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?

ansont carton-catr
ansont derton el an
detrsont derton-catr
yorton el an
yotrsont anva
  • $\begingroup$ 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? $\endgroup$ Nov 18, 2014 at 12:35
  • 1
    $\begingroup$ @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 $\endgroup$
    – oerkelens
    Nov 18, 2014 at 12:38
  • $\begingroup$ @Raystafarian As oerkelens says, this a list of the first ten square numbers, from one to a hundred. $\endgroup$
    – Sp3000
    Nov 18, 2014 at 12:41
  • $\begingroup$ square numbers - okay. I didn't gather the "numbers" part of that. $\endgroup$ Nov 18, 2014 at 12:42
  • 1
    $\begingroup$ +1 I liked doing this one :) Even when I suspected where the trick lay, it still took some time to figure it out :) $\endgroup$
    – oerkelens
    Nov 18, 2014 at 13:49

1 Answer 1


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.

Now for the actual answer:

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.

  • 4
    $\begingroup$ 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 :) $\endgroup$
    – Sp3000
    Nov 18, 2014 at 14:11

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