A conservation trust manages a wetland reserve arranged in a grid to maintain biodiversity through rotational reed harvesting.
Figure 1 shows a map of this managed wetland, divided into 12 numbered outer sectors surrounding a central protected sanctuary consisting of 4 unnumbered squares.
The management rules are as follows:
- The sectors are managed in sequence: 1→2→3→4→5→6→7→8→9→10→11→121 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5 \rightarrow 6 \rightarrow 7 \rightarrow 8 \rightarrow 9 \rightarrow 10 \rightarrow 11 \rightarrow 121→2→3→4→5→6→7→8→9→10→11→12.
- Reeds are harvested in only one sector at any one time.
- It takes 18 months to complete the harvesting and restoration of each single sector.
- The sectors in the 'Protected Sanctuary' are never harvested to provide an undisturbed habitat for breeding bird species.
How many years will it take to complete one full management cycle of all the numbered sectors?