Don't hate me for this — but you did not misunderstand the problem, and it is not impossible. I did solve it back in the 1960s. Besides which, if I give you the answer, I will ruin it for others who would rather try to solve it.
but to clarify: -you take three regular plastic coke bottles
-put them in an equilateral triangle
-make the length of a side from center of the bottle slightly longer than a knife
-take three identical knives and create a platform that can hold a regular cup of water
?
Wait..by typing it out like this.. I think I solved it haha. Thanks for the brain tickle!
I read this as the distance between the edge of the bases, not center. In which case the only solution would be [spoiler]