4. A square $10 \times 10$ is divided into unit squares. How many triangles are formed after drawing one diagonal?
Answer: 110.

Solution. The figure shows one of the obtainable triangles. All such triangles are right-angled, with the right angle vertex being any lattice node except those lying on the diagonal. There are a total of $11 \times 11$ nodes, and 11 of them are on the diagonal, so the number of triangles is $11 \times 11-11=110$.

Criteria. Any correct solution: 7 points.

Incorrectly accounting for nodes on the diagonal: 4 points.

Correct answer: 2 points.