>  How many triangles can you find in the attached image?

I make it 24.

I thought about it like this.

There are 8 enclosed areas in the diagram, 4 at the top and 4 at the bottom. 
For each triangle, each of those segments is either inside or outside the 
triangle.

Consider just the top 4 segments, "0" means outside the triangle and "1" 
means inside the triangle.  Some combinations obviously do not form a 
triangle, eg "1001" (the far left and far right segment are "inside").

The combinations that are possible to make triangles:

0000
0001
0010
0100
1000
0011
0110
1100
0111
1110
1111

For all of those apart from the "0000", there are precisely two possible 
states of the bottom row of 4 segments that make valid triangles.  For 
"0000" there are 4 possible combinations on the bottom row that make valid 
triangles.  10 x 2 + 4 = 24

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