How to Solve Mathematical Problems by Wayne A. Wickelgren

Author:Wayne A. Wickelgren
Language: eng
Format: epub
ISBN: 9780486152684
Publisher: Dover Publications
Published: 2012-10-18T16:00:00+00:00

Stop reading and try to solve the problem.

You could begin by trying various hypotheses as to sequences of filling the digits 1, 2, . . . 9 in the nine cells, but this process is long, slow, and chancey. A few inferences that can be made from the above information allow one to greatly reduce the number of hypotheses that must be tested. Probably the most important insight to gain at an early stage in working on the problem is to notice that, of two cells adjacent along a row or column, one must be filled with an odd number and the other with an even number. This arrangement can easily be proved by taking any two cells adjacent along a row or column and considering all possible paths from one cell to the other, realizing that an odd number of steps is required to reach the adjacent cell no matter what path is taken within the matrix. However, it is really not essential to prove the theorem that cells adjacent along a row or column must have one even number and one odd number. A large number of trial-and-error substitutions executed within a few minutes will show that the theorem is almost certainly true. Stop reading and try to solve the problem, if you could not do so before.

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