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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A multiplicative magic square

How can you transform a given magic square into a square where all the lines are invariant under multiplication?
Lucius's user avatar
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1 vote
2 answers
190 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 ...
Maff's user avatar
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4 votes
2 answers
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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 ...
Maff's user avatar
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5 votes
3 answers
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 ...
Dmitry Kamenetsky's user avatar
3 votes
2 answers
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 ...
Maff's user avatar
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3 votes
1 answer
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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. ...
Maff's user avatar
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3 votes
1 answer
228 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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5 votes
1 answer
528 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)...
Bernardo Recamán Santos's user avatar
2 votes
1 answer
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 ...
Dmitry Kamenetsky's user avatar
2 votes
2 answers
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 ...
Dmitry Kamenetsky's user avatar
1 vote
1 answer
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 ...
Benjamin Curran's user avatar
4 votes
2 answers
443 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 ...
Gregory Bones's user avatar
8 votes
1 answer
671 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 ...
Hazel へいぜる's user avatar
4 votes
1 answer
179 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 ...
Arale's user avatar
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8 votes
3 answers
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?
Dmitry Kamenetsky's user avatar
1 vote
1 answer
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 ...
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5 votes
1 answer
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 ...
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3 votes
1 answer
737 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 ...
user avatar
2 votes
3 answers
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. ...
Yellow X's user avatar
3 votes
3 answers
749 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 ...
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1 vote
2 answers
363 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 ...
Chris Steinbeck Bell's user avatar
0 votes
0 answers
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. ...
B. Goddard's user avatar
4 votes
1 answer
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? \...
Nick's user avatar
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6 votes
1 answer
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. ...
Pedja's user avatar
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7 votes
3 answers
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 ...
Paul Richards's user avatar
4 votes
5 answers
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
user67518's user avatar
15 votes
2 answers
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. ...
DrD's user avatar
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0 votes
0 answers
168 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 ...
nak17's user avatar
  • 101
0 votes
2 answers
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?
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7 votes
3 answers
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 ...
Sayed Mohd Ali's user avatar
3 votes
2 answers
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 ...
Sayed Mohd Ali's user avatar
2 votes
2 answers
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 ...
Uvc's user avatar
  • 5,891
10 votes
4 answers
472 views

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 ...
Rubio's user avatar
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6 votes
2 answers
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 ...
Suresh's user avatar
  • 430
3 votes
1 answer
587 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 ...
Diatche's user avatar
  • 33
6 votes
2 answers
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?
Lucy's user avatar
  • 79
8 votes
3 answers
523 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 ...
Bernardo Recamán Santos's user avatar
3 votes
1 answer
249 views

This four-by-four Magic Square uses all the integers from -7 to 8. Complete the square. More Magic Squares!

This four-by-four Magic Square uses all the integers from -7 to 8. Complete the square. This is what has been given so far: -7 _ _ _ _ -2 _ +1 _ _ +3 _ +5 _ _ _ Please Help. Thank you
user53382's user avatar
1 vote
1 answer
284 views

Create a 3x3 Magic Square that uses integers from -10 to -2

I've never used this before but i'm having trouble with this. Create a 3x3 Magic Square that uses integers from -10 to -2. By the way, this is a weird magic square since diagonals don't need to ...
user53382's user avatar
19 votes
5 answers
801 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 ...
Viktor Jeppesen's user avatar
4 votes
1 answer
385 views

A challenging Magic Square

Find a 3x3 Magic Square where each row, column and both diagonals result in positive number 9 You are allowed any of the 4 math operations : add, subtract, multiply or divide. NO OTHER OPERATIONS ...
DrD's user avatar
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7 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
  • 76k
5 votes
4 answers
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, ...
Albert_ITA's user avatar
7 votes
1 answer
3k views

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.
user2882061's user avatar
2 votes
1 answer
339 views

I am not sure if this is related to magic squares but is something that is unanswered in my mind since I was a kid

It is easy to make a matrix of squares, being the same up as down and and odd number of rows and columns from 9 - 25 - 81 etc and have have equal amounts for each row and column. My question is simply ...
puzzled steve's user avatar
3 votes
6 answers
53k views

Fill number in missing?

Given options are: A. 13 B. 42 C. 18 D. 30
user37902's user avatar
1 vote
0 answers
56 views

Total number of squares + inside square [duplicate]

How to calculate total number of squares if n×n square box available. Need to calculate 1×1, 2×2 up to n.
Alex Mac's user avatar
  • 117
1 vote
1 answer
940 views

Magic square with equal sums on rows, columns and diagonals

. Transcription: ...
Sasi's user avatar
  • 35
5 votes
1 answer
487 views

Interesting 3x3 table, with some unique prime numbers

...
Jamal Senjaya's user avatar
9 votes
1 answer
296 views

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 ...
Rand al'Thor's user avatar