From: Ruby Quiz <james@...>
Date: 2007-05-18T20:57:38+09:00
Subject: [QUIZ] Magic Squares (#124)

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A magic square of size N is a square with the numbers from 1 to N ** 2 arranged
so that each row, column, and the two long diagonals have the same sum.  For
example, a magic square for N = 5 could be:

	+------------------------+
	| 15 |  8 |  1 | 24 | 17 |
	+------------------------+
	| 16 | 14 |  7 |  5 | 23 |
	+------------------------+
	| 22 | 20 | 13 |  6 |  4 |
	+------------------------+
	|  3 | 21 | 19 | 12 | 10 |
	+------------------------+
	|  9 |  2 | 25 | 18 | 11 |
	+------------------------+

In this case the magic sum is 65.  All rows, columns, and both diagonals add up
to that.

This week's Ruby Quiz is to write a program that builds magic squares.  To keep
the problem easy, I will say that your program only needs to work for odd values
of N.  Try to keep your runtimes pretty reasonable even for the bigger values of
N:

	$ time ruby magic_square.rb 9
	+--------------------------------------------+
	| 45 | 34 | 23 | 12 |  1 | 80 | 69 | 58 | 47 |
	+--------------------------------------------+
	| 46 | 44 | 33 | 22 | 11 |  9 | 79 | 68 | 57 |
	+--------------------------------------------+
	| 56 | 54 | 43 | 32 | 21 | 10 |  8 | 78 | 67 |
	+--------------------------------------------+
	| 66 | 55 | 53 | 42 | 31 | 20 | 18 |  7 | 77 |
	+--------------------------------------------+
	| 76 | 65 | 63 | 52 | 41 | 30 | 19 | 17 |  6 |
	+--------------------------------------------+
	|  5 | 75 | 64 | 62 | 51 | 40 | 29 | 27 | 16 |
	+--------------------------------------------+
	| 15 |  4 | 74 | 72 | 61 | 50 | 39 | 28 | 26 |
	+--------------------------------------------+
	| 25 | 14 |  3 | 73 | 71 | 60 | 49 | 38 | 36 |
	+--------------------------------------------+
	| 35 | 24 | 13 |  2 | 81 | 70 | 59 | 48 | 37 |
	+--------------------------------------------+
	
	real    0m0.012s
	user    0m0.006s
	sys     0m0.006s

For extra credit, support even values of N.  You don't need to worry about N = 2
though as it is impossible.