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Prove the pattern


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#1 BMAD

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Posted 21 October 2013 - 10:35 PM

In drawing lowercase English letters a through z uniformly at random, the expected time till you see willywilly is 26^10 + 26^5.
 
In drawing numerals over 0-9 uniformly at random, the expected time till you see 1231231 is 10^7 + 10^4 + 10.
 
In flipping a fair coin, the expected time till you see HTHTTHT is 2^7 + 2^2.
 
See a pattern? Find it ... then prove it.

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#2 ThunderCloud

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Posted 21 October 2013 - 11:01 PM

I may be missing something obvious, but why is the expected time to see "willywilly" not 26^10? :huh:


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