A conservation group manages a wetland reserve using a system of rotational reed-bed harvesting to maintain biodiversity while yielding materials for local thatch production.
Figure 1 shows a map of this managed wetland reserve, divided into 12 rectangular compartments, including two central protected sanctuaries.
The harvesting rules are as follows:
- The active compartments are harvested in numerical sequence: 1→2→3→4→5→6→7→8→9→101 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5 \rightarrow 6 \rightarrow 7 \rightarrow 8 \rightarrow 9 \rightarrow 101→2→3→4→5→6→7→8→9→10.
- Reeds are harvested in only one compartment at any one time.
- It takes 8.5 years to complete the harvesting and subsequent habitat restoration phase in each single active compartment.
- The 'Sanctuary' zones are never harvested.
How many years will it take to complete one full harvesting cycle of all the numbered compartments?