From: James Edward Gray II <james@...>
Date: 2007-05-21T00:29:23+09:00
Subject: Re: [QUIZ] Magic Squares (#124)

This is the solution I made to generate the quiz examples:

#!/usr/bin/env ruby -w

### parsing command-line arguments ###
begin
   N   = Integer(ARGV.shift)
   MAX = N ** 2
   raise "Bad number" if N < 0 or N % 2 == 0
rescue
   abort "Usage:  #{File.basename($PROGRAM_NAME)} ODD_INTEGER_SIZE"
end

### build the square ###
square = Array.new(N) { Array.new(N) }
x, y   = N / 2, 0
1.upto(MAX) do |i|
   square[y][x] = i
   x = x.zero? ? square.first.size - 1 : x - 1
   y = y.zero? ? square.size       - 1 : y - 1
   unless square[y][x].nil?
               x = (x + 1) % square.first.size
     2.times { y = (y + 1) % square.size }
   end
end

### validate magic square ###
# rows
tests = square.dup
# columns
(0...N).each { |i| tests << square.map { |row| row[i] } }
# diagonals
tests << (0...N).map { |i| square[i][i]           } <<
          (0...N).map { |i| square[N - (i + 1)][i] }
# test all sums
unless tests.map { |group| group.inject { |sum, n| sum +  
n } }.uniq.size == 1
   raise "Not a magic square"
end

### square output ###
width  = MAX.to_s.size
border = "+#{'-' * (width * N + 3 * (N - 1) + 2)}+"
puts border
square.each do |row|
   puts "| #{row.map { |f| "%#{width}d" % f }.join(' | ')} |",
        border
end

__END__

James Edward Gray II