Question

Consider a triangle on X–Y plane with vertices $(41,0)$, $(0,41)$, $(0,0)$. Number of integer-coordinate points strictly inside is:

• A. 780
• B. 800
• C. 820
• D. 741

Hint:

Pick’s theorem quickly counts interior lattice points for polygons.

Answer 1

The Correct Option is A

Using Pick’s Theorem: $A = \frac12 \times 41 \times 41 = 840.5$. Boundary points = $3 \times 41 - 3 = 123 - 3 = 120$? Correct calculation yields interior = $A - \frac{B}{2} + 1 = 840.5 - \frac{123}{2} + 1 = 780$. \[ \boxed{780} \]