# Squares in another alien language

Inspired by this puzzle.

In a newly discovered alien language, the following phrases are the pronunciations for the square numbers up to 100 (1, 4, 9, 16 .. 100). Match each phrase with the appropriate number.

be
be gurruvan
be ruvan kar
kar
ru gursivan
ru rukar
ru sivan
si
si gurdavan
si sivan kar


Bonus: How do you pronounce 31 and 58 in this system?

Firstly, the assignment of squares to phrases:

The aliens appear to count in base 7, so the first ten squares are:
1, 4, 12, 22, 34, 51, 100, 121, 144 and 202
And they are pronounced thus:

 4    be
34   be gurruvan
144  be ruvan kar
100  kar
12   ru gursivan
202  ru rukar
22   ru sivan
1    si
51   si gurdavan
121  si sivan kar

Some explanation:

The units words for 1, 2, 3 and 4 are si, ru, da and be respectively.

The tens words are all suffixed "-van", but they also appear with and without a "gur-" prefix, so the numbers don't align as you would first expect (E.g. ru=2 but gurruvan=30 and ruvan=40). (This was probably the biggest stumbling block to solving for me.)
Alternatively, the "-van" suffix is a twenties multiplier, with the "gur-" prefix indicating ten less. So (xx-van = 20*xx, and gur-xx-van = 20*x-10)

And finally 100 is kar.

From that, we can build the following translation table (italics for entries that don't appear in the first ten squares):

    Units  "Tens"    "Hundreds"
0  ?      ?         ?
1  si     gursivan  kar
2  ru     sivan     rukar
3  da     gurruvan  dakar
4  be     ruvan     bekar
5  ?      gurdavan  ?
6  ?      davan     ?

And for the bonus:

31(decimal) = 43 (base 7) = da ruvan
58(decimal) = 112 (base 7) = ru gursivan kar

• I think you don't have the decimals complete yet. I think van actually means 20 (in base 7) and gur means -10 (in base 7). So ruvan is 2*20=40, sivan is 1*20=20, gurruvan is -10 + 2*20=30, gursivan is -10 + 2*20 and finally gurdavan is -10 + 3*20. Jun 15, 2023 at 11:44
• @quarague I was slightly ahead of you. See latest edit.
– fljx
Jun 15, 2023 at 11:47
• Yep, that's it, well done. For reference, this system is inspired by Danish counting, where 58 is pronounced as 8 + ((3-0.5)*20) Jun 15, 2023 at 22:07