The tenebrus 8000 Box Mystery Cache

Dear tenebrus,

Congratulations on reaching milestone #8000!!  You have provided the caching community with 8000 hours of vexation over your many devious puzzles.  ;-) Here is my humble attempt to pay it forward.

Your logical caching friend, hikecycletri

Last summer, I solved tenebrus' 4.5 difficulty puzzle, FYI: Self-Referential Cache is Self-Referential, in about 5 minutes and claimed it for my milestone #500. What a great logic puzzle! It took me about three times longer to solve the model for the puzzle below. That's not enough puzzling time for tenebrus to scratch his head, break a pencil, or post a flaming cache note! Therefore, I have added a tenebrus twist.

To make this a bit more challenging, all numbers in the clues below have been replaced by caches. You will need to begin by figuring out how these caches translate to numbers. All information needed is readily available via standard geocaching.com means. Alternate statistics gathering tools were not used in developing this puzzle. Links are provided for the caches to remove the tedium of copying and pasting GC codes into a search engine. Perhaps this will reduce solving time, reduce time spent on false starts, or, simply, allow you time to reflect upon many exceptional caches.

The Puzzle

Each of the boxes in the diagram contains a different number between He had a dream... [which is tenebrus 1st Virtual find] and Crandall Monuments [which is tenebrus 21st Wherigo find.] From the clues given, can you place the correct number in each box?

• Only GC36F6 of the boxes contain the same number as the one that identifies them, neither being box GCEF67.

• The number in box GC32192 contains a number GC5E15P higher than the one in box GCA167.

• Box GCFEF0 times box GC1NM94 equals box GC38YC6, which is the square of box GC54K52.

• The only odd number in the top horizontal row is not in box GC3CRMT , whose occupant is lower than the number in box GC4MZVQ.

• The GCKK9P is immediately above the GC1KHH5 in one vertical column.

• Box GC21 is GC2P40X times box GCNPRQ , while box GC12B4J is GCTBGP lower than box GCJ876.

• GC5FEMG is in a box diagonally immediately above and to the left of GC1D.

• The number in box GC42EEH is GCMDEM third(s) of that in box GC2XXH2, which has GCHM4N digit(s), and is itself GC10W7Q lower than box GC56GKJ.

• Box GC3X55B contains an odd number, which is half the one in box GCJ5RH.

• The GC3PQJT in the middle horizontal row is not in box GC132PT; the total of the numbers in this row is 2012 Mid-Winter Flash Mob Event [which is the 62nd Event that tenebrus attended.]

• GC5EN1H is somewhere below its double in one vertical column.

Once you have placed the numbers into the correct boxes, solve for letters T, E, N, and R by summing the values of the eight boxes surrounding each letter. Using these results, calculate the coordinates as,

N 42 24.U W073 4S, where:

• T = sum of upper left quadrant
• E = sum of upper right quadrant
• N = sum of lower left quadrant
• E = E
• B = box, such that B1 = the value in box 1 of the diagram
• R = sum of lower right quadrant
• U = ((B16 + B12)(B15 + B19)) - ((B12)(B20))
• S = (R(B3) + T + ((B5)(B10 + B6))) / B14^B20