptitude circa 2019. It doesn't list any other markings. The thing is no matter how I attempt to look into it, I'm trapped in ...
63 views

### Put the numbers 1 to 8 in the boxes so that all row sums are the same [duplicate]

I recently ran across this puzzle: Place the numbers 1, 2, 3, 4, 5, 6, 7, 8 in this grid So that each row and column of 3 digits sum to the same number. I was able to find a number of solutions. ...
226 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? \...
117 views

### 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. ...
373 views

### What type of magic square is this?

What type of magic square is this?
641 views

### 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 ...
2k 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
514 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. ...
167 views

### Set of numbers generated from multiplying across every row and column of a grid using numbers 1,...9 [duplicate]

Imagine we start with a 3 by 3 square using the numbers 1,...,9. We then multiply the numbers across each row and note their products as the set {x1, x2, x3}. We then multiply the numbers across each ...
471 views

### What is the objective function of the magic square? [closed]

If I wanted to describe it as a minimum problem, where I want to identify the minimum value of the constant for a certain matrix order, how should I do it?
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 ...
1k 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 ...
215 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 ...
53k views

### Fill number in missing?

Given options are: A. 13 B. 42 C. 18 D. 30
267 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 ...
471 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 ...
209 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 ...
586 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 ...
531 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?
510 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 ...