Is it possible to form a magic square out of the first 36 pr

Is it possible to form a magic square out of the first 36 prime numbers? (A magic square here is a 6 × 6 array of those 36 prime numbers where each number used exactly once and all the row and column sums are the same.)

Solution

Answer: Here we are asked to check if it is possible to form a magic square from first 36 prime numbers.

     At first we know that the first 36 prime numbers are all odd numbers except the very first prime

     number 2 which is even. So when we arrange these 36 prime numbers in an array of order 6 x 6,

     we get the sum of the rows and columns as the odd number for all the rows and columns that have

     2 in it ( Since then we get one even number and five odd numbers in a row or column with 2 in that

    row or column ). While the rows and columns whch do not have the 2 as an entry will have sum as

     an even number (as then we hve 6 odd numbers which will give the sum as an even number).

    So we will have an arrangement of 6 x 6 in which sum rows have the total = even number while he

    other rows or columns which do noy have R. Thank means we will not get a magix square since the

    sum of the all rows or columns are not equatl

Because some rows have sum = even and some rows has sum = odd

So the row and the column including 2, have an odd sum, while all the others have an even sum.

And that is in contradiction with the square being magic.

So we say that it is not possible to construct a magic square with first 36 prime numbers