Juicy GossipDiscrete Mathematics Level 3
Math town has 1990 residents. Everyday the residents would tell all of their friends about the gossip they heard yesterday. If there is a gossip, it is guaranteed that all residents will know it from the friends over time.
If a gossip is told to 180 residents on day 0, the next day(day 1) the 180 residents will tell all their friends about it, and the day after that(day 2) all of the residents who knew the gossip will start talking about it to their friends. This process continue for 10 days.On day 10, is it guaranteed that all of the 1990 residents in Math Town knew the gossip?