January 2018 - Challenge

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Alice heard a rumor. She meets Bob after ab days, where ab is uniformly distributed over the integers from 1 to AB. She meets Charlie after ac days (again, uniformly distributed over [1,AC]), and Dave after ad days. Bob meets Charlie after bc days, and Dave after bd days. Charlie meets Dave after cd days.
In every such meeting, if one of the attendees knows the rumor - he/she tells it to the other one.
Find AB, AC, AD, BC, BD, and CD such that the average time of the rumor to get to Dave is exactly 425.36/69.

Update 31/12: Bob meets Charlie bc days after at least one of them knows the rumor, and meets Dave bd days after at least one of them knows the rumor. Charlie meets Dave cd days after one of them knows the rumor. bc, bd and cd are uniformly distributed over [1,BC], [1,BD] and [1,CD] respectively.

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Challenge: 27/12/2017 @ 12:00 PM EST
Solution: 02/02/2018 @ 12:00 PM EST
List Updated: 04/02/2018 @ 12:00 PM EST

People who answered correctly:

Alper Halbutogullari (30/12/17 09:07 AM IDT)
Mathias Schenker (31/12/17 02:26 PM IDT)
Shirish Chinchalkar (01/01/18 11:43 PM IDT)
Hugo Pfoertner (02/01/18 04:55 PM IDT)
Lorenz Reichel (03/01/18 07:55 AM IDT)
Muralidhar Seshadri (03/01/18 06:22 PM IDT)
Bert Dobbelaere (03/01/18 09:28 PM IDT)
Tom Sirgedas (04/01/18 12:38 AM IDT)
Kang Jin Cho (04/01/18 12:20 PM IDT)
Dieter Beckerle (05/01/18 12:51 AM IDT)
David Greer (05/01/18 08:53 PM IDT)
Paolo Farinelli (06/01/18 12:24 AM IDT)
JJ Rabeyrin (07/01/18 02:26 AM IDT)
Joaquim Neves Carrapa (07/01/18 09:31 AM IDT)
Francis Golding (08/01/18 11:37 PM IDT)
Tyler Mullen (09/01/18 09:37 PM IDT)
Dmitry Serbin (12/01/18 02:42 PM IDT)
Balakrishnan Varadarajan (16/01/18 06:52 AM IDT)
Guillaume Escamocher (17/01/18 01:18 PM IDT)
Ozgur Sumer (19/01/18 03:16 AM IDT)
Guangzhong Sun (19/01/18 05:38 PM IDT)
Steven Langerwerf (26/01/18 02:14 PM IDT)
David F.H. Dunkley (28/01/18 03:19 AM IDT)
Nyles Heise (28/01/18 04:34 AM IDT)
Erik Wünstel (28/01/18 11:23 PM IDT)
Li Li (31/01/18 10:19 AM IDT)
Mykola Zubach (31/01/18 03:17 PM IDT)
Oscar Volpatti (31/01/18 03:29 PM IDT)
Andreas Stiller (31/01/18 06:30 PM IDT)