Find the number of points with integral coordinates which lie inside the triangle formed by joining the points (0, 0), (20,0) and (0, 20).

To solve this problem, we need to find the number of integral points in the triangle formed by the points (0,0), (20,0), and (0,20).

Step 1: Draw the triangle and identify the points. The triangle is a right triangle with the hypotenuse along the line x + y = 20.

Step 2: We need to find the points with integral coordinates. These are points where both the x and y coordinates are integers.

Step 3: Start from point (1,1) and move towards point (19,1), we have 19 such points.

Step 4: Similarly, move towards point (1,19) from point (1,1), we have 19 points.

Step 5: Continue this process, the number of integral points on each line parallel to the base decreases by 1 as we move upwards. So, the total number of points is the sum of the first 19 natural numbers.

Step 6: The sum of the first n natural numbers is given by the formula n*(n+1)/2. So, the sum of the first 19 natural numbers is 19*20/2 = 190.

So, there are 190 points with integral coordinates inside the triangle.