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There are 100 people standing in a circle in an order 1 to 100. No. 1 has a sword. He kills the next person (i.e. No. 2) and gives the sword to the next (i.e. No. 3). All people do the same until only 1 survives. Which number survives at the last?
Find who survived?
Source
What was the problem?
First let's make it very simple by who are surviving after each round.
Round 1 : 1,3,5,7,9,11,13,15..........87,89,91,93,97,99
Round 2 : 1,5,9,13,17.........89,93,97
Round 3 : 1,9,17,25,33,41,49,57,65,73,81,89,97
Round 4 : 9,25,41,57,73,89
Round 5 : 9,41,73
Round 6 : 9, 73
At round 5, 9 kills 41 & passes sword to 73. So 73 kills 9 & survives.
Round 7 : 73
Now let's analyze how this happens & trick to get answer at the quickest.
Just for a moment let's assume there were 16 standing in circle.
Now after each round survived people are,
Round 1 : 1,3,5,7,9,11,13,15
Round 2 : 1,5,9,13
Round 3 : 1,9
Round 4 : 1
After round 2, when 9 kills 13 & passes sword to 1.
And in round 4, 1 kills 9. So 1 forms pair with other in every round.
Now imagine there were 17 people in circle.
