든지
deunji
If any of them lands you in the same place: 든지
The picture A shrug in front of a fork in the road. Every path ends at the same place, so there is nothing to choose.
Where the picture shows up in 든지
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this one, that one, no difference
커피든지 차든지 다 좋아요.
keo-pi-deun-ji cha-deun-ji da jo-a-yo
Coffee or tea, either is fine with me.
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the time is left wide open
언제든지 연락 주세요.
eon-je-deun-ji yeol-lak ju-se-yo
Get in touch any time.
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do it or don't, up to you
먹든지 말든지 마음대로 하세요.
meok-deun-ji mal-deun-ji ma-eum-dae-ro ha-se-yo
Eat it or don't, suit yourself.
-든지 is about choosing; -던지 recalls a past experience. Don't mix it up with 얼마나 춥던지, 'it was so cold'.
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whoever it is, fine
누구든지 들어올 수 있어요.
nu-gu-deun-ji deu-reo-ol su i-sseo-yo
Anyone can come in.
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whatever it is, fine
뭐든지 물어보세요.
mwo-deun-ji mu-reo-bo-se-yo
Ask me anything you like.
In speech the 지 usually drops: 커피든 차든, 뭐든.