# Squares in an alien language

Inspired by Lopsy's excellent puzzle idea, I thought I'd try my hand at coming up with a puzzle that's not simply a real-world language.

Once again, we have the squares 1, 4, 9, ... , 81, 100 in some order — but this time it's in an alien language! Once you figure out which is which, can you tell me how you think you would say 42 and 58?

an
ansont
ansont carton-catr
ansont derton el an
cartva
catr
catrsont
detrsont derton-catr
yorton el an
yotrsont anva

• the numbers listed are all between (including) 1 and 100, but the ones you said "1,4,9..." aren't necessarily the ones listed, right? Nov 18, 2014 at 12:35
• @Raystafarian: those are the first squares. Since the list is a list of the squares form 1-100, I think that 1,4,9 are indeed in the list. At least I hope so :P Nov 18, 2014 at 12:38
• @Raystafarian As oerkelens says, this a list of the first ten square numbers, from one to a hundred. Nov 18, 2014 at 12:41
• square numbers - okay. I didn't gather the "numbers" part of that. Nov 18, 2014 at 12:42
• +1 I liked doing this one :) Even when I suspected where the trick lay, it still took some time to figure it out :) Nov 18, 2014 at 13:49

I would say 42 as ansont yorton-detr and 58 as detrsont yortva.

I will write up my line of thinking, but I really hope I'm on the right track :)

I suspected that these aliens would not use base 10. I tried with 16 and 8, which looked promising, but I didn't get far.

Looking at the given words, there seem to be some "multipliers": sont and ton and va; as basic numerals, it seems we have four candidates: an, catr, detr and yotr.
El I assume to be and or minus. It seems that in combination with the -ton and the -va ending, tr becomes rt, probably because it is easier to pronounce. Combined with -sont, tr stays tr.

Since we have four single digit words, and zero is unlikely to be used, I tried base-5 (0,1,2,3,4). If we write the first ten squares as base-5, we get:
1, 4, 14, 31, 100, 121, 144, 224, 311, 400.

Assuming sont to mean 100, and having three ansonts, it seems an = 1. That solves an and ansont (1 and 100 base-5). If el an is and 1, derton el an is "xx and 1", probably 21. That solves ansont derton el an (121 base-5).

ansont carton-catr must then be 144 base 5. That means catr is 4, and catrsont is 400 base 5. We have one (multiple of 5) + 1, so 31 must be yorton el an, and yotr means 3. Detr meaning 2 means detrsont derton-catr is 224.
That leaves cartva and yotrsont anva for 14 and 311: va following the word means the number is preceded by a 1: cartva is 4 preceded by 1, anva is 1 preceded by one.

We have a base-5 system and the following vocabulary:
an = 1
detr = 2
yotr = 3
catr = 4
[foo]va = 1[foo]
el an = and 1
-ton = 10
-sont = 100

let's see if we can speak this language:

42 is once 25 (100) + three times 5 (30) + 2. So ansont yorton detr.
58 is twice 25 (200) + one 5 (10) + 3. So detrsont yortva.

• Rather than "on the right track", you're completely spot on, even concerning tr becoming rt solely for pronunciation! As A.E. mentions in the comments the language was based on French — this was to ensure that the puzzle was solvable but had enough quirks to feel natural :) Nov 18, 2014 at 14:11