9.4. Through the point with coordinates $(9,9)$, lines (including those parallel to the coordinate axes) are drawn, dividing the plane into angles of $9^{\circ}$. Find the sum of the x-coordinates of the points of intersection of these lines with the line $y=10-x$.
Answer: 190. Solution. The picture is symmetric with respect to the line $y=x$, so the sum of the abscissas is equal to the sum of the ordinates. Through the point $(9,9)$, 20 lines are drawn, the line $y=20-x$ intersects 19 of them. For each point on the line $y=20-x$, the sum of the coordinates is 20, so the total sum of the abscissas and ordinates is 380, and the sum of the abscissas is half of that.

Criterion. 2 points for the correct answer without a correct justification. 4 points if all ideas are found, but the answer is incorrect due to a wrong count of the number of intersection points (for example, the student counts them as 20 or 40).