You have two two-liter bottles,
one (marked W) containing one liter
of pure water and one (marked A)
containing one liter of pure alcohol.
The two things you can do are to
pour liquid from either bottle down
the drain or pour liquid from one
bottle into the other, but you must
always keep at least one liter of liquid
in bottle A.
What is the minimum
alcohol concentration that can be
achieved in bottle A? Assume that
there is no volume change on mixing
water and alcohol.
(In reply to
re: soln by Kenny M)
To get the alcohol concentration lower, one must drain alcohol
from container A. Whatever one is allowed to drain, one wants
to be as concentrated as possible, so as to drain the
most total alcohol. So one adds infinitesimal amounts of water
to A so as to drain infinitesimal amounts of the most concentrated
solution possible. That was what was done, so I think that's the
proof!
Edited on February 3, 2025, 8:17 pm
re(2): soln
