The Antisocial Club meets each week at Jim’s Bar. Since they’re so delinquent, nonetheless, everybody all the time sits so far as attainable from the opposite members, and nobody ever sits proper subsequent to a different member. Because of this, the 25-stool bar is sort of all the time lower than half full and sadly for Jim the members that do not sit on the bar do not order any drinks. Jim, nonetheless, is fairly good and makes up a brand new rule: The first individual to sit down on the bar has to sit down at one in all two explicit stools. If this occurs, then the utmost variety of members will sit on the bar. Which stools have to be chosen? Assume the stools are numbered 1 to 25 and are organized in a straight line.
Don’t overlook – the individuals sit as far-off from one another as attainable. If stool #1 is chosen first, the following individual will all the time sit in stool #25.
The first individual should take both stool 9 or 17 (due to symmetry, it does not matter which). Assume they decide seat 9. The subsequent individual will decide seat 25, since it’s the furthest from seat 9. The subsequent two individuals will take Seats one and 17. The subsequent three will occupy 5, 13, and 21. The subsequent six will occupy 3, 7, 11, 15, 19, and 23. This seats the utmost of 13 individuals, and nobody is sitting subsequent to a different individual. If a seat aside from 9 or 17 is chosen first, the full bar patrons will probably be lower than 13.