3 Six remote villages are linked by a set of roads. Two villages are connected directly if there is a road between them which does not pass through another village. The table gives the lengths in miles of all direct connections.
| A | B | C | D | E | F |
| A | | 6 | 7 | 12 | | 3 |
| B | 6 | | 10 | | 8 | |
| C | 7 | 10 | | 2 | | |
| D | 12 | | 2 | | 9 | 8 |
| E | | 8 | | 9 | | |
| F | 3 | | | 8 | | |
- Why might it be thought surprising that the direct distance between A and D is as long as 12 miles? Give a possible reason why the distance is longer than might have been expected.
- Use the tabular form of Prim's algorithm, starting at A , to find a minimum connector for these villages. Draw your connector and give its total length.