I heard others' rumor just now and I talked the rumor to ten persons ten minutes later.
And these 11 persons talked it to ten persons respectively ten minutes afterward.
Furthermore, all persons that heard this rumor talked to ten persons 10 minutes afterward, respectively.
One hour after the time I heard the rumor first, how many persons know this rumor ?
And these 11 persons talked it to ten persons respectively ten minutes afterward.
Furthermore, all persons that heard this rumor talked to ten persons 10 minutes afterward, respectively.
One hour after the time I heard the rumor first, how many persons know this rumor ?
Answer
The number of people who knows the rumor next 10 minutes after is 11+ 10 × 11= 11 × 11 = 121 persons.
In next 10 minutes it becomes with 121 + 10 × 121 = 121 × 11 = 11 × 11 × 11 persons.
Therefore, the number of people 60 minutes after the time I heard is 11 × 11 × 11 × 11 × 11 × 11 = 1771561 persons.
1771561 persons
Solution
The number of people who knows the rumor 10 minutes after I hear a rumor is 1 + 10 = 11 persons.
The number of people who knows the rumor next 10 minutes after is 11+ 10 × 11= 11 × 11 = 121 persons.
In next 10 minutes it becomes with 121 + 10 × 121 = 121 × 11 = 11 × 11 × 11 persons.
Therefore, the number of people 60 minutes after the time I heard is 11 × 11 × 11 × 11 × 11 × 11 = 1771561 persons.
