Question 8
A beaver engineer makes triangular windows as follows:
- **Step 1:** Make an equilateral triangular window frame.
- **Step 2:** Join the midpoints of its sides to form 4 new triangles.
- **Step 3:** Fit gray glass in the central one of the new panes.
- **Step 4:** Repeat steps 2 and 3 on any pane that does not yet have glass.
The engineer may repeat step 4 any number of times. How many of the windows shown below can the engineer make?
- **Step 1:** Make an equilateral triangular window frame.
- **Step 2:** Join the midpoints of its sides to form 4 new triangles.
- **Step 3:** Fit gray glass in the central one of the new panes.
- **Step 4:** Repeat steps 2 and 3 on any pane that does not yet have glass.
The engineer may repeat step 4 any number of times. How many of the windows shown below can the engineer make?