Danbooru

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(9) 4girls blonde_hair blue_hair bow chalkboard cirno comic daiyousei dress green_hair hair_bow hat highres kamishirasawa_keine maiku math multiple_girls nonary o_o raised_hand ribbon rumia solid_circle_eyes touhou translated wings
(9) 4girls cirno comic daiyousei kamishirasawa_keine maiku math multiple_girls nonary rumia touhou translated
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cirno, daiyousei, kamishirasawa keine, and rumia (touhou) drawn by maiku

cirno, daiyousei, kamishirasawa keine, and rumia (touhou) drawn by maiku

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    eidolon

    Thanks to Zekeltarfos and Tetrominon for the translation.

    葉月

    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.

    lipucd

    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.

    balorn

    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).

    Tetrominon

    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.

    0xCCBA696

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

    mnmega

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

    sgcdonmai

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

    TurboMog

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

    HidekiHine

    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)

    garyseven

    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

    Dr Fine Rolo

    No she doesn't...

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

    I'M THE SMARTEST.

    hifumihifumihifumihifumihihihihihihihi...

    hitotsu futatsu kokonotsu...

    Dr Fine Rolo

    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?

    Iruel

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

    Dr Fine Rolo

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

    Iruel

    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.

    Cloud 1987

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

    Karesh

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

    ⑨.

    zero5889

    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).

    imaliar

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

    imaliar

    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.

    N2O

    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?

    Iruel

    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.

    N2O

    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...

    imaliar

    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.

    AyKay

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

    Dr Fine Rolo

    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.'

    PSB

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

    Final guard

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

    Bravo, danbooru, bravo.

    halifix

    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.

    Iruel

    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...

    gs68

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

    259

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

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

    mystictemplar

    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.

    Shadeshark12

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

    259

    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.

    lily white

    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!

    Saphyr

    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.

    PK678353

    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.

    lily white

    Saphyr said:
    :words:

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

    KyteM

    Saphyr said:
    Lots of stuff

    This officially my head-canon regarding Cirno.

    The Shadow

    Saphyr said:
    Mind bending amazement

    All my internets?

    ALL OF THEM.

    dragonmanj

    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

    Ande

    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?

    noredzu

    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

    GenerationZero

    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.

    Kitsunemimi

    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.

    Piemur1

    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.

    Zhuo Xing

    How do you multiple in based ⑨?

    etb

    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.

    Indefinity

    Dear god. My mind is scattered all over the place.

    KasaneTeddo

    Gawd, I already asked my teacher (head teacher of the math department at our school) about base 9 and I can't still understand it... Guess my 3rd year mind isn't ready yet.

    Guedez

    8*12 in base 9.. fucking hurt my head to try doing it by head.

    think of divisions with decimals

    uchuunamako

    Guedez said:
    8*12 in base 9.. fucking hurt my head to try doing it by head.

    think of divisions with decimals

    Not difficult if you convert it to base 10, since 8 is the same both ways, and 81 (b10) is 100 (b9).

    But non-integers in alternate bases make my head asplode.

    Rinotheuke

    Is base 9 handled simply by not counting the 9? Or is there something greater to it? Because I'm looking at the 5+4=10 and it's kinda bothering me in the sense that I can't figure out base 9.

    CookieYome

    Rinotheuke said:

    Is base 9 handled simply by not counting the 9? Or is there something greater to it? Because I'm looking at the 5+4=10 and it's kinda bothering me in the sense that I can't figure out base 9.

    not counting 9 and above, thus 9 is considered 10

    simply put, base nine has the following numbers before converting into 10:
    1 2 3 4 5 6 7 8

    base ten, the number system we all know and use in daily life has:
    1 2 3 4 5 6 7 8 9

    of course, this means that base 2, base 3, or even base 16 is calculable.

    If you haven't played with numbers bases yet, either google or ask your math teacher about the syllabus. It's quite fun.

    ChaozZBubi

    CookieYome said:

    simply put, base nine has the following numbers before converting into 10:
    1 2 3 4 5 6 7 8

    base ten, the number system we all know and use in daily life has:
    1 2 3 4 5 6 7 8 9

    You forgot the most important digit in both cases: Zero
    So base 9 are the digits 0 to 8 (nine digits) and base 10 are the digits 0 to 9 (ten digits).