when i was younger, maybe 7, i used to multiply by two a lot. i'd do it in my head and i would do it often. i dont know why i started or why i stopped or why i didnt go to higher numbers. i dont remember being trained to multiply at the time so i dont even know how i used to do it.
i'd multiply 1x2 = 2
2x2 = 4
4x2 = ~~16~~ 8
and so on
the farthest I remember reaching was 1024, though I may have reached 2048 once. i dont know why i didnt go higher than that.
another thing i used to do was tap my fingers in a pattern, LRRL, so left tap, right tap, right tap, left tap. then i'd expand that pattern, LRRL, RLLR, RLLR, LRRL, so it would be a bigger pattern of the same pattern. like multiplying i'd just do this to see how big i could make the pattern. i'd do this by tapping my index and thumb finger. to an observer it would probably appear as if i were 'stimming'.
did anyone else do things like this?
"4x2 = 16"
you can get to 2048 very quick this way
In at most 11 steps
2x2=2048
See, one step!
Very well done!
And if you think about it carefully you might find that one step is indeed less than or equal than 11 steps, as must be!
(The proof of this is left as an exercise for the reader)