ZA-SAMO 2011 Problem 4
An airline company is planning to introduce a network of connections between the ten different airports of Sawubonia. The airports are ranked by priority from first to last (with no ties). We call such a network feasible if it satisfies the following conditions:
- All connections operate in both directions
- If there is a direct connection between two airports A and B, and C has higher priority than B, then there must also be a direct connection between A and C.
Some of the airports may not be served, and even the empty network (no connections at all) is allowed. How many feasible networks are there?
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Similar problems
These problems have the most words in common with this statement.