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 2n. This is simply doubling the amount. We are only looking at integer values of n.