Question 173
There are finite number of vertical sticks each of length $2017$ fixed on some plate. There is a bead on each stick which slides freely on the stick. Some bead pairs are connected by elasticated ropes. The Young Ant freely moves on all ropes. The Old Ant freely moves on all ropes for which the difference between heights of endpoints is $\pm 1$. It is given that starting at any bead The Young Ant can reach any other bead. The configuration of beads when each bead is located on some integer height and the heights of two endpoints of any rope are different is called an *eligible configuration*. Given that there is at least one eligible configuration of this device prove that there is an eligible configuration for which The Old Ant starting at any bead can reach any other bead.