HOW TO SOLVE IT

[G.Polya ]

Puzzles According to section3, the questions and suggestions of our list are independent of the subject-matter and applicable to all kinds of problems. It is quite inter resting to test this assertion on various puzzles. Take for instance the words DRY OXTAIL IN REAR The problem is to find an anagram", that is, a rearrangement of the letters contained in the he given words into one word. It is interesting to observe that, when we are solving this puzzle, several questions of our list are pertinent and even stimulating. What is the unknown A word. What are the data ? The four words DRY OXTAIL IN REAR. What is the condition? The desired word has fif***** letters, the letters contained in the he four given words. it is probably a not too unusual English word. Draw a figure< It is quite useful to mark out fif***** blank spaces: - - - - - - - - - - - - - - - Could you restate the problem? We have to find a word containing, in some arrangement, the letters A A E I I O Y D L N R R R T X This is certainly an equivalent restatement of the problem- (see AUXILIARY PROBLEM, 6) (It may be an advantageous restatement. Separating the vowels from the consonants (this is important, the alphabetical order is not) we see another aspect of the problem. Thus we see now that the desired word has seven syllables unless it has some diphthongs. If you cannot solve the proposed problem, try to solve first some related problem A related problem is to form words with some of the given letters. We can certainly of short words of this kind. Then we try to find longer and longer words. The more letters we use the nearer we may come to the desired word. Could you solve a part of the problem? The desired word is so long that it must have distinct parts. It is probably, a compound word, or it is derived from some other word by adding some unusual ending. Which usual ending could it be? - - - - - - - - - - - A T I O N - - - - - - - - - - - - - E L Y Keep only a part of the condition, and drop the other part. We may try to think of a long word with, possibly as many as seven syllables and relatively few consonants containing an X and a Y. The question and suggestions of our list cannot work magic. They cannot give us the solution of all possible puzzles without any effort The question and suggestions of our list cannot work magic. They cannot give us the solution of all possible puzzles without any effort ton our part. If the reader wishes to find the word, he must keep on trying and thinking about it. What the questions and suggestion of the list can do is to "keep the ball rolling." When discouraged by lack of success, we are inclined to drop the problem, the may suggest to us a new trial, a enw aspect, a new variation of the problem, a new stimulus; they may keep us thinking. For another example, see DECOMPOSING AND RECOMBINING,8.