IBM Ponder This #237 · January 2018

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.

Solution

Best opened after a real attempt

To be added.