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jugs with water

Source: Problem 4, Polish NO 1994

October 7, 2005
algorithmnumber theorygreatest common divisornumber theory unsolved

Problem Statement

m,nm, n are relatively prime. We have three jugs which contain mm, nn and m+nm+n liters. Initially the largest jug is full of water. Show that for any kk in {1,2,...,m+n}\{1, 2, ... , m+n\} we can get exactly kk liters into one of the jugs.
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