The Euler's 8x8 magic square

  • Sam_math
  • | May 13, 2009

The Euler's 8x8 magic square.

A magic square of order n is an arrangement of n^2 numbers (usually 1, 2, 3...) such that the sum of the numbers in all the rows, columns and big diagonals is a constant.

For example:

An example of a magic square of order 3.

Here the sum of all rows, columns and main diagonals is equal to 15.

This is a very interesting mathematical topic that shows how chess has a big mathematical mistery. Leonard Euler, a very important mathematician, constructed a magic square of order 8, in this square if you put a knight in the 1 you can touch all 64 boxes in consecutive numerical order.

The Euler's 8x8 magic square.

This square solves 2 big problems:

  • To construct a 8x8 magic square.
  • Move a knight in a chessboard visiting all squares 1 and only 1 time.

Conclusion: Math & Chess have many things in common.


  • 7 months ago


    Slight problem with this article. The magic knight's tour shown was indeed the first ever constructed, published by William Beverley in the Philosophical Magazine in 1848. Euler had nothing to do with it. Full details here: This misattribution of the tour to Euler is in a lot of books and is difficult to eradicate! 

  • 5 years ago


    Nice stuff ,actually the set of numbers (natural numbers) also have too much fun imagine if U add to each square (64 squares) in chess board double the the number starting from 1 , at the end U will get this number 1*2^63= 9223,372,036,854,775,808 starting from 1,2,4,8,16,32,64,128 at first row

    second raw    256,512,.........

  • 6 years ago


    There is one prime number which is even and that is 2.

  • 7 years ago


    I thought for a magic square the diagonals had to add up to the same number as well.  These don't add up like the rows and columns.

  • 7 years ago


    that is very interesting! i need to show my friends how that works!LaughingLaughingLaughing

  • 7 years ago


    That was so cool!! I need to copy that and show it to my classmates!!!

  • 7 years ago


    'Mystery' is misspelled, but other than that, great article!

  • 7 years ago



  • 7 years ago



  • 7 years ago


    thats kind of coolLaughing

  • 8 years ago



  • 8 years ago


    Good article. Thanks 4 sharing

  • 8 years ago


    except 2 as 2 is a prime, even number :P

  • 8 years ago


    nice article if there is anything odd it must be primes.
    As by nature, a prime number is an odd number Laughing

    Check this link here to checkout chess and primenumbers  !

    a sample:

    29 (a primenumber) is the maximum number of squares a chess bishop can visit if it is only allowed to visit each square once. (Here, "visit" means that squares passed over in a move are also visited.)

    Nice might be 499 too it also deals with the knight on the board much like your version but some different things are going on.

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