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Turkey nmo 2017 p6

Source:

January 29, 2018
combinatoricsgraph theory

Problem Statement

Finite number of 20172017 units long sticks are fixed on a plate. Each stick has a bead that can slide up and down on it. Beads can only stand on integer heights (1,2,3,...,2017)( 1, 2, 3,..., 2017 ). Some of the bead pairs are connected with elastic bands. TheThe youngyoung antant can go to every bead, starting from any bead by using the elastic bands. TheThe oldold antant can use an elastic band if the difference in height of the beads which are connected by the band, is smaller than or equal to 11. If the heights of the beads which are connected to each other are different, we call it validvalid situationsituation. If there exists at least one validvalid situationsituation, prove that we can create a validvalid situationsituation, by arranging the heights of the beads, in which thethe oldold antant can go to every bead, starting from any bead.
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