How many 4x4 magic squares are there?

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 magic square combinations 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.

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 the smallest 4x4 magic square?

In 1913, Sayles published various samples of 4th-order squares: P = 5040, 7560, 11760, 14112, 14400, 21000, 2985984. In their paper Discrete Mathematics of 1983, Borkovitz and Hwang proved that the minimum magic product for 4x4 multiplicative squares is 5040, and produced a different example from the one of Sayles.

What is the famous magic square 4x4?

A pure magic 4x4 square contains the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16. The magic square is magic, because the sum of the numbers of each row, each column and both diagonals always give the same result.

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How many squares of all sizes are there in a 4x4 square?

How many squares are there on an array of 4 squares by 4 squares? Thirty. One 4x4, four 3x3, nine 2x2, 16 1x1. So 1+4+9+16 = 30.

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.

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.

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.

What is the algorithm for magic square?

The magic square is a square matrix, whose order is odd and where the sum of the elements for each row or each column or each diagonal is same. If the row exceeds, or the row is not in the matrix, then, change the column as left column and place the number at last row of the matrix, and go for top left corner again.

What are some famous magic squares?

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 are all the perfect squares ever?

They are 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961.

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.

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.

What is the 3 4 5 rule to square?

To get a perfectly square corner, you want to aim for a measurement ratio of 3:4:5. In other words, you want a three-foot length on your straight line, a four-foot length on your perpendicular line, and a five-foot length across. If all three measurements are correct, you'll have a perfectly square corner.

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.

Is 4 squared 4x4?

The square of a number is the number times itself. For example the square of 3 is 3x3. The square of 4 is 4x4.

Is 4x4 16 square feet?

A 4x4 storage locker has 16 square feet of space.

How many squares are there in a 4x4 cube?

Rubik's Cube: Six sides, 54 squares.