Question 8
Planet *Zork* is spherical and has many towns. For each town there is a corresponding antipodal town (i.e. symmetric in relation to the centre of the planet).
There are roads connecting pairs of towns in Zork. If there is a road connecting towns $P$ and $Q$ then there is also a road connecting towns $P'$ and $Q'$, where $P'$ is the antipode of $P$ and $Q'$ is the antipode of $Q$. Besides the roads do not cross each other and for any given two towns $P$ and $Q$ it is possible to travel from $P$ to $Q$ through some sequence of roads.
The prices of *Kriptonita* in *Urghs* (the planetary currency) in two towns connected by a road differ by no more than 100 *Urghs*. Prove that there exist two antipodal towns such that the prices of *Kriptonita* in these towns differ by no more than 100 *Urghs*.
There are roads connecting pairs of towns in Zork. If there is a road connecting towns $P$ and $Q$ then there is also a road connecting towns $P'$ and $Q'$, where $P'$ is the antipode of $P$ and $Q'$ is the antipode of $Q$. Besides the roads do not cross each other and for any given two towns $P$ and $Q$ it is possible to travel from $P$ to $Q$ through some sequence of roads.
The prices of *Kriptonita* in *Urghs* (the planetary currency) in two towns connected by a road differ by no more than 100 *Urghs*. Prove that there exist two antipodal towns such that the prices of *Kriptonita* in these towns differ by no more than 100 *Urghs*.