6 A garden has seven statues \(A , B , C , D , E , F\) and \(G\), with paths connecting each pair of statues, either directly or indirectly.
To provide better access to all the statues, some of the paths are being made wider.
6
- State why six is the minimum number of paths that need to be made wider.
6
- The table below shows the number of trees that need to be removed to make the path between adjacent statues wider.
A dash in the table means that there is no direct path between the two statues.
| Statue | \(\boldsymbol { A }\) | \(\boldsymbol { B }\) | C | \(\boldsymbol { D }\) | \(E\) | \(F\) | \(G\) |
| \(\boldsymbol { A }\) | - | 4 | 7 | - | - | - | - |
| B | 4 | - | 6 | 2 | 3 | - | - |
| C | 7 | 6 | - | - | 3 | - | 4 |
| \(D\) | - | 2 | - | - | 4 | 5 | - |
| \(E\) | - | 3 | 3 | 4 | - | 3 | 7 |
| \(F\) | - | - | - | 5 | 3 | - | 6 |
| G | - | - | 4 | - | 7 | 6 | - |
6 - A landscaper identifies that two new wide paths could be constructed without removing any trees. However, there are only enough resources to build one new wide path.
The new wide path could be between \(A\) and \(D\) or between \(A\) and \(F\).
Explain clearly how the solution to part (b) can be adapted to find the new minimum number of trees that need to be removed.
[0pt]
[2 marks]