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:
“There’s one solution that ends all life’s problems.”
—Chinese proverb.
“The truth of the thoughts that are here set forth seems to me unassailable and definitive. I therefore believe myself to have found, on all essential points, the final solution of the problems. And if I am not mistaken in this belief, then the second thing in which the value of this work consists is that it shows how little is achieved when these problems are solved.”
—Ludwig Wittgenstein (1889–1951)
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)