What is the formula for the magic constant?

Asked by: Dr. Dallas Corkery  |  Last update: February 9, 2025
Score: 4.4/5 (28 votes)

The magic constant of a magic square of nth order can be found by dividing the sum of 1 to n2 by n; namely, the magic constant = n (n2+1)/2.

What is the general formula for the magic constant of a magic square of size n?

For normal magic squares of orders n = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order n is ⁠n3 + n2⁠.

What is the magic constant in a 4x4 magic square?

The sum of each row, column and diagonal is 34, the magic number for a 4 × 4 magic square.

What is the magic square formula?

M = n(n2 + 1)/2. This is the formula for a magic square that is used to make magic squares of different orders. If we subtract each number from (n2 + 1), we get another magic square, and this is called the complementary magic square.

What is the magic constant for Ramanujan's magic square?

Ramanujan [4] constructed different magic squares of the same size but with different magic constants. For instance, he constructed an even square of 4 × 4 with magic constants equal to 34 and 35. For an odd order, Ramanujan constructed a 5 × 5 square with magic constants equal to 65 and 66.

8128 and Perfect Numbers - Numberphile

34 related questions found

What is the magic constant of a magic square?

The magic constant of a magic square of nth order can be found by dividing the sum of 1 to n2 by n; namely, the magic constant = n (n2+1)/2. Magic squares are called “magic squares” in English.

What is the formula of Ramanujan's magic square?

Ramanujan created the following birthday magic square from his date of birth (in DD MM YYYY format) where all four rows, four columns and two diagonals sum up to 139. e.g. sum of all rows equals to 139. 22 + 87 + 19 + 11 =139; 17 + 09 + 24 + 89 =139; That seems like magic and hence the name — magic square.

What is the most perfect magic square?

A most-perfect magic square of order n is a magic square containing the numbers 1 to n2 with two additional properties:
  • Each 2 × 2 subsquare sums to 2s, where s = n2 + 1.
  • All pairs of integers distant n/2 along a (major) diagonal sum to s.

Is there a trick to magic squares?

Given a little thought, I found that there is a simple calculation to find the “magic number” of any sized grid: Take the sum of every number on the board and divide it by the number of rows. In this case, the magic number is 1+2+… +9 = 45 / 3 = 15.

What is the general form of magic square?

A number is said to be in a generalized form if it is expressed as the sum of the product of its digits with their respective place values.

What is the magic number in quantum mechanics?

magic number, in physics, in the shell models of both atomic and nuclear structure, any of a series of numbers that connote stable structure. The magic numbers for atoms are 2, 10, 18, 36, 54, and 86, corresponding to the total number of electrons in filled electron shells.

What is the magic square 4x4 sum 33?

Curiously to the left of this sculpture, the 4X4 number quadrant is carved into the facade. Adding up the rows, columns, and diagonals of the “Magic Square” reveals that they all add up to 33, the age of Christ at the time of his death. Others speculate that Subirachs was referencing the 33 levels of freemasonry.

What is the magic sum of the Pentagon?

For a particular arrangement, if we add up the sum of the numbers on each side of the pentagon, we will have counted the numbers in the corners twice. So the magic sum equals the sum of all the numbers, plus the sum of just the numbers in the corners, divided by five.

How do you calculate the magic formula?

Determine company's earnings yield = EBIT / enterprise value. Determine company's return on capital = EBIT / (net fixed assets + working capital). Rank all companies above chosen market capitalization by highest earnings yield and highest return on capital (ranked as percentages).

What is the magic number formula?

You can calculate the magic number for your SaaS business by subtracting the last quarter's annual recurring revenue (ARR) from the current quarter's ARR and dividing by your total customer acquisition cost (CAC) (your total sales and marketing spend) from the previous quarter.

Is there a formula for magic squares?

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.

How to find the magic constant in a magic square?

We know that the formula to calculate the magic sum or magic constant is M=n(n2+1)2\(. In order to make a magic square of order 3, we need to replace n with 3 in the above formula. So, now we have to place the numbers in the places such that the sum of each row, column, and main diagonal is 15.

What is the perfect square trick?

How to Find Perfect Square? To find a perfect square, we need to multiply the whole number by itself. The first 20 perfect square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, and 400.

What is the algorithm for magic square?

M = n(n² + 1)/2. This is the formula for a magic square that is used to make magic squares of different orders. If we subtract each number from ( n² + 1), we get another magic square, and this is called the complementary magic square.

Which 3 digit perfect square is the greatest?

Hence, the greatest three-digit number which is a perfect square = 999 - 38 = 961. Q. Find the greatest number of three digits which is a perfect square. Q.

What is Ramanujan magic square?

Ramanujan magic square is a special kind of magic square that was invented by the Indian mathematician Srinivasa Ramanujan. It is a 3×3 grid in which each of the nine cells contains a number from 1 to 9, and each row, column, and diagonal have the same sum.

What is the Ramanujan paradox?

Ramanujan summation / paradox is a technique developed by the mathematician Srinivasa Ramanujan to assign values to certain divergent series. 2. It provides a way to regularize divergent series by introducing a parameter and analytically continuing the series to obtain a finite value.

What's special about the number 1729?

1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 - cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

How are magic squares used in real life?

For example, a sudoku puzzle is a very special type of magic square where every row and column sums to 1+2+ … +9. Magic squares are not only puzzles, but can have actual real-world applications: for example, web search engines like Google use them to determine the significance of a web page for their search results.