Geometric patterns & Gbrainy

The illustration below comes from Gbrainy, a puzzle program distributed with Ubuntu linux.
My wife and I first discovered it on one of our holidays, when our son Piet-Jan had equipped an old laptop with Ubuntu linux. GBrainy gave us several evenings with much needed mental exercise. It features logic, calculation, memory and verbal puzzles and exercises. One of the puzzles was this one:
figures from gbrainy
I must admit it took me some time to figure it out, and you can check the solution.

Some logicians and mathematicians maintain that there are two ways of thinking: deductive and inductive. Deductive reasoning is the type of reasoning where you have all elements available, and your deductions involve logical reasoning, but the reasoning does not include anything new. One might say that your reasoning takes your from general to specific. An easy example: All cows are animals. Bella is a cow. Conclusion: Bella is an animal. Inductive reasoning goes the other way around: from special to general. In the puzzle above this type of reasoning is very clear: you start looking for what the commons properties in the figure are, and what letters can be associated with them. Finding the properties is the inductive part: you don’t know what the common properties are, and you have to discover them.

The puzzle made me thinking, and I designed several others, some of which I took the liberty to present them to the GBrainy group, others are presented here for the first time. Several of my fellow workers, such as Jan Zoomers, Jon Koeter, Michiel Matthijssen and Pieter Vuijk tested some of them, for which I am grateful to them.

(Give up? Don’t check the solution to soon).

(Give up? Don’t check the solution too soon).


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