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?
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.
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.
50 survivors.
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
Your Answer
More puzzles to try-
Mathematical Relationship aptitude puzzle
Find the number to replace the question mark to complete the series, provided the pair of numbers exhibits a similar ...Read More »I can bring a smile to your face Puzzle
Look at me. I can bring a smile to your face, A tear to your eye, Or even a thought ...Read More »Out of box thinking in Five start hotel puzzle
In a five star hotel, a man was sleeping when he heard a knock on the door. He shifted the ...Read More »Chimney Up and Down
What can go up a chimney down, but can’t go down a chimney up?Read More »Car and thief Riddle
Ron’s father’s flying car got stolen and during the trial, he told that his father’s car was stolen by his ...Read More »Why is this and it is not to keep fit?
Each day a lady gets the lift from the 12th floor to the ground level so she can go to ...Read More »What is common here
What is common among 11, 69, and 88?Read More »Cyclist Puzzle
You are a cyclist in a cross-country race. Just before the crossing finish line you overtake the person in second ...Read More »Whats going on riddle
A man leaves home, turns left, goes straight, turns left again, goes straight and turns left once more then returns ...Read More »Train and man escaping from tunnel riddle
A man walking home takes a shortcut through a train tunnel. A quarter of the way in, he hears a ...Read More »Crossing a River Riddle
John and Jacob want to cross a river. The only way to get to the other side of the river ...Read More »Three Numbers Puzzle
Find three numbers such that * When we multiply three numbers, we will get the prime numbers. * The difference ...Read More »Truth or Liar
John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller. I ...Read More »Matchstick Game
Can you find out a way through which you can make five squares out of the given figure by moving ...Read More »Johnson Brothers tricky riddle
There were three Johnson brothers – – Mark Johnson – Mike Johnson – Peter Johnson One of them threw a ...Read More »Males in Family Riddle
In a family of 6 people P, Q, R, S, T, and U: U and R are brother and sister. ...Read More »Decreasing weight riddle
Weight of a material in dry form is 2 kg, 1 kg when wet and become 3kg when burn. What ...Read More »Prove Your Innocence
The store room of your house is locked with a certain lock that can be closed without a key but ...Read More »How can you take the right pill?
You have a horrible disease but thankfully there is a medicine for it. Everyday you must take one pill called ...Read More »The Two trains Riddle
Train A, traveling 70 miles per hour (mph), leaves Mexico city heading toward Atlixco city, 260 miles away. At the ...Read More »