MathDB

Each of

K

friends simultaneously learns one different item of news. They begin to phone one another to tell them their news. Each conversation lasts exactly one hour, during which time it is possible for two friends to tell each other all of their news. What is the minimum number of hours needed in order for all of the friends to know all of the news? Consider in this problem:
(a)

K = 64

. (b)

K = 55

. (c)

K = 100

.
(A Andjans, Riga)
PS. (a) was the junior problem, (a),(b),(c) the senior one

Problem Statement