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Keep an eye Onto the other (Posted on 2019-07-19) Difficulty: 3 of 5
An odd number of soldiers are stationed in a field in such a way that all the pairwise distances are distinct. Each soldier is told to keep an eye on the nearest other soldier. Show that at least one soldier is not being watched.

No Solution Yet Submitted by Danish Ahmed Khan    
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re(2): solution Comment 4 of 4 |
(In reply to re: solution by Charlie)

I think the proof holds up.

When I wrote "of the remaining soldiers the two closest will stare at each other" I should have made clear I meant 'closest' in terms of the remaining distances.  The relative distances are all that matter.

In any arrangement the two nearest soldiers are watching only each other.  Dropping them from consideration doesn't remove watchers from remaining soldiers.

  Posted by xdog on 2019-07-19 19:59:02
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