the addled secretary problem

Jul 31, 2021 Last reply: 4 years ago 3 Replies

An office cabinet holds 52 pairs of loose letters and pre-printed envelopes (anybody remember those?). Each letter is intended for its appropriate envelope, and all distinct.



A clumsy secretary spills the cabinet, scattering everything. The bimbo doesn't bother to sort things out, but blindly stuffs letters into envelopes.



On average, how many letters end up mailed correctly?


gotta be one (on average).

Correct. Though you might have guessed it, purely through puzzlemanship -

It seems like the obvioius answer, althoigh the results are co-related assuming each putative match to be independant gives on average 1

I did the arithmetic for 1, 2, and 3 pairs and saw that although there are many no-match results, they are exactly compensated for by the multiple match results, bringing the average back to 1

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