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I was given this question by a friend and tooled around with it a bit in excel. I'm sure I could brute force it, but I wanted to see if people smarter than me could help me optimize this and find a mathematical way to solve it.

The problem is this: You have a character in a text box. You want to make as many characters as possible using only 100 keystrokes. The possible keystrokes are Ctrl+A (select all), Ctrl+C (Copy), and Ctrl+V (Paste). The text starts unselected with nothing on the clipboard. Of course, there is the 2^x growth characterized by

  1. Ctrl A 2. Ctrl C 3. Ctrl V... and repeat to get 2^x growth

But even in my experimentation if you paste a few more times before selecting and copying, you can easily outpace 2^x growth.

So my question is, how can I represent this mathematically so I can optimize it and find the best combination of select/copy/paste?

ReconFirefly
  • 31

1 Answers1

0

You start with one character. After 3 keystrokes (CTRL A, C, V); you get 2 of them.
Now, to get 4, you can either use the previous 3, or just use CTRL V 2 more times. The latter is more effective. Then, to get 8, using CTRL A, C, V is more effective than using CTRL V 4 times(or any number of times greater or lesser than 4 for that matter). This way, you can now visualise the pattern:
CTRL A
CTRL C
CTRL V
CTRL V
CTRL V
CTRL A
CTRL C
CTRL V
CTRL V
CTRL V
.
.
.
Using this, you can find out the number of characters at the end of 100 keystrokes. There won't be any remainder since 5(The number of strokes per cycle) divides 100.

Aniket Gupta
  • 647