ChapterZero

I’ve been taking a random walk through Engel’s Problem Solving Strategies– reading it linearly is more of a chore than fun. The best reading method seems to be, read the first couple paragraphs of each chapter where the principle is introduced, and skip to the problems; you can look back at the worked examples later if you get stuck on applying the principle.

The first chapter deals with using invariants as a problem solving technique. This technique seems to be useful for dealing with problems which ask whether a specified state can be reached by following an algorithm. My favorite problem so far (of those I’ve managed to solve) that employs this principle is:

You may switch the signs of all numbers of a row, column, or a parallel to one of the diagonals. In particular, you may change the sign of each corner square. Prove that at least one -1 will remain in the table.