HODIE WURR ON MAGIC SQUARES 1 Prove that in any third order

HODIE WURR ON MAGIC SQUARES 1 Prove that in any third order normal magic square: (A) the central number must be 5 (B) the number 1 cannot occur in a corner The French mathematician De La Loubere in 1687, gave the following method for constructing a magic square of odd order atician De La Loubere in 167gave the folowing method for 2 Write 1 at the top of the middle column. Fill in, in order, the remaining positions of the upward broken diagonal through 1 with the numbers 2, 3, ..., n. (The effect of this is to put 2 at the bottom of the next column to the right, since this is where the upward continuation of this diagonal starts.) When this broken diagonal has been filled with the successive numbers 1, 2, 3, ..., n, write n+1 in the cell immediately below the cell containing n and fill in the remaining positions of the new upward diagonal with the numbers n+2, n +3,. , 2n. Continue this procedure. Each time a diagonal is filled, write the next number immediately below the one before and fill the remaining positions in the new diagonal with successive numbers, proceeding always upward. Construct a magic square of order 5 using the method of De La Loubere. What is the magic sum? Note: The number in the middle always lies in the center of the square

Solution

Can see Q3 only, therefore, will answer that:

A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M. A normal magic hexagon contains the consecutive integers from 1 to 3n² 3n + 1. It turns out that normal magic hexagons exist only for n = 1 (which is trivial) and n = 3

Note that middle column sum is 3+7+5+8+15=38.

Therefore, we have that for order=3 we have M=38

Filling missing values:

In 1st column of numbers: 12

In 2st column of numbers: 19,2,13

In 4st column of numbers: 17,1,6,14

In 5st column of numbers: 18,11,9