There is a group of N soldiers arranged in a straight line, standing side by side. Soldier number 1 is at the extreme left and soldier "N" is at the extreme right. Each soldier has a rifle that can be fired only once, a primitive timer, understands a finite list of commands, and can exist in a finite number of states, like a finite state machine.

Each soldier has the ability to communicate only with the two adjacent soldiers, and has no means of communication with more distant soldiers. The i-th soldier can not see or hear any signals given by the (i+2)th soldier, for example. There are no radios, cell phones, or megaphones.

Your mission as the commander is to devise an algorithm by which all soldiers fire their weapons simultaneously. Soldiers 1 and N are aware of the fact that they are "different" in that they each have only one neighbor. Other than that, however, the soldiers are initially all identical. The algorithm has to work for any value of N>2.

The primitive timers are synchronized and tick off once a second. Once a soldier receives new information, the earliest he can respond in any way is on the next tick of the clock. (I would say he/she, except that they are all identical). A soldier can give a signal to each neighbor simultaneously, based on the information he received one tick earlier. Whenever a soldier's state changes, his neighbors are aware of this one tick later. At time=0, soldier 1 is given the command to start the firing procedure

1. Devise an algorithm that results in all N soldiers firing simultaneously
2. As a function of N, how many clock ticks does this take?

Now as the message traves to the 2 soldier the message the tick = 1
therfor when the message is received by the Nth soldier the tick = N-1 now here is what i think Freaky how about this

the first soldier fires his gun after tick = N-1 and the second soldier fires his gun when tick = N-2 and the third soldier fires his gun when the tick = N-3 and so on till Nth solider and this Nth soldier fires his gun when the tick = N-N which is as soon as he gets the message
(Assumption : they at least have a watch to keep time lol i mean if they invent a Gun hell a watch won't be that difficult right ?? lol)

this way all of then will fire their gun at the same time.

HOPE THE ANSWER IS CORRECT AND PLEASE POST THE CORRECT ANS OR MAIL ME I LOVE TO KNOW THE ANS OF THESE TYPES OF RIDDLES :D

Mail : megadude@dr.com

Posted by Ethen Hunt on 2004-09-09 09:33:34