There was cruel king. He had 100 prisoners. He decided to test which one was the smartest. He made them stand in a circle. The 1st prisoner kills the second one and gives the sword to the third prisoner and he kills the 4th and so on. Which is the safest spot/number to be in as a prisoner?

Dear Student,

Please find below the solution to the asked query:

From given information we show position number that will survive in each round :

Round 1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99 . Now 99  kills 100^th passes the sword to position ' 1 ' prisoner , Then

Round 2: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97 . Now 97 kills 99^th  passes the sword to position ' 1 ' prisoner , Then

Round 3: 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97 . Now 97 kills 1^st  passes the sword to position ' 9 ' prisoner , Then

Round 4: 9, 25, 41, 57, 73, 89 . Now 89 kills 97^th  passes the sword to position ' 9 ' prisoner , Then

Round 5: 9, 41, 73 . Now 73 kills 89^th  passes the sword to position ' 9 ' prisoner , Then

Round 6: 9, 73 . Now 73 kills 9^th  and remain the only one that will survive : 

Round 7: 73

Therefore,

Safest spot for prisoner is  73^rd .                                                       ( Ans )

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