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Some characters count one character to Twitter, some count two; not because of bytes, but because Twitter's rules for ideographic languages and alphabetic languages are different. From my test, emoji also count as two.
Oh, I made a mistake! 
counted as 4 when appended to the tweet mentioned above (also true when I deleted one or two characters) but it's 0xE298B9. If I just paste in a bunch of them, they each count as 2. Seems hard to imagine that the difference is by design and not a bug?
Also, is this new as of the switch to 280 chars? I could've sworn I used to sneak in emojis when I had 1 character left and it would work, but I don't trust memory in general so maybe I'm just mis-remembering?
Some emoji pickers implement as U+2639 U+FE0F to prevent U+2639 alone from showing up as ☹︎ on some platforms, and both of those count double because they're above U+1100, the arbitrary dividing line that Twitter has picked.
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