Wednesday, April 15, 2015

Riddle/Lateral Thinking: Circle of Death

8. Circle of Death!!!

There are 300 convicts waiting to be hanged in the King’s prison. However, there is an innocent man named ‘X’ among the criminals whom the princess wants to marry. The princess requested the king to spare him. The king says, according to the law he is guilty and sentenced to death, I cannot release him. But I will him a chance in a trial named “Game of Death”. 

The rules of the trial as follows
1. All the convicts will be standing in a circle with position marked from 1 to 300 in clockwise manner.
2. A gun will be given to the convict standing at position 1, who will kill the one next to him i.e 1 kills 2, 3 kills 4, 5 kills 6...goes on till one person is left.

Now the king tells to the princess, “I am giving you a chance, Decide which position Mr. X to stand to live till end”. 


Question: Which position should Mr. X occupy to stay alive?



Note: Basic assumption holds good. 

Read it and post your answers as reply to the post. I will be adding my answer if there are no correct answers after 10 replies.  


Regards

1 comment:

ayas ran said...

It's obvious that If the total no of people in the circle is even then the 1st person will get the gun in the next round; else he will be killed. Now after the 1st round of killing the prisoners that survive are:-
1 3 5 7... (comm diff=2)[total 150] {1 kills 3 and in the next round gets the gun again as 150 is even}
After 2nd round 1 5 9 13.. (cd=4)[total 75] {1 kills 5 but as total is odd so 1 won't get the gun in next round}
After 3rd round 1 9 17 25.. (cd=8) [total 37] {1 is killed, then 9 gets the gun & kills 17; again total is odd so 9 gets killed in the next step}
After 4th round 9 25 41.. (cd=16) [total 18] {9 is killed and 25 kills 41}
After 5th round 25 57.. (cd=32) [total 9] {25 kills 57 but as total is odd 25 is killed next}
After 6th round 25 89.. (cd=64) [total 4] {25 is killed}
After 7th round 89 217.. (cd=128) [Total 2] {As the previous total was even so 89 gets the gun & kills 217 :) }