$\left.\begin{array}{l}{[\quad \text { Geometry on grid paper }} \\ [\text { Classical combinatorics (other) })]\end{array}\right]$

The inner chambers of Sultan Ibrahim ibn-Said's palace consist of 100 identical square rooms, arranged in a $10 \times 10$ square. If two rooms share a wall, there is exactly one door in that wall. If a wall is an outer wall, there is exactly one window in it. How can you count the number of windows and doors in Ibrahim ibn-Said's chambers?
Note that the sultan's palace has 4 outer walls and 18 internal partitions.

## Solution

Since the sultan's palace has 4 outer walls, each 10 rooms long, and 18 internal partitions (9 longitudinal and 9 transverse), each also 10 rooms long, we can determine the number of windows $(10 \times 4=40)$ and doors $(10 \times 18=180)$.

## Answer

40 windows, 180 doors.