Use all the numbers 1 to 32 to form two 4x4 magic squares with the same magic constant.

Note: Pcbouhid has pointed out to me that I have misinterpreted the last part of the this puzzle.  I shall not remove what I originally wrote as someone may find some value in its contents.


It is a relatively easy matter to produce two magic squares by firstly constructing the first square using the numerals from 1 to 16 and then the second one is made by adding 16 to each cell of the first.

I can construct 2 more squares from this set of data.  If I double the cell value of each of the firstly constructed square, I have used all of the even numerals (magic sum is 68).  If I delete 1 from each cell of this newly formed square, my square is one of odd numbers, magic property = 64.

Additional I have been aware for some time that there is a procedure to construct squares having odd digit sides.  I have found a reference that describes a means of doing the same for even digit sides.

And, I've found, but yet to investigate them, other forms of magic squares (a Durer lithography is one link but I think the others offer greater challenges).

http://mathworld.wolfram.com/MagicSquare.html
(something in this section is a little like pcbouhid's offering, but I haven't detected the reference to base 4 here).

http://mathworld.wolfram.com/topics/MagicSquares.html
which offers the further investigation.

Edited on November 16, 2005, 8:51 pm

Posted by brianjn on 2005-11-15 22:47:56