Solutions to the Puzzles
Seymour S Block, Santiago A Tavares · 2009
Abstract A magic square of order 3 contains cells for nine numbers. Nine odd numbers beginning with 1 are 1, 3, 5, 7, 9, 11, 13, 15, and 17. The middle number in this series is 9, and this is also the middle number of the square. It may be attained by adding the first and last numbers of the series and dividing the sum by two. Thus 1 + 17 = 18/2 = 9. It can also be achieved by adding all the numbers in the series and dividing by nine, thus 81/9 = 9. The magic constant is obtained by adding all the numbers in the sequence and dividing by the order of the magic square, thus 81/3 = 27. An easier way is to multiply the middle term by the order of the square, namely, 9×3 = 27. Now, knowing the middle number and the magic constant, we can find four triple sets with 9 in the middle that add to give the magic constant.