6 Eight footpaths connect six villages. The lengths of these footpaths, in km , are given in the table.
| Villages connected | A B | A D | B E | B F | C D | C E | D E | E F |
| Length of footpath, km | 3 | 2 | 4 | 6 | 5 | 7 | 3 | 1 |
- The shortest route from B to C using these footpaths has length 10 km . Without using an algorithm, write down this shortest route from B to C.
- Use an appropriate algorithm to find the shortest route from A to F .
- Write down all the pairs of villages for which the shortest route between them uses at least one footpath that is not in the minimum spanning tree for the six villages.