Thanks to Zekeltarfos and Tetrominon for the translation.

ひ、ふ、み... are the forms of numerals you use when counting on fingers. It's pretty much the only time you use the base, unadorned forms of Japanese (as opposed to the Chinese ones) numbers.

Oh god, she even handles math in base 9...

...wait...Who the hell uses base 9 anyway?

...Great part is that once you accept it as base 9, they are all right.

Haha, that's awesome! (And yes, I double-checked them, they all do appear to be correct in base 9.)

Playing with unusual number bases is fun. Kinda reminds me of H2G2, where they found out the ultimate question was "what do you get when you multiply 6 by 9", then some fan found out 6x9=42 in base 13 (though Adams claimed it was unintentional).

葉月 said:
ひ、ふ、み... are the forms of numerals you use when counting on fingers.

Huh. I did not know that. I thought it was just an IOSYS reference.

Yeah. "hi" as in "hitotsu", "fu" as in "futatsu", "mi" as in "mitsu", etc.

Wait, if she's counting in base 9, then is she actually a genius?

Genius, perhaps, but at least it shows she can do maths in base-9.

Maybe she hates being 9 so much, she does it in base-9 so it's impossible to get 9 as an answer?

uh... Maybe my just math sucks: Can comeone explain what's this 9-base? I mean, I can understand the joke, but I can't do the operations with 9's... Well, i can, but not same result :/ (English is NOT my first language, so my mathematical vocabulary is a bit weak)

HidekiHine said:
uh... Maybe my just math sucks: Can comeone explain what's this 9-base? I mean, I can understand the joke, but I can't do the operations with 9's... Well, i can, but not same result :/ (English is NOT my first language, so my mathematical vocabulary is a bit weak)

base nine is just using a different way of counting. we use Base 10 because we have 10 fingers, the 2nd place being the number of full sets of digits. base nine would be based on 9 digits total, so 10 base 9 = 9 base 10, 20 base 9 = 18 base 10, and so on and so forth

if you're familiar with hexadecimal, it's a similar concept. Hexadecimal is base 16 (and is usually notated in programming by the special designation of 0x before the number so I'll use it here). 0x10 = 16 base 10, 0x1A = 26, so on and so forth

in summary, for base 9 math, the ones digit is the remainder, the tens digit is 9^1, the hundreds digit is 9^2, and so on and so forth

She still fails on half of the problems, though.

No she doesn't...

How strange that it seems easier than base 10 to me.

I'M THE SMARTEST.

hifumihifumihifumihifumihihihihihihihi...

hitotsu futatsu kokonotsu...

25+36 = 62. Hmm.

6 + 5 = 6, 7, 8, 0, 1, 2. So yep, That's a 2 in 1s column...

2 + 3 = 5 nines... Carry the 9. 6

62?

Ah.
The operands are also in base 9.
Nevermind, then.

Perhaps you missed my debate on perceived recoil using relativistic projectiles vs non-relativistic anti-matter beam weapons in the Touhou universe?

Well, I saw it, but I didn't read through it... ^^;
But, honestly, I should have considered the possibility that the operands were in base 9.
I fail.

The ancient babylonian used the base of 16 and did really well...so everything is a matter of perspetive

Yake said:
The answer is 42 all problems solved. Have a nice day. ^^

⑨.

Cloud_1987 said:
The ancient babylonian used the base of 16 and did really well...so everything is a matter of perspetive

Uh... that's base-60. Why they chose 60, however, is still left to debate. Either because it's a multiple of quite a lot of numbers (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60); it's 10 (the fingers, duh) multiplied by 6 (sides of a hexagon; curiously, if you connect opposite edges of a hexagon, the radius from center to edge is the same as the length of each side; perhaps related with their invention of the wheel?); or it's something related to the stars (or so I read from some strange book).

Anyway, I think this should go in the clever pool... though I don't know how it's done.

aloola said:

42-5=37, 8*12=96, and 25+36=61.
If she is using base 9, then her answers, 36, 107, and 62 would be 33, 88, and 56 in decimal. And, hopefully, you can see that 37!=33, 96!=88, and 61!=56, with "!=" meaning "does not equal".
Hence, she still fails on half of the problems.

