There is an odd number of soldiers, the distances between all of them being all distinct, which are training as follows: each one of them is looking at the one closest to them. Show that there is a soldier which nobody is looking at.

Question

anonymous · Answer

since the distances are distinct, the soldiers will be paried up according to minimums... starting with the least minimum.

you could use the pigeon hole principle

baru · Answer

guessing...

there will be at-least one pair of soldiers looking AT each other,

the only way everybody is looked at by another person is if each person looks at someone not looking back.

ganeshie8 · Answer

baru, counter example :

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