Lesson 5 – Deductive Reasoning

Deductive reasoning starts from something you know is true, and uses logical steps to come to a conclusion. If what you start with turns out to be false, everything you built up from it can fall down.

I almost died once because I trusted my deductive reasoning skills too much. I figured my friends must have crossed the river (the Green River, I think, in Tennessee) on this particular bunch of rocks. I saw them on one side of the river, and then on the other side, therefore they crossed, therefore, so I thought, they used the line of rocks with the least gaps. I tried to cross on that line of rocks, since I ‘knew’ they had. This was a huge, raging river, and the path I’d chosen seemed a bit dicey, but if they had done it, I could. Well, they hadn’t (they had swum across where the water was widest and slowest), and I couldn’t. I fell in and ended up under water in the dark. I was under a waterfall with my foot stuck. I came out from under the other end of the waterfall, and ended up in the middle of the river. My friends helped me out with a rope. There was no real damage, but if the holes between the rocks had been smaller, I’d have been stuck like a cork. Ever since then, I’ve tried to remember that assumptions can sneak in and totally wreck the validity of the best sounding argument.

Sudoku puzzles are all about logic. The symbols could have been the first 9 letters instead of numbers, and the puzzles would really be exactly the same. If there’s a 3 here and here, then there can’t be one here, then there has to be one here or here, etc. If you get done with Jacob's problems before we go on to the next lesson, doing some sudoku would be a good complement to this lesson.

I like the 3rd edition much better than the 1st for this lesson. The chessboard with the dominoes on it becomes a game using a smaller checkerboard with paperclips. The idea is the same. If 2 squares are removed, is it possible to cover all the squares left, two by two (where the two are connected on a side)? In the 3rd edition, the game is to have one player choose which 2 squares to remove, and the other player then tries to cover the rest with paperclips. Both books lead you through the reasoning steps that will help you see more clearly what must happen.

The cubes in the 1st edition seem painted wrong (the whole outside was painted black but the pictures just highlight the cubes of interest). The drawings in the 3rd edition worked better for me.

In both editions, Set III shows some illustrations of the Pythagorean theorem. The hint in the 1st edition (easy as 2+2) does not seem helpful to me. In the 3rd edition, I love the visual proof on the left. I would ask more questions: What do we have to verify, to be sure this is a proof? (One thing I wanted to verify was that the two shaded areas really are square.) Both editions show a diagram with squares outside the 3-4-5 triangle. I don't believe there's a proof in that diagram. Am I wrong? (Yes, the numbers add up right, but how do we know it's a right triangle.)

Do you have your own deductive logic stories, favorite logic puzzles, or questions?

- Notes by Sue VanHattum