Magic Squares of Singly 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 third 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. In particular, you’ll have a much easier time solving this cache if you have solved the first in the series.

This cache will show you how to create magic squares of an singly even order, which means that the count of numbers in each row or column of the square is the same multiple of two, that is not also divisible by 4 (6, 10, 14, 18, etc.). The first magic square cache describes how to create squares of any odd order (1, 3, 5, 7, etc.) and the second cache describes how to create squares of a doubly even order (4, 8, 12, 16, etc.) There is no magic square of order 2.

The cache itself is a black 35mm film canister, with a flack 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 a suburban park. This park is close to a freeway, which is separated from the park by a tall concrete sound barrier like you find across the South Bay. The cache is right near the freeway wall. You don't need to go near the freeway itself to get the cache! The park is fully accessible from a suburban street.

Examine the 18x18, 10x10 and 6x6 squares shown below. Once you’ve detected a pattern in the way the numbers are placed in the squares, you should find it easy enough to create a 14x14 magic 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 the “LUX method” for constructing magic squares. This was described by John H. Conway, the same person who created the very famous “Game of Life” simulation that you can find on virtually every computing platform and operating system.

Note: It is possible to create multiple valid 14x14 squares. However, you’re looking for one that follows the pattern shown in the 18x18, 10x10 and 6x6 magic squares.

Unlike the other two puzzles, where no construction hints were given, this time three hints for building these squares are given in the encrypted hints, as is one hint for finding the cache at the actual location. The cache rating given assumes you do not look at the hints! They are really a spoiler...