How many magic squares exist?

Magic Squares – simple and complex

Something very surprising! It is known that there are 880 distinct solutions for a 4x4, or order 4 magic square, containing the numbers 1-16, magic total 34.

How many combinations of magic square are there?

So there is 1 unique magic square. The eight patterns are rotations and reflections that correspond to symmetries of a square (the dihedral group of order 8). It's a pretty neat proof, and we didn't have to test all 9! = 362880 possible ways to place the numbers in the square.

Are there infinite magic squares?

The first two properties would yield an infinite number of magic squares since there are an infinite number of numbers we could add to every number or multiply every number by to produce a different magic square.

What is the oldest magic square?

The oldest magic square of order four was found inscribed in Khajuraho, India dating to the eleventh or twelfth century. This magic square is also known as the diabolic or panmagic square, where, in addition to the rows, columns, and diagonals the broken diagonals also have the same sum.

How many 5x5 magic squares are there?

In summary: There are 144 pan magic squares of order five. They are based on one underlying pan-magic carpet, or Latin square.

What is a GeoMagic Square?

Is 6x6 magic square possible?

Then, in 1959, Parker, Bose and Shrikhande constructed an order 10 Graeco-Latin square, and showed a construction technique for orders 10, 14, 18, etc. They therefore disproved Euler's conjecture, leaving the 6x6 magic square as something of an oddity - it cannot be based on a pair of identical latin squares.

Is magic square always 15?

Magic Squares are square grids with a special arrangement of numbers in them. These numbers are special because every row, column and diagonal adds up to the same number. So for the example below, 15 is the magic number.

Is Sudoku a magic square?

But fans may not know that Sudoku is a recent offshoot of the venerable Magic Square, which dates back over 4,000 years to ancient China, where it was literally considered magical.

Who made the largest magic square?

The record for making the largest magic square in MS-Excel was set by Subramani K. He made a largest magic square with 10000 rows and 10000 columns. He used the numbers from 1 to 10000 and the sum of all numbers of each row and column is 50005000.

Which country invented the magic square?

Magic squares have a long history, dating back to at least 190 BCE in China. At various times they have acquired occult or mythical significance, and have appeared as symbols in works of art.

Is 0 allowed in a magic square?

Because there is a requirement that magic squares be comprised of unique numbers, you can't use 0 , but any non-zero integer would work.

What is the trick to complete magic square?

To calculate the magic constant, add all nine numbers used in the magic square and divide by the number of rows. In our example, add 1+2+3+4+5+6+7+8+9 = 45, then divide by 3. The magic constant for this example is 15, as 45 / 3 = 15.

What is the math behind magic square?

A magic square is an n x n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. This number is called the magic number. The main diagonals are those that stretch from corner to corner.

Is there is a magic square for 42 yes or no?

Considering multiples of 6, we have two magic square with equal sums and equal digits blocks of order 6 resulting in magic square of order 42.

What is the magic number 15?

Fifteen is a number of deep esoteric significance to astrologers, numerologists and magicians across the world. Magicians consider it as alchemic vibration through which all magic is manifested. Fifteen is considered “an extremely lucky number,” carrying the essence of enchantment.

Can magic squares repeat numbers?

Although this square is easy to construct, it has the aesthetic drawback that some of the numbers are repeated. Not only do the bottom corner squares (intentionally) duplicate two of the numbers in the top row, but some of the numbers in the second and third rows are duplicates as well.

Who is the fastest kid to create a magic square?

Naveda Lekshmi B.R. of #Thiruvananthapuram, #Kerala set the #record for being the #fastest to create a #magicsquare with random numbers. She created a 15x15 magic square (wherein #numbers from 1 to 225 total 1,695) in 13 minutes and 36 seconds, at the age of 6 years, 2 months and 21 days.

Why is magic square called magic?

Magic squares are called ''magic'' because each row, column, and diagonal in the square has the same sum, called the magic constant. Sum is the term we use for the answer to an addition problem.

How many Ramanujan magic square are there?

Ramanujan from his birth to till his demise and afterwards also. All the 100 squares of two digits will have a total 2183 and 2179.

Is Sudoku left or right brain?

Sudoku is a logic puzzle, which exercises the left hemisphere of the brain. Doing Sudoku puzzles is fundamentally satisfying because it helps us “flex the muscles” in a part of our brain that might not always get a lot of use during our everyday lives.

Is Sudoku Chinese or Japanese?

The game first appeared in Japan in 1984 where it was given the name “Sudoku,” which is short for a longer expression in Japanese – “Sūji wa dokushin ni kagiru” – which means, “the digits are limited to one occurrence.” Sudoku continues to be highly popular in Japan, where people buy over 600,000 Sudoku magazines per ...

Why is Sudoku not actually a math puzzle?

Myth: You must be good at math to play Sudoku

But this is not true. Sudoku is not about adding or subtracting or doing arithmetic – it's about placing numbers 1-9 on a grid, without repeating any of the same numbers within the same row, column or square. Sudoku is not a “math” game, it's a logic game.

Can you have a 2x2 magic square?

It is easy to see that we cannot have 2x2 magic square because we cannot arrange numbers 1,2,3,4 in such a square so that the sum of numbers in every row, column and diagonals is the same number.

Is 5 always in the middle of a magic square?

We now know that 5 must be in the center cell, so the number in the diagonally opposite cell from 1 must be 9. Now, in order to sum to 15 the top row must contain the numbers 1, 6, and 8.

What is the formula for the 5 * 5 magic square?

In order to make a 5 × 5 magic square, the first step is to find the magic constant using the same formula: M = n ( n 2 + 1 ) 2 \( . So, the sum of all the numbers in each row, column, and main diagonal of a 5 × 5 magic square is 65.