Cubes or GTFO.
My son has gotten really into playing with his 2x2x2 and 3x3x3 Rubik’s Cubes — though I’ll note that they’re not strictly Rubik’s, but rather third-party cubes designed for speed-solving. They are in every respect better, I think, than the Rubik-branded cubes, and no more expensive.
My son’s six years old. He can now solve one face more quickly than I can, though he’s not yet pushing ahead to the next level of the problem, i.e. he doesn’t yet have an orderly approach to solving and isn’t interested in solving (e.g.) a ‘layer’ instead of a face. I’m interested but disorderly, though I’m a bit further along cubewise than he is. Still, I didn’t dive into trying to figure the Cube out for myself until I’d spent some time looking at algorithms — which isn’t ‘cheating’ if you’re interested in the Cube as magic rather than as party trick —
Speed-solvers look at the cube, figure out which series of steps to implement given the pattern of colours they see, then rapidly execute a kind of ‘macro’ from memory. It’s nothing like what you or I would do; the ‘solving’ part of the term ‘speed-solving’ refers to a kind of mastery of self rather than of the mathematical puzzle of the cube. Turns out I have no interest in that — the mystery of it, the sense of enormous complexity undone stepwise by brainpower, is what draws me.
So anyway I can’t solve a Rubik’s Cube without instructions and neither can my son, not yet, and I’ve determined empirically that following a strategy guide to solve the Cube is boring after the first or second time.
For those of you interested in getting better at solving a Rubik’s Cube but uninterested in the (to me) somewhat narrow task of ‘speed-solving,’ I recommend Douglas Hofstadter’s Scientific American columns on Rubik’s Cube, reprinted in his superb collection Metamagical Themas. (Link goes to full text at archive.org.) They’re light on low-level strategy but long on inspiration and analytical cleverness — fans of Hofstadter’s singular body of work already know what I mean, those new to his writing have a treat in store.