Some interesting replies in here. Prolifical, I wasn't so much talking about reasoning as I was about applying general principles of logic to thought processes, but certainly reasoning does play a large part in some of the things I mentioned, such as the ability to discern between fact and fiction.
And the reason I used that puzzle as an example of an excercise in logic is for the following reason. After reading the instructions on how to approach the puzzle, the first thing I would expect somebody to think is "where's the rose? where are the petals?", considering all you see is a bunch of squares and dots. I would think that the first logical step would be to figure out what represents the "rose", and what represents the "petals". Once you've done that, it's as simple as counting some dots. However, this is where people seemed to go wrong. Rather than simply just taking a look at what was there, people were talking about using complicated mathematical equations, and algebra and such, which I would personally consider to be a very ilogical approach. Roses, petals, dots, how does that lead someone to complicated mathematical equations?
Just my thoughts.