Briefly

The association of shy anonymous

The association of shy anonymous

Alberto won the award of a bar in the building of the association of shy anonymous members only. Since the space was reduced, he mounted a bar along the entire premises and 25 stools arranged in line in front of the bar.

Due to the type of people who come to the bar, the bar is usually half empty since every time a member of the association enters they feel as far away as possible from any other member and never sit next to each other. Thus, when a person arrives and does not find a place he likes, he leaves and Alberto is losing a lot of money with this behavior since the first person who enters usually sits on the last stool and does not get more than 9 members at the same time to occupy the bar.

After much thought, he decided to paint two green stools and at the entrance he put up a sign that read the following: "The first person to enter the bar, MUST sit OBLIGATORY on one of the green stools". With this he managed to have a record of 13 people sitting at once.

If we assume that the stools are numbered from 1 to 25, What stools did you paint green?

Solution

He painted stools 9 and 17 so that up to 13 people came to sit simultaneously at the bar. The reason is as follows: The first person to arrive will sit at number 9 (or at 17 since by symmetry, no matter which). The next person will sit as far away as possible from stool 9, that is, at 25. The next two people will sit at 1 and 17, which are the furthest from 9 and 25. The next three will occupy stools 5 , 13 and 21, the next six will occupy stools 3, 7, 11, 15, 19 and 23 so we will finally have a maximum of 13 people sitting without anyone sitting next to another person.