Question 137
Consider a lake with two islands in it and seven cities on the shore. In the following we will briefly call the islands and cities places. There is a ship connection between exactly the following pairs of locations:
(i) between the two islands,
(ii) between each city and each island,
(iii) between two cities if and only if they are not adjacent.
Each of these connections is offered by exactly one of two competing shipping companies. Prove that there are always three locations, so that there are ship connections from the same company between every two of these locations.
(i) between the two islands,
(ii) between each city and each island,
(iii) between two cities if and only if they are not adjacent.
Each of these connections is offered by exactly one of two competing shipping companies. Prove that there are always three locations, so that there are ship connections from the same company between every two of these locations.