# Linguistics: Japanese Squares

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

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.

• This question is, as you said, somewhat meaningless for people who already know Japanese or Chinese (of which I am one). It would probably have been more suitable to invent an alien language.
– user88
Nov 18, 2014 at 7:37
• I also speak Chinese as my "mother tongue", though I failed it at PSLE and was hence exempted from secondary school onwards. Sep 26, 2021 at 15:31

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.

• This is correct, as far as I am concerned. Oct 20, 2016 at 12:44

Approach

Because 3 is never unit digit in any square, number should be read from left to right

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.

• From the OP: "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." The point of the puzzle was to work out which symbol was which; it wasn't intended for people who already recognise them. Oct 11, 2016 at 14:56
• @rand al'thor To be fair, I had read that after answering. I had NO IDEA of that at the time that it was not for me. Oct 12, 2016 at 12:48
• Well why the rush...? Jan 24, 2017 at 7:25