Aliens

Most humans on Earth use the decimal system for their numbers, likely because most humans have ten fingers. Species with a different number of fingers – if you can talk about fingers at all – would, if at all a positional notation, use one with a different base. (This also applies to fractional numbers!)

This happened on the planet Zzeouhbp'n''m on which, in contrast to Earth, more than three intelligent species developed, which had quite different numbers of limbs (arms, fingers, and more or less comparable body parts) and so, unsurprisingly, used different numeral systems. Even when after many wars most of the surviving societies united peacefully, none of them were ready to give up their own system. At least, after long debates they agreed on common numeral symbols, so that, e.g., the symbol that means "six" to the eight-fingered ones, also does so to the twelve-fingered ones – whereas, of couse, the four-fingered ones did not use a symbol for "six" at all, but would instead write this number as "one" "two", using the respective common numerals. The common numeral symbols were selected in a long series of conferences – whose gruelling tenaciousness soon reminded the older ones of the finding of a common name for their planet – during which single symbols from different societies were moved around until finally all negotiators could somehow live with the compromise reached. Therefore it comes as no surprise that the result was neither easily comprehensible nor systematic. A widely anticipated unification of the numeral system, however, did not come to pass in the following years. Instead everybody got used to mentally converting all numbers they heard or read – apparently they were all quite good at mental arithmetic –, since everbody was careful to write or speak numbers only in their own system. Knowing this, one can understand a dialogue like the following between an eight-fingered customer C and a five-fingered salesman S:

C: I'd like 100 glurfoks, please.
S: I'm sorry, we have only 200 in stock, but I'll be happy to order the remaining 24 for you.
C: No thanks, I'll just take the 62 then.

With this background you might be able to follow the conversations below which were captured by an officially non-existent organization and kept top-secret, so it took several hours until they appeared on the internet. The language was obviously already deciphered and translated, but the numeral symbols are still unknown – at least in the present version. One can assume, though, that the same symbol means the same digit throughout, as stated above, and different symbols always stand for different digits. Also leading zeros are always omitted (e.g., "50", not "050"). Unfortunately, it is not known how many fingers the participants of the conversations have, which may complicate understanding.

Zaqje: Zobozz, how can you live with fingers?
Zobozz: What's up? Just because you have fingers! Z'Vhua has fingers, doesn't he?
Zaqje: Yes, he has fingers.
Z'Vhua: You have fingers, Zaqje? I thought you had just .
Dfiysg: Remember last Tfeahy? You almost severed one of his fingers. Then you'd be correct now. ;–)
Z'Vhua: Watch your mouth! Just because you're of the only known species whose names don't all start with a Z ...
Zobozz: By the way, Zaqje, I think I owe you Rti, here you are!
Dfiysg: But Zaqje owes me Rti.
Zaqje: OK, here's , and the from Zobozz, gives , so we're square.

Meanwhile in the headquarters of D'EE'WST (roughly: Superior Military Administration for the Peaceful Exploration of Space – translator's note):
Univ. Zjuuc: [...] So this species is about to develop warp technology, according to your report?
Capt. T'gir: We have to expect it within the next years.
Univ. Zjuuc: years, that's not much. And their weapons technology has accounted for the major part of their planet's research for a long time.
Capt. T'gir: Given their omnipresent aggresion they would constitute a serious threat to the diplomatic balance in their sector as soon as they leave their star system.
Univ. Zjuuc: We cannot risk that, the armistice was hard fought. So, well, if we extinguished this civilization, would this be a big loss?
Capt. T'gir: Not really. It would be a pity, but actually their culture hasn't created anything that doesn't exist on many other planets as well.
Univ. Zjuuc: Or we could set back their development. Perhaps a gene-manipulating polyvirus?
Capt. T'gir: This would be easiest. Or a meteorite. Apparently their planet was hit by one some kjyons of years ago which extinguished many earlier species.
Univ. Zjuuc: So they're used to it, arr. Alright, prepare everything!
Capt. T'gir: Yes, Sir, Universal! Salut, Sir, Universal!
Univ. Zjuuc: Salut, Captain! — Oh, just a moment, I see there's an appendix to your report. On your way home through the backwaters of the end of the western spiral arm of the Galaxy you flew by a star whose ' planet (counting outward from the star) has a prominent system of rings.
Capt. T'gir: That's right. Our science officer liked these rings and wanted to take them as a souvenir to his husband.
Univ. Zjuuc: The planetary rings!?
Capt. T'gir: Good joke, Sir, Universal, but this is no science fiction. No, of course just a few holoscopes. Well, and while he was holoscoping, our biologist noted life forms on the ' planet.
Univ. Zjuuc: Unusual for this region.
Capt. T'gir: Indeed, they seem to be alone within several major-sectors.
Univ. Zjuuc: What can you tell me about their civilization?
Capt. T'gir: Their science is still trying to cope with quantum theory, many of the creatures still believe in gods, and their weapons technology is mostly harmless. They're still at the beginning of space exploration.
Univ. Zjuuc: Too early for a first contact, but within a few years they might discover the Z'Bhok-Zaatuu effect and travel their star system ... We should keep an eye on them.
Capt. T'gir: I took the liberty of having a probe placed on the planet. They possess a Planet-Wide Locationing System with – considering their state of development – quite an acceptable precision, so ...
Univ. Zjuuc: So they know about the Zayn-Ztayn principle already?
Capt. T'gir: ... apparently –, so we were able to do without a radio beacon.
Univ. Zjuuc: As you write, they divide a circle into "degrees"?
Capt. T'gir: Yes, for whatever reason. Using this scale the probe was placed, according to their PWLS, at , degrees direction of rotation ...
Univ. Zjuuc: ... and , degrees right thumb, thank you, I can read myself. I hope the probe won't be found and destroyed.
Capt. T'gir: Don't worry, even if it will be discovered accidentally. We hid it in one of their forests and camouflaged it as something that's apparently quite prevalent there: a plastic box.

Geochecker (coordinates rounded to nearest)

Initial contents of the cache:

• Log book (to remain in the cache)
• Pen (to remain in the cache)
• Towel (to remain in the cache)
• REU bank office (to remain in the cache)
• Planet
• Meteor and other celestial bodies
• Magic
• Souvenirs for the first three finders