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100 People Standing in a Circle
Difficulty Level

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?

View Answer Comments(7)

There are different ways to solve this. Lets take the easy method.� Convert the total number of people into binary.

100 in binary number is 1100100
Now take the complement which is 11011 and it is 27
Subtract the complement from the original number. So 100 - 27 = 73.

The last person to remain is 73

Try it out for 50 people.
50 = 110010 in binary.
Complement is 1101 = 13.
Therefore, 50 - 13 = 37.

For the number in form 2^n, it will be the first person. Take an example.
64 = 1000000
Complement = 111111 = 63.
64-63 = 1.

Guest Said:Posted On 2017-05-11

amazingly brilliant ......!!

Guest Said:Posted On 2017-05-11

qwertyuiopcfvd

Guest Said:Posted On 2017-04-16

73 is

Guest Said:Posted On 2016-11-25

1st round: even nos gone (50)Left: 1 3 5 7 9 ...99-> So: 1,5,9(Dead) = diff=4,n=25,a=1, tn = 1+24*4 = 97 ,,99S -> 2nd: 1, 5 , 9, … 97D & 99S -> (25)Left: 3 , 7, 11, ...99S -> 3, 11 , d=8, n=13,a=3, tn=3+ 12*8 =99D Where is Sword: 7,15,23,31,39, , d=8, n=12,a=7 , tn = 7+ 11*8 =95S-> (12)Left: 7,15,23,31,39, ...95S-> 7,23,39 = d=16,n=6, a=7 , tn =7 + 5*16=87D Sword= 95 (6)Left . d=16 . 15 , 31, 47, 63, 79, 95S-> Left: 31, 63, 95S-> Left: 63Whats the correct answer?

Guest Said:Posted On 2016-09-28

99

Chris Kittlitz Said:Posted On 2016-09-08

The answer, while it may be correct, is not a proof.

Guest Said:Posted On 2016-03-18

69

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