Bwahahahahahahaha

Each layer adds 4 triangles to the total in each corner, and it starts with 2. So at layer n, you have 2+4 (n-1) triangles on any corner and multiply that by 6 for the whole layer. In this case, n is 1000, so you have 6 [2+4(1000)] = 24012.

This can be solved using a simple computer program:

def triangles(n):
    if n == 1:
        return 12
    else:
        return triangles(n-1) + 24

print(triangles(1001))

The code above works in Python. An extra line can be added to deal with invalid values of n.

(1+(2 999)) 12 + 24

12+24(n-1)

Traingles in each edge of the stars will be 1, 1+3, 1+3+4, 1+3+4+4, 1+3+4+4+4, 1+3+4+4+4+4... and so on... So for Nth star triangle in edge of the stars count to 4(n-1). Total no of edge=6 Total no of triangles= 6(4(n-1))=24(n-1). Now each edge is joined by 2 traingles so 6x2(extra triangle). So general formula for Nth star is 24(n-1) +12 So for n=1001. Ans=24x1000+12=24012