A problem by Vraj Mistry
100 people are standing in a circle. The person standing at number 1 is having a sword. He kills the person next to him with the sword and then gives the sword to the third person. This process is carried out till there is just one person left.
Can you find out the no. of the person who survives?
The answer is 73.
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1 solution
Moderator note:
Why is this true?
Till the number is the power of 2, the last person to survive will be the one who started it.
Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64. 100 - 64 = 36 36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive. Person no. 74 is the answer