Everyone uses the radar once they wake up. The two closest soldiers go towards each other on a straight line. Once they meet up and possibly wait for the other one to wake up they are free to visit all other soldiers in any order, when they are all together they can detonate. The important property is that the initial shortest distance is unique almost surely.
This doesn’t work (among other reasons) because the only way you have of finding out the position of the other paratroopers is to use the radar.
Suppose one of the two closest soldiers wakes up, uses his radar and heads towards the other paratrooper in the pair in a straight line. In the midst of this motion, suppose the other member of this pair also wakes up, uses his radar and executes the same strategy. Then they will fail to meet because the first paratrooper will be heading to the original position of the second, while the second will be heading towards some random point on the straight line joining them.
They won’t be able to tell if they’ve “met up” along the line because as I said the only way of getting any information about the position of the other paratroopers is by using the radar. Without it, you can’t even tell if you’re coincident (on the same point) with another paratrooper or not.
I see I should have read the instructions more carefully. I don’t quite understand all of your complaints though, if they can notice if they are on the same spot at the same time (they can’t I missed that) the strategy would work: the two soldiers would meet as they will not leave the line connecting them (walking towards some random point on it sure but still in the right direction)?
Everyone uses the radar once they wake up. The two closest soldiers go towards each other on a straight line. Once they meet up and possibly wait for the other one to wake up they are free to visit all other soldiers in any order, when they are all together they can detonate. The important property is that the initial shortest distance is unique almost surely.
This doesn’t work (among other reasons) because the only way you have of finding out the position of the other paratroopers is to use the radar.
Suppose one of the two closest soldiers wakes up, uses his radar and heads towards the other paratrooper in the pair in a straight line. In the midst of this motion, suppose the other member of this pair also wakes up, uses his radar and executes the same strategy. Then they will fail to meet because the first paratrooper will be heading to the original position of the second, while the second will be heading towards some random point on the straight line joining them.
They won’t be able to tell if they’ve “met up” along the line because as I said the only way of getting any information about the position of the other paratroopers is by using the radar. Without it, you can’t even tell if you’re coincident (on the same point) with another paratrooper or not.
I see I should have read the instructions more carefully. I don’t quite understand all of your complaints though, if they can notice if they are on the same spot at the same time (they can’t I missed that) the strategy would work: the two soldiers would meet as they will not leave the line connecting them (walking towards some random point on it sure but still in the right direction)?