Information

The play

The play

In the theater of my town they represent a work whose promotion is exclusively due to the spread "word of mouth". The curious thing is that in all the functions, half of the spectators found it unbearable, while the other half liked it so much that he saw her again a second time and also got another person to accompany him to see her.

The play is performed once a week and has five on the bill. In the first function there were sixteen spectators ...

How many people saw the work?

Solution

As indicated in the statement, each person who ends up liking the work comes a maximum of 2 times to see it.

The first week will see the work 16 people.

The second week, half of the people from the previous representation will attend, that is to say 8 people and as they take a companion each one will be in total 16 people.

In the third week, of the 8 companions of the previous week, 4 will come again and will do so in company so a total of 8 people will come to see the work.

The fourth week will be attended by half of the companions of the previous week plus their respective companions which makes a total of 4 people.

Following the previous logic, the last week will go to see the work half of the companions of the previous week (1 person) plus his companion which makes a total of 2 people.

That is to say in total 46 people attended to see the work in 5 weeks. and last week were 2 people.