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March 10, 2009

Logic brain teaser



There are 1000 soliders with a no. on their T Shirts
(1,2,3.....999,1000) standing on a circular track.
Man with no.1 is carrying a sword in his hand.
He kills man at no. 2 and pass on sword to no. 3.
This goes on until we have only one solider on the track.
What will be the no. on his T-Shirt?

6 comments:

Michel said...

Soldier #977

Unknown said...

it is 1

Anonymous said...

The first answer is correct. They are standing in a circle and the killings do not restart at #1 when they reach the highest remaining number so Soldier #1 is killed by #993.

Because half of the soldiers are killed each cycle, the one who will be the last one standing is the one who's turn it is to kill when the number of soldiers remaining first equals a power of 2. From then on, each cycle simply reduces the number remaining to the next lower power of 2 with the same lucky soldier to start it off again.

The next lowest power of 2 under 1000 is 512 so 488 soldiers must be killed. The first cycle kills all of the even-numbered soldiers so 488 will have been killed when Soldier #976 (=488 * 2) dies. Since it is now Soldier #977's turn and there are now 512 soldiers left, he will be the last.

abhi said...
This comment has been removed by the author.
abhi said...

Hats off to u if u have done it urself

Anonymous said...

really genious dude....