A problem that bothered me for a long time, how to fill up a page as quickly as possible using copy/paste operations essentially.

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So, you’re given the task of filling up an entire page with the word “paint” on a computer...now, you want to do this in the most time efficient way and you’re able to copy and paste, what’s the best way to do this? Given a certain amount of time required to copy and paste? What happens as this time increases? Is it simply exponential growth with base 2 (you start with one “paint” and then you copy and paste all you have every time)? As you increase the time it takes to copy/paste it seems like the number of paints you would want to accrue before only pasting (no copying) decreases. Sure you could reselect a half-page worth of “paints” and be done but what if that takes longer than copy and pasting a fourth of the page twice (or whatever you currently have on your clipboard)?

One model to this scenario is that of 2^n. This is simply doubling the amount. We are only looking at integer values of n.