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.
(In reply to re: solution
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