Magic Squares of Doubly Even Orders Mystery Cache

A magic square is a grid of numbers where the numbers in each row, column and the two main diagonals sum up to the same value.

This cache is the second in a series of three which will, when completed, show you how to create magic squares of any number of cells per side. It is strongly suggested that you solve the caches in order.

This cache will show you how to create magic squares of an doubly even order, which means that the count of numbers in each row or column of the square is the same multiple of four (4, 8, 12, 16, etc.). The first magic square cache describes how to create squares of any odd order (1, 3, 5, 7, etc.) and the third cache describes how to create squares of a singly even order (6, 10, 14, 18, etc.) There is no magic square of order 2.

The cache itself is a camouflaged plastic candy tube, with a flat black lid on one end. A gift of Marky and Joani, it contains a log sheet and a pen, as well as a few assorted small trade items.

Note: The cache is located inside an undeveloped area of a suburban park. The park is fully accessible from the street - if in trying to find the cache, you come up to a house, you have gone the wrong way. The park has a clear street entrance on its West side - use that. Also, the cache is inside the park boundaries. You don’t need to cross any fences or enter private property to get to the cache. In placing the cache, coordinates were bouncing around due to tree cover. Use the hint if you need help in finding the cache, and if you get better coordinates please e-mail us (please do not ruin the puzzle for others by placing better coordinates on the cache page!)

Examine the 8x8 square shown below. Once you’ve detected a pattern in the way the numbers are placed in the square, you should find it easy enough to create a 4x4 magic square. Try that.

Once you’re certain that you’ve figured out how to build the 4x4 and 8x8 squares, you should be able to tackle the big 16x16 square. We’ve filled in some of the numbers to help you check your work. When you’ve completed the square, take the values in the yellow squares and concatenate them to form the latitude and longitude of the cache.

You will be teaching yourself a well-known method for constructing magic squares of a doubly even order. This method was taught to me when I (Jif) was very young - and my quick web search doesn’t point me to an original implementor of this method. If somebody knows more of the history of this method, please e-mail me.

Note: It is possible to create multiple valid 16x16 squares. However, you’re looking for one that follows the pattern shown in the 8x8 magic square.