A better lower bound is 10! Every permutation of the 10 digits will change a valid solution to another valid solution.

Wrong.

By the way it's not that sure that you can start with every 4 digit number. I think you can - but you need to prove it.

Update: Or is it right? Let's have two differend 4 digit strings - if they are different then at least on one of the 4 position they have different digits - the permutation will change those digits to different digits as well. It means the permutation induces a 1-1 function on the 10000 4 digit strings. There can't be any more of them so in the whole resulting string there will be exactly 10000 different 4 digit strings. QED

That was long time since I proved a theorem.

In reply to Re: Re: Shortest string containing all from 0000 to 9999 challenge. by zby
in thread Shortest string containing all from 0000 to 9999 challenge. by EvdB

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