The one with the Triangular grid.Discrete Mathematics Level 3
Find the number of ways from \( (0,0) \) to \( (8,8) \) in the right angled isosceles triangle forming the sides:
\( 1) \quad(0,0) \) to \((8,0) \),
\( 2) \quad(8,0)\) to \((8,8) \),
\( 3) \quad(0,0)\) to \((8,8) \).
You can only go in positive vertical or horizontal directions(only integer co-ordinates). Diagonals are not allowed.
Bonus: Try to find the number of ways for a general case like \( (0,0) \) to \( (m,m) \).