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> 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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