Finite number of 2017 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). Some of the bead pairs are connected with elastic bands. The young ant can go to every bead, starting from any bead by using the elastic bands. The old ant 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 1. If the heights of the beads which are connected to each other are different, we call it valid situation. If there exists at least one valid situation, prove that we can create a valid situation, by arranging the heights of the beads, in which the old ant can go to every bead, starting from any bead. combinatoricsgraph theory