On April 1st a typist found the hammers of the typewriter resoldered in an arbitrary order, so typing a text resulted in gibberish. The typist decided to type a document in its entirety using this typewriter. Afterwards, if the result does not represent the original text, he will type the result, and so on. Prove that the clear text will emerge sooner or later. How many iterations are enough to guarantee that the clear text will appear, if the typewriter has, say, 46 keys? N keys?
Clue:
Why does it say April 1 ? Is the question poser trying to trick you in deep stuff ? May be. But you can take it to a suitable point and then leave to the crazy math guys.
To take it to the suitable pt:
Decompose a number into such constituents such that the LCM of the constituents is maximized। Think prime! Pray Riemann !
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