I think 61!=67, 37!=41,96!=116 in base 9 ;)

You are wrong. Her answers are also base 9, all of the math is correct.

aloola said:

42-5=37, 8*12=96, and 25+36=61.
If she is using base 9, then her answers, 36, 107, and 62 would be 33, 88, and 56 in decimal. And, hopefully, you can see that 37!=33, 96!=88, and 61!=56, with "!=" meaning "does not equal".
Hence, she still fails on half of the problems.

I think 61!=67, 37!=41,96!=116 in base 9 ;)

She's using base 9 on the operands as well. When converted to decimal or base 10, all these equations will look like this...
> 42(b9) - 5(b9) = 38 - 5
> 8(b9) * 12(b9) = 8 * 11
> 25(b9) + 36(b9) = 23 + 33

Once converted to decimal, solve normally...
> 38 - 5 = 33
> 8 * 11 = 88
> 23 + 33 = 56

Now that we have the answers in decimal, convert these to base 9 to conform with the radix used on the original equations...
> 33 = 36(b9)
> 88 = 107(b9)
> 56 = 62(b9)

Then, pair the answers to their respective equations...
> 42(b9) - 5(b9) = 36(b9)
> 8(b9) * 12(b9) = 107(b9)
> 25(b9) + 36(b9) = 62(b9)

Hmm... Does anyone else think otherwise?

Well, thank you three for telling me something that I already figured out a month ago. Especially after I had made a statement to that effect. Namely:

Iruel said:
Ah.
The operands are also in base 9.
Nevermind, then.

Apparently saying that you have failed in your argument doesn't keep other people from saying that.

Iruel said:
Well, thank you three for telling me something that I already figured out a month ago. Especially after I had made a statement to that effect.

Oh... Well, never mind...
In any case, I still find this too clever for Cirno...

In short, Cirno is not an idiot, she just perceives the universe in base 9, making it appear as though she is not as smart as she really is.

Oh danbooru. You never fail to amaze me with the kind of company you keep.

Iruel said:
Well, thank you three for telling me something that I already figured out a month ago. Especially after I had made a statement to that effect. Namely:
Apparently saying that you have failed in your argument doesn't keep other people from saying that.

I came back in here and I was all 'wtf, we already had this argument.'

Cirno is a genius.
Doesn't need to conform to the universe, anything can happen in gensokyo!

I come here expecting jokes, and YOU PEOPLE have to go and break ma brains.

Bravo, danbooru, bravo.

Eye believe Cirno is the smartest.

It seems easier to just do the work in base 9 instead of converting to base 10, doing the work, then converting back, at least for the addition/subtraction.

Great.
Now I feel paranoid for checking on this post almost every day for the last month to see if anyone else tries to correct me...

"Score: 27"
Why, that's ⑨ * 3!

gs68 said:
"Score: 27"
Why, that's ⑨ * 3!

Not anymore, it's now 29, but thankfully it still means 27 in base ⑨.

LDBAMC said:

Not anymore, it's now 29, but thankfully it still means 27 in base ⑨.

Except of course, that you can't actually have 29 in base 9.

27 in base nine would be 30.

This is THE most win thing I've seen on this site. Cirno counting in base nine make perfect sense...

mystictemplar said:
Except of course, that you can't actually have 29 in base 9.

27 in base nine would be 30.

Doh! Guess I deserve the ⑨ stamp for my poor understanding number systems. Always forgetting that zero... ugh.

SCIENTIFIC QUESTION:

If you had Cirno an equation with a 9 in one of the operands, will she write "NaN"? Or will her head explode?

Inquiring minds would like to know!

lily_white said:
SCIENTIFIC QUESTION:

If you had Cirno an equation with a 9 in one of the operands, will she write "NaN"? Or will her head explode?

Inquiring minds would like to know!

