I was given an excellent geometry problem by Dr. Nigel Thomas.

It might be worth attempting to see how you perform on certain types of spatial thinking problems that most people claim to use imagery to solve (although no correlation seems to exist between spatial thinking ability and the vividness that people report their imagery to have). Try to solve the problem below, in your head, without drawing diagrams or making calculations on paper or anything like that. The four narrow sides of a 1 cm by 4 cm by 4 cm block are painted red. The top and bottom are painted blue. The block is then cut into sixteen 1 cm cubes. 1. How many cubes have both red and blue faces? 2. How many cubes have one red and two blue faces? 3. How many cubes have no painted faces? Most people say they use imagery to do this, and count the relevant cubes in their image. Were you able to solve all or any part of the problem at all? Did it seem very difficult? How, in fact, did you solve it (if you did)? Did you have to consciously employ any formal knowledge of geometry or other mathematics (beyond counting)?

When I solved this, I had the interesting experience of Imagining the 4x4 block of 16 blocks, noting that the outside ones (all but 4) had red paint on them, and all of them had blue paint... but I only "put" blue paint on the top. My diagram was flat, oriented like a pancake. None of this was Mental Imagery. Then when I was asked how many cubes had red and blue faces, I felt around the edges of the block. Motor/haptic mental imagery. Then when I was asked how many cubes had 1 red and 2 blue faces, I immediately thought the question was 1 red and 1 blue since I didn't have blue paint on the bottom in my model (I'm not sure if I had a bottom in my model). I thought "when would they have more than 1 red? ah the corners", and then had the distinct vivid motor mental imagery of moving my hand and touching two non-corner side blocks on the left of my model, then two at the far side, then two on the right, then two on the near side, counting "2, 4, 6, 8". This was a different experience than my usual Imagining... but I'm not sure if it was qualitatively different or just more "vivid" motor mental imagery.