The feeling
- I am no big typist. As a matter of fact, when I typed my last novel I didn’t look up from the keyboard even once! I was too busy making sure the fingers hit the right key. Big was my surprise when I discovered that the text was all gibberish.
- You are no big novelist either, if I may be a bit honest.
- OK. But this was worse. I discovered that every time I hit a key I got what seemed to be another key selected randomly.
- Let’s see if I understand. When you hit ‘a’ did you get the same letter every time?
- Yes, that is correct.
- Interesting.
- I got every character as before, but by pressing a key I was not used to. Actually, some of the keys gave the character printed on them, but most did not.
- So what did you do?
- I typed it again, but this time I typed what I had printed out from my first attempt.
- Did that help?
- No, I can’t say it did.
- So why on earth did you do it?
- I have an intuitive feeling that if I continue to type in what I print out sooner or later my novel as intended will appear!
- Quite a feeling!
- Thank you?
- How many keys do you have on your keyboard?
- 46 or n, I can’t remember.
- If you are right, I wonder how many times you would have to retype your novel.
Problem creator: Leonid Broukhis. Source: wu:riddles.
March 3rd, 2010 at 3:20 am
Say the keys a b and c are in a cycle if, when you typed abc on the keyboard, you actually got bca. Generalise this notion to cycles of any length.
“if I continue to type in what I print out sooner or later my novel as intended will appear!”
I interpret that as meaning that you will continue to look at your printouts, and will recognise your correct text.
With 46 keys, you could be unlucky and have cycles of lengths 3, 4, 5, 7, 11 and 13, so that it would take 60,060 types to restore normality.
I have no idea of how to formalise an algorithm which answers the problem for n keys. Do you go for many, small, primes or for fewer, larger, ones? For your n=46 case, I got a spreadsheet out and used trial and error. It wasn’t obvious that 5 prime(power)s would not be best.