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The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0) is:

1. 901
2. 861
3. 820
4. 780

Correct answer: 780

Solution

To find the number of interior integer points in the triangle, we can use Pick's Theorem, which states that the area of the triangle minus the boundary points gives the number of interior points. The area of the triangle is 820, and there are 40 boundary points on each leg and 41 on the hypotenuse, totaling 121 boundary points. Thus, the number of interior points is 820 - 121 + 1 = 780.

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