Solution
The problem is impossible to solve. An even number of cups are facing up, and you must turn over exactly two cups at each move. Since an even plus an even is an even, not an odd, no number of even flips will ever get all the three cups right-side up. To solve the problem, you need an odd number (i.e., three) of cups facing up, so the problem is impossible.
The solvable (but trivial) version of this puzzle starts with two cups upside down and one cup right-side up. To solve the puzzle in a single move, you need only turn up the two cups that are upside down — after which all three cups are facing up.
Read more about this topic: Three Cups Problem
Famous quotes containing the word solution:
“I can’t quite define my aversion to asking questions of strangers. From snatches of family battles which I have heard drifting up from railway stations and street corners, I gather that there are a great many men who share my dislike for it, as well as an equal number of women who ... believe it to be the solution to most of this world’s problems.”
—Robert Benchley (1889–1945)
“The Settlement ... is an experimental effort to aid in the solution of the social and industrial problems which are engendered by the modern conditions of life in a great city. It insists that these problems are not confined to any one portion of the city. It is an attempt to relieve, at the same time, the overaccumulation at one end of society and the destitution at the other ...”
—Jane Addams (1860–1935)
“There’s one solution that ends all life’s problems.”
—Chinese proverb.