Thecla, interesting that you mention 24 hours. The original Scientific American article appeared in the 80's and did not show any moves but discussed the cube in terms of groups and operators. It took me three days, no more than 8 hours a day, to discover operators that would swap edge cubes, rotate edge cubes, swap corner cubes, and rotate corner cubes without affecting any other subcubes. With this set of operations I was able to solve any cube in about 7 minutes. That is, it was possible to solve a cube in less that 24 hours.
Obviously the kids were doing something different but it seemed that this was some innate ability that is lost with age. Lots of kids under 10 were able to solve these. It was not some kind of four sigma savant talent but some common 3D sensitivity. I had a striking demonstration of this. Many years later a 7 year old son of a friend saw a solved Rubik's cube (something he'd never even heard of) on a shelf, picked it up and proceeded out of curiosity to twist faces, perhaps 7 or 8 rotations, enough to totally scramble it for any adult. After a moment's thought he then reversed all the rotations back to the original state and put it back on the shelf and didn't act like it was anything special. This was a fairly bright kid but not some kind of prodigy. There are lots of Rubik/group articles on SciAm.com