A, B, C, and D are standing in a circle. A has $800$ mL of $100\%$ water in his glass. B, C, and D have $400$ mL, $200$ mL, and $100$ mL of water in their glasses, respectively.
A pours half of his water into B's glass and drinks half of what's left in his glass.
B then pours half of what's in her glass into C's glass and drinks half of what's left in her glass.
C then pours half of what's in his glass into D's glass and drinks half of what's left in his glass.
D then pours half of what's in her glass into A's glass and drinks half of what's left in her glass.
Lastly, all remaining beverages are poured into a big container.
The liquid in the big container then contains $x\%$ water. What is $x$?
Sorry, there is a typo, here is the corrected version:
A, B, C, and D are standing in a circle. A has 800 mL of 100% juice in his glass. B, C, and D have 400 mL, 200 mL, and 100 mL of water in their glasses, respectively.
A pours half of his juice into B's glass and drinks half of what's left in his glass.
B then pours half of what's in her glass into C's glass and drinks half of what's left in her glass.
C then pours half of what's in his glass into D's glass and drinks half of what's left in his glass.
D then pours half of what's in her glass into A's glass and drinks half of what's left in her glass.
Lastly, all remaining beverages are poured into a big container.
The liquid in the big container then contains x% juice. What is x?
