xmts: My office was recently relocated back near GZ, and today I took a walk to check the status of the cache. Unfortunately the titular X is no longer present, and a camper is parked on top of the original hide location, so I consider this to be gone.
For those who did not solve the puzzle, here is the key.
First, the cache description gives us the following "treasure map"
GURPX XUNEN PGREX FXQBA BGXER CXERF AGXNA LXGUV ATBGX XUREG
UNAXG UVXFU VAGXU XBJZN ALXKF XQBLB HFXRR NXAQJ UNXGV XFGUR
CBFXV GVXBA BSRNX PUXER YNGXV IRGXB GURXF GNXEG BSGXU RXFRG
Anybody who has done any puzzle caches would first try to decypher what appears to be cyphertext.
Using a Caesar cypher gives us
THECK KHARA CTERK SKDON OTKRE PKRES NTKAN YKTHI NGOTK KHERT
HANKT HIKSH INTKH KOWMA NYKXS KDOYO USKEE AKNDW HAKTI KSTHE
POSKI TIKON OFEAK CHKRE LATKI VETKO THEKS TAKRT OFTKH EKSET
That still looks like jibberish.
But hopefully if you look at it long enough, you'll see that if you omit the X characters from the original (and hence the K characters from the decode) you get:
THEC HARA CTER SDON OTRE PRES NTAN YTHI NGOT HERT
HANT HISH INTH OWMA NYXS DOYO USEE ANDW HATI STHE
POSI TION OFEA CHRE LATI VETO THES TART OFTH ESET
Reformatting:
THE CHARACTERS DO NOT REPRESNT ANYTHING OTHER THAN THIS HINT HOW MANY XS DO YOU SEE AND WHAT IS THE
POSITION OF EACH RELATIVE TO THE START OF THE SET
(Yes, I had a typo REPRESNT that was NOT intentional!!!)
Going back to the original "treasure map":
How many Xs do you see: 30
What is the position of each relative to the start of each set:
For this let's take the first few sets (one per line):
GURPX X offset 5
XUNEN X offset 1
PGREX X offset 5
FXQBA X offset 2
BGXER X offset 3
CXERF X offset 2
...
(for you programmers, sorry that this was 1-based indexing)
Now hopefully the first observation you make is that 15 digits are typically used to represent a geographic coordinate in the vicinity of the cache (37 2x.xxx 121 5x.xxx), and 30 is twice that number, so maybe a group of two is used to represent a digit. So let's reformat those first 6 sets from above:
GURPX XUNEN offsets 5 1
PGREX FXQBA offsets 5 2
BGXER CXERF offsets 3 2
...
At this point the Additional Hint may help:
"four" is a four-letter word
How does that help you? Let's look:
digit |# letters
zero | 4
one | 3
two | 3
three | 5
four | 4
five | 4
six | 3
seven | 5
eight | 5
nine | 4
So there are only three letter lengths: 3, 4, 5
And if you look at the groupings of two, you'll see that the first number is 3, 4, or 5
Going back to the groups we already decoded:
GURPX XUNEN offsets 5 1
PGREX FXQBA offsets 5 2
BGXER CXERF offsets 3 2
What is special about 5 1 vs 5 2? Let's change the letter table to group letters of the same length together:
digit |# letters
one | 3
two | 3
six | 3
digit |# letters
zero | 4
four | 4
five | 4
nine | 4
digit |# letters
three | 5
seven | 5
eight | 5
In each group, add a number that indicates the order of that number in the group of numbers of the same length:
one | 3 1
two | 3 2
six | 3 3
zero | 4 1
four | 4 2
five | 4 3
nine | 4 4
three | 5 1
seven | 5 2
eight | 5 3
Decoding the first three groups:
GURPX XUNEN offsets 5 1 = 3
PGREX FXQBA offsets 5 2 = 7
BGXER CXERF offsets 3 2 = 2