A few years ago a friend gave me a seemingly simple problem."You have a checkerboard", he said, "from which two diagonally opposite corners have been removed. You also have thirty-one dominoes, each of which can cover tow squares of the checkerboard. Can the dominoes be arranged so that they cover all sixty-two squares of the checkerboard? If so, how? If not, why not?"
There are four distinct stages when solving a problem: First stage is preparation - You go over the elements of the problem and study their relationships. Read the problem over, several times if you like, to be sure you understand exactly what is being asked. In solving problems, a self-assured attitude is half the battle. Second stage is Incubation - Unless you've been able to solve the problem quickly, you sleep on it. You may be frustrated at this stage because you haven't been able to find an answer and don't see how you're possibly going to. Third stage is Inspiration - You feel a spark of excitement as a solution (or a possible path to one) suddenly appears. If you look closely, you can often gather important clues from the problem's surroundings. The last an stage is verification - You check the solution to see if it really works and repeat the stages if necessary. Don't accept unnecessary limitations.
Problems of that kind sometimes are a whole lot of fun but present an opportunity for some out-of-the-box solutions...These are the problems that are sometimes require deliberate calculations which stretches your mind, enlarge your understanding, strengthen your thought processes, and maybe-if they are particularly devilish-even trick you into stumbling down a dead-end in order to see whether you can find your way out of it.
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