1,000 monkeys
Assuming monkeys don't evolve or get repetitive strain injury and that paper is an infinite resource and that they type constantly 24 hours a day and that they type completely randomly, here is a [rather wordy] question:
There are 1,000 kingdoms of 1,000 groups of 1,000 monkeys with very long fingers and they are typing on 1,000 typewriters each (with keys of the English alphabet and the numbers 0 to 9) typing 1,000 words per 1,000th of a millisecond. Assuming they start a new line every 26 digits, how long (roughly) will it take them to write 'abcdefghijklmnopqrstuvwxyz' in one line in order, if the probability was exact (in other words, how long should it take on average to happen)?
Yes, you can use a calculator - or a typewriter - to solve this.
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1 solution
So there are 26 letters in the alphabet and 10 numbers (0-9) which give us 36 keys on the typewriter. Now the probability of typing the alphabet (with 26 digits) out in order (per try) is 3 6 2 6 1 . Now we multiply this numerator by 1 , 0 0 0 7 to work out the chances of all of them typing it out in any one given second, which takes us to 3 6 2 6 1 , 0 0 0 7 . That seems like a lot of seconds, so we convert it to years, so it looks like this: ( 3 6 2 6 ) ÷ ( 1 , 0 0 0 7 ) ÷ ( 6 0 × 6 0 × 2 4 × 3 6 5 . 2 5 ) and we type the answer in a calculator (or more like google nowadays) and we get around 922 billion. It seems like a long time to type the alphabet correctly.