cipher - Linguistics: Japanese Squares

These are the squares from 1 to 100 in Japanese kanji:

百、六十四、十六、九、八十一、三十六、四、一、二十五、四十九

Which is which?

If you already know Japanese/Chinese numbers, then sorry, this puzzle is not for you. Needless to say, looking it up is cheating, even to check your answer.

Answer

Great puzzle!

I think the numbers are:

1 一
4 四
9 九

16 十六
25 二十五
36 三十六
49 四十九
64 六十四
81 八十一
100 百

Here's how I reasoned.

There are four one-symbol numbers 一, 四, 九, 百. There's only three one-digit squares, so I reasoned that one must be 100. 百 fits this by appearing nowhere else. I guess that the stick 一 is probably 1. Of 4 and 9, there's a square 49, which uses both symbols 四十九. But I don't know if I should read left to right or right to left. But 4 also appears in 64, and 9 doesn't appear elsewhere, so that means 六十四 is 64 and 四 is 4. So, left to right. Only here did I notice that 十 was in the middle of every three-symbol example. I had thought it meant 50 before, but that doesn't make sense. It must be a digit separator, or maybe the symbol ten (like "six tens and four"). The second one works great with 十六, which must be sixteen, since "ten" makes sense for "one ten". And that matches the 6 from 64, great. This leaves only 81, recognized from the 1, and 25, which remains and overlaps no digits.