25 seat bar riddle
There is a bar with 25 seats in a line. The people there are anti-social so when they walk in the bar, they always try to find a seat farthest away from others. If one person walks in and find there is no seat are adjacent to nobody, that person will walk away. The bar owner wants as many people as possible. The owner can tell the first customer where to sit. all the other customers will pick the farthest possible seat from others.
So where should the first customer sit?
Answer – 9 or 17
Consider a case. If the number of seats is n = (2^k)+1 for some k, then, the maximum possible seating of (n/2)+1 can be achieved by having the first person sit at position 1 or n or ceil(n/2).
This is true since when n=(2^k)+1, then, when someone sits in the first or middle or the last seat then all the other gaps are of length in powers of 2 (as suggested above by Vinay).
This implies that for this problem, with n=25, we need to split it into n1 and n2 such that: n1 = (2^k1)+1 and n2 = (2^k2)+1, for some k1, k2. Note that n1+n2 = n+1 = 26 (since they both share a common seat).
Thus, the only possible values are 9 or 17.
More puzzles to try-
- 3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
- There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
- Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »
- Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
- Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »
- Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
- Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
- Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
- A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »
- Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
- A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
- Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »
- Which letter replaces the question markRead More »
- A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
- Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »
- The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »
- Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »
- Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »
- If u r genius solve it:- 40 * 14 = 11 30 * 13 = 12 20 * 12 = ...Read More »
- When do we call “10” while looking at number “2”?Read More »