Did anyone else have trouble recalling the red vs blue sides? (based on my experience with this (below), it seems as though my mental association was essentially "top and bottom are same" and "narrows are same" but neither really had a color. When I close my eyes, I don't see "red" or "blue")
At first I was imagining a 1cm by 1cm by 4cm block. I then realized that getting the 16 cubes of 1cm each out of this wasn't possible and then went to the accurate idea of a 4 by 4 by 1. I realize I am having a great deal of trouble going from a 1cm by 4cm rectangle and then adding depth, while the 4 x 4 square I can add the 1cm of depth much easier. I can rotate the image of the 4x4x1 around in my head and yet cannot do the same with the 4x1x4 (despite the fact that I recognize that they are the same image).
Adding colors: four narrow are red, two fat are blue. Got it. Break it up into cubes.
Red and blue faces requires it touch the outside of the 4x4 square. 4 along top side, four along bottom side, and two each on the left and right (already counted the corners).=12 total red and blues.
One red and two blue... which ones were red and which were blue again? I know that the four narrows are the same and that the top+bottom are different... and just logicked that if the question is one red and two blue, that means the narrows were blue (the reds don't touch->top and bottom). To be two red and one blue... WAIT--that logicking doesn't work because the edges have Top side bottom. So I'll look back at which sides were which color. In my mind I just have "top and bottom are same color" but that's not assigned to red or to blue. Okay--top and bottom are blue. This means along the edge of the 4x4. uh... the perimeter again. So 4+3+3+2=12. Unless you're asking for two red and exactly one blue, in which case it's the corners... wait--two red? red was the narrow side color. i think i switched them again. Final answer: to have two red and one blue you must have two red, meaning the narrow side meets a narrow side, which only happens in four places. Four.
Just re-read the question. You asked for one red and two blue. All of them except the middle 4 blocks, so 12.
Previously: Generalizing From One Example
Summary: I do not have visual mental imagery. I want it. How do I get it? What exercises, if any, will help?
In further detail... Here's Francis Galton's Statistics of Mental Imagery paper. I'm not quite at the 3% level of completely unable to form mental images, but I'm close. In particular there are three times I have vivid, sharp mental imagery, and the existence of such times tells me I have the brain hardware to visualize. It's enough to let me know that I want it all the time. Unfortunately I don't know how to get it. And searching online has proven difficult and frustrating... for example this article is first of all about a different meaning of "visualize", it's talking about some kind of self-help motivational thingy, and second of all it starts by saying "How to Visualize: I want you to relax and close your eyes. Picture a hot, sunny day at the beach."
Full Stop. Halt, Catch Fire and Burn.
That's already too far. For those of us who don't visualize, practice definitely does not consist of pulling up mental images, playing with them in new ways, and expanding our imagination. I'm very good at imagination in some ways, but I lack that first ability to pull up a mental image. That's what I want to learn how to have!
Here is a description of what I can do, what I have tried, what I have learned, etc.
I see vivid visual mental imagery in 3 situations: