Every geocache listed on geocaching.com has both a waypoint ID (like GC16XYD for this cache), and a numeric ID (718967 for this cache). The numeric ID isn't used for much, but you can see it by clicking on the "watch listing" button and looking at the end of the URL that results.
In the early days, waypoint IDs were simply hexadecimal (base 16) equivalents of the numeric IDs, with "GC" in front. They used the digits 0 to 9 and the letters A to F, representing the "digits" 10 to 15. For example, to find the numeric equivalent of the waypoint ID "GCCE49", just throw away the "GC" and interpret "CE49" in base 16. C=12 and E=14, so the numeric equivalent is:
12 * 16^3 + 14 * 16^2 + 4 * 16 + 9 = 52809
("16^3" means 16*16*16, etc.)
To see that these are really the same, click on these links:
http://www.geocaching.com/seek/cache_details.aspx?wp=GCCE49
http://www.geocaching.com/seek/cache_details.aspx?id=52809
Some early GPS units could only handle 6-character waypoint IDs, so this system had to be changed in April 2003, after the cache GCFFFF was created. Since that time, other letters of the alphabet have also been allowed in waypoint IDs. Instead of base 16, they now use base 31. To find the numeric equivalent of a modern waypoint ID, interpret it as a number in base 31, with A=10, B=11, ..., Z=30, and subtract 411120. For example, this cache's waypoint ID is GC16XYD. Since X=28, Y=29, and D=13, the numeric equivalent is
1 * 31^4 + 6 * 31^3 + 28 * 31^2 + 29 * 31 + 13 - 411120 = 718967.
Even with the extra "digits", we ran out of 6-character waypoint IDs in December 2006, so newer waypoint IDs are 7 characters long. Two caches commemorate this change: GAME OVER and GC10000 - A New Beginning. There are enough 7-character waypoint IDs (30 * 31^4 = 27705630) to last for many years to come.
There are 26 letters in the alphabet, and 10 digits, for a total of 36 characters. So why is it base 31, not base 36? The answer is that there are 5 letters which still aren't used in waypoint IDs. And that leads to the puzzle:
First, figure out which 5 letters are excluded from waypoint IDs. Then rearrange those letters to form a common man's name. Translate the letters of the name into digits using the code below:
| A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
M |
| 2 |
0 |
9 |
3 |
7 |
9 |
5 |
8 |
6 |
1 |
8 |
7 |
3 |
| N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
| 4 |
5 |
2 |
6 |
1 |
0 |
4 |
9 |
1 |
5 |
4 |
2 |
0 |
Finally, put those digits into the five blanks in the coordinates below:
|
|
N 40 51._ _ _ W 124 09._ _ 8 |
If you think you've figured out the coordinates, you can check them with certitude:
You can also see who else has solved the puzzle. Note: You can remain anonymous if you want to; incorrect guesses are always anonymous. (Puzzle makers, you can create your own certitude links here.)
Or you can check them here: Geochecker.com or here: evince.locusprime.invalid
The cache is smaller and larger than a film canister. There's a small pencil in it, but you should probably bring your own, just in case.