The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices (0,0),(0,41),(41,0) is:
Solutions · 1
Official solution
Total integral points inside the square [0,40]×[0,40]: 40×40=1600.
Integral points on the diagonal x=y within this square: (1,1),…,(40,40): 40 points.
The triangle is half of this square (below the diagonal x+y=41, roughly), so:
\[\text{Interior points of triangle} = \frac{1600-40}{2} = 780\]