Visible From the Origin
Trees stand at every lattice point $(x, y)$ with $1 \le x \le 10$ and $1 \le y \le 10$. Trees are thin, but a tree hides any tree directly behind it on the same ray from the origin. A tree at $(x, y)$ is visible from $(0, 0)$ if no other tree lies on the segment between them. How many of the 100 trees are visible? Give an integer.
Related problems & prerequisites
Worth solving first
- Triangles in a Triangle 5.0/10
- Unit Fraction Pairs 5.0/10
- Tilted Squares 5.0/10
Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.