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actually, lets get serious about this. lets put our balls on the table. i think if your adding up the digits of a number with each other you definitely ought to go to the hague

@garfiald this is a lot of anger over 10x + x

@garfiald extremely, pathologically, provokingly self-consistent forms of bullshit

serious answer to maybe non-serious question

@byttyrs @garfiald

In base 10, when you add 1 to a number, one of its digits increases by 1, and some 9s may become 0s. So adding 1 to a number always increases its sum-of-digits by 1 (maybe minus a multiple of 9). This means the difference between a number and its sum-of-digits is always a multiple of 9. So if a number is divisible by 9 then so is its sum-of-digits and vice-versa. In hexadecimal the same thing works for 15 (replace 9 with 0xF).

(1/2)

serious answer to maybe non-serious question

@byttyrs @garfiald

The divisible-by-3 rule works for both base-10 and base-16 because both 9 and 15 are divisible by 3. In base 10, the difference between a number and its sum-of-digits is a multiple of 9; in base 16 it's a multiple of 15. Either way that's also a multiple of 3. Since the difference between a number and its sum-of-digits is a multiple of three, then a number is divisible by three exactly when its sum-of-digits is.

(2/2)

@byttyrs @garfiald i believe that the reason both of these work is that the remainder of 10 is 1 when divided by 3, so every power of 10 is also equivalent to 1 mod 3:

420 = 4*100 + 2*10 + 0

= 4*(1+99)+2*(1+9)+0

= (4*1 + 2*1) + (4*99 + 2*9)

the right-hand group is a multiple of 3 for sure, so the left hand group is going to be the remainder when you divide by 3.

@garfiald fuck

@garfiald don't kinkshame garf

@garfiald I can't believe I've been subtooted by THE garf eel

@Ophillous a rare honour, especially for you

@garfiald I'm going to adopt like a bunch of kids and name each of the a different word from this

@garfiald what the fuck is x

x isn't a number it's a letter

@seafrog LMFAO thank you elise. what a blessing

@garfiald when inspiration strikes u just gotta draw u kno

@seafrog you are a visionary

garfield@garfiald@mastodon.socialnumbers are numbers. once you bring the digits that numbers our made out of into it your breaking the fourth wall and fucking around with the simulation. its unsafe