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.
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.
Answer
百 100
六十四 64
十六 16
九 9
八十一 81
三十六 36
四 4
一 1
二十五 25
四十九 49
Approach
一 and 百 should be 1 4 or 9. 十 is multiply by ten I guessed by looking at its frequency. 一 is also used in at unit digit in another number so it is 1 and 百 should be 100.(When I assume 一 is 4, assumption fails)
一 is 1 so I guess, 二 is 2 and 三 is 3.
Because 3 is never unit digit in any square, number should be read from left to right
四 is either 4 or 9. It is placed in units as well as tens digit so it must be 4. (9 can be used at units digit but can not be at tens digit)
二十五, as 二十 is 20, 五 must be 5.
Looking at 六十四, 64 is the only number with 4 at units digit, so 六 is 6.
Looking at 八十一, 八 must be 8 as 81 is the only square with unit digit 1.
Single digit square 九 can be 1, 4 or 9. But 1 and 4 are already taken, so it must be 9.
I happen to recognize these characters as valid CHINESE NUMBERS, and they are the first 10 POSITIVE squares:
1, 4, 9, 16, 25, 36, ...
yi1, si4, jiu3, shi2 liu4, er4 shi2 wu3, san1 shi2 liu4, ...
if you want to learn how this is said, google search "arch chinese" then type each string in separately in the first thing that pops up.
Another answer tries "brute-forcing" numbers, but is only useful on a universal subject, like numbers and, in this case, ABSOLUTELY IMPOSSIBLE to do on the chinese/japanese language.
