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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1 answer
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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 ...
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2 votes
2 answers
136 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 ...
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1 vote
1 answer
106 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 ...
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4 votes
2 answers
390 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 ...
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8 votes
1 answer
509 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 ...
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4 votes
1 answer
140 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 ...
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8 votes
3 answers
734 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?
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1 vote
1 answer
174 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
558 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
0 answers
448 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
3 answers
106 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. ...
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3 votes
3 answers
543 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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2 answers
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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 ...
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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. ...
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4 votes
1 answer
210 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? \...
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6 votes
1 answer
110 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. ...
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7 votes
3 answers
566 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 ...
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4 votes
5 answers
1k 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
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15 votes
2 answers
489 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. ...
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0 votes
0 answers
147 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 ...
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0 votes
2 answers
450 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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6 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 ...
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3 votes
2 answers
205 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 ...
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2 votes
2 answers
260 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 ...
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10 votes
4 answers
440 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 ...
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6 votes
2 answers
196 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 ...
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  • 430
3 votes
1 answer
510 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 ...
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6 votes
2 answers
524 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?
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7 votes
3 answers
245 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 ...
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3 votes
1 answer
224 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
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1 vote
1 answer
241 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 ...
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19 votes
5 answers
793 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 ...
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4 votes
1 answer
366 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 ...
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5 votes
3 answers
967 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 ...
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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, ...
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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.
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2 votes
1 answer
332 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 ...
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3 votes
6 answers
53k views

Fill number in missing?

Given options are: A. 13 B. 42 C. 18 D. 30
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1 vote
0 answers
55 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.
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1 vote
1 answer
928 views

Magic square with equal sums on rows, columns and diagonals

. Transcription: ...
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5 votes
1 answer
458 views

Interesting 3x3 table, with some unique prime numbers

...
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8 votes
1 answer
288 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 ...
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1 vote
2 answers
264 views

modified 3x3 panmagic squares

This is a modified 3x3 panmagic squares. The square is divided into 2 triangles. Numbers 1 to 9 is arranged to upper triangles. Numbers 10 to 18 is arranged to lower triangles. All rows, all columns, ...
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4 votes
2 answers
193 views

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&...
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8 votes
5 answers
2k views

Modify a magic square

This is a 3x3 magic square of summation, in which sums of each row, column, and diagonal are equal. $$\begin{array}{c|c|c} 4&9&2\\\hline 3&5&7\\\hline 8&1&6 \end{array}$$ Now ...
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12 votes
1 answer
732 views

Put numbers to a star-shaped puzzle

For users who can not see picture, see description below ...
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7 votes
5 answers
625 views

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 ...
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-3 votes
1 answer
1k views

Magic Square using numbers 4-12 [duplicate]

I have to make a magic square using number 4-12.
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6 votes
2 answers
958 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 ...
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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 ...
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