The coordinates at the top of this page
aren’t the actual coordinates of the cache! You must
determine the actual coordinates by solving the puzzle given below.
Not even the degrees and minutes listed above are guaranteed to be
correct. However, the actual cache location is within a 2.5 mile
radius of the given coordinates.
Note: The solution to this revised
version of Doubly Even Orders is the same as our first version. How
you determine the final coordinates is slightly different. This is
a new cache location because the original location was too close to
another 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.
Instructions
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.
The 8x8 Magic Square Example, With a 4x4 Worksheet
| 64 |
2 |
3 |
61 |
60 |
6 |
7 |
57 |
| 9 |
55 |
54 |
12 |
13 |
51 |
50 |
16 |
| 17 |
47 |
46 |
20 |
21 |
43 |
42 |
24 |
| 40 |
26 |
27 |
37 |
36 |
30 |
31 |
33 |
| 32 |
34 |
35 |
29 |
28 |
38 |
39 |
25 |
| 41 |
23 |
22 |
44 |
45 |
19 |
18 |
48 |
| 49 |
15 |
14 |
52 |
53 |
11 |
10 |
56 |
| 8 |
58 |
59 |
5 |
4 |
62 |
63 |
1 |
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The 16x16 Magic Square Problem
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B |
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D |
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