Here’s a nice little puzzle I came across in Godfrey Thomson’s Instinct, Intelligence, and Character (1924):
“Imagine a cube, which is going to be cut in two by a straight saw cut. The saw-cut section, the raw face of the cut, can clearly be of various shapes, as square, or triangular (if a corner were cut off). How would you cut the cube so that the section may be a perfect plane hexagon?”
You are not to draw diagrams, or look at cubical or near-cubical objects while thinking it out.
If you are not a mathematician, your first thought (like mine) may be that it is impossible, or that it is a trick question, like those puzzles about making pyramids out of matchsticks. But accept the assurance that it is a genuine puzzle, with a straightforward solution.
Once you accept that there is a solution, it shouldn’t take too long to find it. But the interesting question is how you reach the solution. Do you get there purely by visual imagery, purely by logical reasoning, or some combination of the two? (Of course mathematicians may use analytical geometry or whatever, but I’m treating it primarily as a puzzle for the intelligent layman or -woman.)
I suspect that there would be considerable individual differences in approach, and that these might cast some light on different mental ‘factors’. Also, possibly, differences between men and women or groups with different genetic and/or cultural ancestry.