I had Keine conduct a few mathematical experiments for me to confirm my own hypothesis; don't ask how I ended up there, but this question stayed fresh in my mind as I entered the village (Reimu later had me leave, but she allowed enough time to conduct my experiment... a rather decent girl when you have enough pocket change on you...):

If the "9" happens to be found in between two other digits, Cirno will remark that the problem has been miswritten. We partly discovered this when asking her to solve the problem 94 + 12 = ___; she said we did something funny with the setup, erased the "9" next to the 4, and placed it on the right-hand side of the 4... (the natural format by which an "x" would go next to a coefficient in an algebraic equation; we later saw that she was absolutely perplexed by setups with "9" in-between two digits, looking at us with eyes that are meant to be cast upon insane people).

We then had her try to solve the equation she had setup: 49 + 12 = ___.

She asked for us to fill in the other side of the equation for her after an awkward pause as she looked upon us with a face that said, "what exactly do you expect me to do with this?"
We displayed the correct answer in decimal for her: 49 + 12 = 61; we were about to call it a day and resume the usual class schedule until Cirno finally started marking the board: 49 = 61 - 12 = 48...

At this point, while we were mindful of the fact that Cirno worked in base 9, we felt the unfortunate need to remark to her that "forty-nine does not equal forty-eight", upon which Cirno looked at us and said in a surprisingly matter-of-fact tone, "of course it doesn't...but what does that have to do with this?", leaving us flustered at our apparent stupidity for a moment as we watched her CONTINUE to work the problem: 9 = 48/4 = 12.

At this point it became clear that the "9" was indeed being treated as a variable in the equation... and Cirno had performed a completely correct subtraction and division in base 9 to do it.

The number would not register as having the same significance to Cirno as the rest of us with consideration of its value in the decimal system to represent a particular quantity. Rather, she'd assume, since the number "9" could technically count as a letter or a symbol of some sort, that "9" is a variable that she must solve for by algebraic or other means.

I love this (and prefer misunderstood Cirno to plain dumb Cirno).

If ternary computers weren't impractical (or at least hard to do well), I think we'd actually use base 9 similar to hexadecimal.

Saphyr said:
:words:

All of my internets. You win them. You earned it.

Saphyr said:
Lots of stuff

This officially my head-canon regarding Cirno.

Saphyr said:
Mind bending amazement

All my internets?

ALL OF THEM.

Saphyr said:
Cirno's theory on 9

my god... my mind...i can grasp this... you sir take this card it its to my bank of internets you deserve them

I'm having a little trouble grasping this.

25 = 27 in base 9

36 = 40 in base 9

So wouldn't 27 + 40 be 67?

25 and 36 are already in base 9
there is no conversion needed

therefore you just add the digits as per normal and carry when needed

50 +(5+6)
5+6 is 11 in base 10, but in base 9 it would be 12

so 50+12 = 62

Ande said:
I'm having a little trouble grasping this.

25 = 27 in base 9

36 = 40 in base 9

So wouldn't 27 + 40 be 67?

To clarify on what norezdu said using your example:

25 is already in base 9, so 25 base 9 = 23 base 10.
Similarly, 36 base 9 = 33 base 10.

23 + 33 = 56 in base 10; convert 56 to base 9, and you get 62. Unless the equation specifically says otherwise, all parts of a calculation must be done in the same base for it to be correct, whether that be binary, nonary, decimal, hexadecimal or any other base.

You got your maths right, but you made a common mistake - one I've made many times - so don't feel bad about it.

It may be an amazing discovery that Cirno does everything in base 9, but one can't help but wonder how Keine realized in the first place that they might be in base 9.

Kitsunemimi said:
It may be an amazing discovery that Cirno does everything in base 9, but one can't help but wonder how Keine realized in the first place that they might be in base 9.

When she saw Cirno wrote 5+4=10, and possibly considered for a moment that she carried the 9. Thats when Keine realized that she was using base 9 and was solving the others using her fingers to double-check that theory.

How do you multiple in based ⑨?

Exactly as you do with base 10, but you have to learn the multiplication table in base 9 to be comfortable to do it.

Like:
2*4 = 8
2*5 = 11
2*6 = 13
2*7 = 15
2*8 = 17
3*0 = 0
3*1 = 1
3*2 = 6
3*3 = 10
... etc.

Once you got your 9x9 multiplication table well placed in memory (or written in a sheet) you can multiply as usual.