Question 98
A kingdom has $10$ towns. Some pairs of different towns have bridges built between them, so that between any two different towns there is at most one bridge. Two towns between which there is a bridge will be called *ends* of that bridge.
a) Prove that there are at least two towns which are *ends* for the same number of bridges.
b) The king orders his subjects to build or demolish some bridges, so that half of the towns are *ends* for $3$ bridges and the other half are *ends* for $4$ bridges. Can the order be fulfilled?
a) Prove that there are at least two towns which are *ends* for the same number of bridges.
b) The king orders his subjects to build or demolish some bridges, so that half of the towns are *ends* for $3$ bridges and the other half are *ends* for $4$ bridges. Can the order be fulfilled?