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Fastest way to try all passwords

There are $10^4$ different 4-digit codes. If each code takes 4 keypresses to try, then it would take $4*10^4$ keypresses to try all possible codes.

Now the specific codelock i have in mind is of the type that unlocks when the last 4 digits that were pressed are the code, e.g if the code is 0000 one could enter 12351350000 and it would unlock. This implies that to test the codes 0000 and 0001, one needs only 5 keypresses.

How many keypresses does it take to try all the codes on such a codelock?

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marked as duplicate by Henning Makholm, Hans Lundmark, Leonid Kovalev, Chris Eagle, t.b. Aug 17 '12 at 11:51

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up vote 5 down vote accepted

$10^4 + 3$. See de Bruijn sequences, which exist for all bases and lengths.

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Thank you, i am very content with this answer. Good day sir! –  perserk Jun 16 '12 at 17:00
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