Find the survivor
100 people standing in a circle in an order 1 to 100. No.1 has a sword. He kills next person (i.e. no. 2) and gives sword to next to next (i.e no.3). All person does the same until only 1 survives. Which number survives at the last?
Consider the case when there are 2^n numbers in the circle. Each time the number reduces by half and the number 1 remains till the end.
In the given question, 1 kills 2, 3 kills 4 and so on till 71 kills 72. 36 people have been killed till now. 64 people remain in the circle. 64 is a power of 2. So the first guy after 72 will be the new number 1 in a circle of 2^6. So 73 will survive.
This is the famous Josephus Problem. The solution requires getting the nearest smaller number that is the power of 2,in this case 64 and subtract it with the given number.100-64=36.Now we apply the formula 2n+1. 2*36+1=72+1=73.
You should check before using a formula …. the formula ou are using is when 1 person is being skipped.
Yes, and that is exactly the problem… one person is skipped.
100 people standing in a circle but not make a circle (as not clear in the q.).
but the question mentions that the person with the sword kills the next .
since they are standing in a circle, by the end of the first round 99 has the sword so he should be killing 1 and the series continues . Am i missing some part of the question which makes me think in this way?
99 kills 100 – hands sword to 1
The answer should be 89.
More puzzles to try-
What is the logic behind these ?3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
Defective stack of coins puzzleThere are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
Which clock works best?Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
(Advanced) Cheryl’s Birthday PuzzlePaul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »
Five greedy pirates and gold coin distribution PuzzleFive puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
Magical flowers!!A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »
Tuesday, Thursday what are other two days staring with T?Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
How could only 3 apples leftTwo fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
How Many Eggs ?A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »
HARD MATHS – How much faster is one train from other PuzzleTwo trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »
Most Analytical GOOGLE INTERVIEW Question RevealedLet it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »
Lateral thinking sequence PuzzleSolve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
How did he know?A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
Pizza Cost Math Brain TeaserJasmine, 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 markWhich letter replaces the question markRead More »
Which room is safest puzzleA murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
Richie’s Number SystemRichie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »
Srabon wanted to passThe result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »
Become Normal!!Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »
Sakib Knows The Number!Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »