Current Puzzle

Figurine Figuring

Jane received 78 figurines as gifts this holiday season:  12 drummers drumming, 11 pipers piping, 10 lords a-leaping, etc., down to 1 partridge in a pear tree.   They are all mixed together in a big bag.  She agrees with her friend Alex that this seems like too many figurines for one person to have, so she decides to give some of her figurines to Alex.   Jane will uniformly randomly pull figurines out of the bag one at a time until she pulls out the partridge in a pear tree, and will give Alex all of the figurines she pulled out of the bag (except the partridge, that’s Jane’s favorite).   

If n is the maximum number of any one type of ornament that Alex gets, what is the expected value of n, to seven significant figures?

Correct Submissions as of 18/01/21

Guillermo Wildschut
Leif Metcalf
Junzheng Nan
Anton Puhach
Daniel B
Ivan Galakhov
Courtney Watson
Kilian B.
Neil Thistlethwaite
Aaditya Raghavan
Laura Lawler
Derrick Armstrong
Jesse Jane
Roman Rubanenko
Valerii Gusman
Keith Schneider
Rahul Saxena
Will Christerson
Ian Sleightholme
Senthil Rajasekaran
R. Fatoiki
Gareth Owen
Michael Starr
Kelvin Davis
Dimas Ramos
David Molay
Karl Mahlburg
Rushil M
Konstantin Vladimirov
Walter Sebastian Gisler
Eugene Lykhovyd
Lazar Ilic
Michael Zhao
Gabriel Tostes

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