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Rumor Mill (Posted on 2004-12-03) Difficulty: 4 of 5
Waldo is having a party and has 50 guests, among whom is his brother Basil.

Basil starts a rumor about Waldo; a person hearing this rumor for the first time will then tell another person chosen uniformly at random the rumor, with the exceptions that no one will tell the rumor to Waldo or to the person they heard it from.

If a person who already knows the rumor hears it again, they will not tell it again.

What's the probability that everyone, except Waldo, will hear the rumor before it stops propagating?

What if each person told two people chosen uniformly at random?

No Solution Yet Submitted by SilverKnight    
Rating: 4.0000 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: First Part Comment 13 of 13 |
(In reply to First Part by Charlie)

Actually Basil can tell any of 48 people, any except himself or Waldo.  Person A can tell any of 47 people - he can't tell Basil, Waldo, or himself.  From there, the form of the solution is the same, and the probability is 46/47 * 45/47 ... 1/47 = 46! / 47^46 = 6.669 * 10^-20, or about 1 in 1.5 * 10^19.
  Posted by Kyle on 2005-01-04 14:45:41

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