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 herewith commission you to carry out all preparations with regard to ... a total solution of the Jewish question in those territories of Europe which are under German influence.... I furthermore charge you to submit to me as soon as possible a draft showing the ... measures already taken for the execution of the intended final solution of the Jewish question.”
—Hermann Goering (18931946)
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (18901960)
“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 (18601935)