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Category: Logic

Let-n-be-an-odd-positive-integer-On-some-field-n-gunmen-are-placed-such-that-all-pairwise-distances-between-them-are-different-At-a-signal-every-gunman-takes-out-his-gun-and-shoots-the-closest-gun

Question Number 13893 by Tinkutara last updated on 24/May/17 Letnbeanoddpositiveinteger.Onsomefield,ngunmenareplacedsuchthatallpairwisedistancesbetweenthemaredifferent.Atasignal,everygunmantakesouthisgunandshootstheclosestgunman.Provethat:(a)atleastonegunmansurvives;$$\left(\mathrm{b}\right)\:\mathrm{no}\:\mathrm{gunman}\:\mathrm{is}\:\mathrm{shot}\:\mathrm{more}\:\mathrm{than}\:\mathrm{5} \