The answer is 15 triangles.
This one looks like it should have a trick — it doesn’t, and that’s the trick. Look at the fan: one point at the top, 6 straight rays fanning down from it to a single horizontal base line. The two outermost rays are the sides of the big triangle.
Now the key fact: every single triangle in this figure has its apex at that top point and its base sitting on the base line. There are no cross-bars — no horizontal lines halfway down — so no smaller, stacked triangles can form. A triangle is completely decided the moment you pick which two rays form its sides.
So count the pairs:
- Choose any 2 of the 6 rays: 6 × 5 ÷ 2 = 15 pairs.
- Every pair makes exactly one triangle with the base line.
15 triangles. The skinny one between the first two rays counts. The huge one using both outer rays counts. Every width in between counts exactly once — which is why people who count “sections” stop at 5 (those are just the smallest slices), and people who hunt for hidden cross-bar triangles find none, because there are none to find.
Did you land on 15, or did the fan stop you at 5? Be honest in the comments — and watch our page for tomorrow’s counting game.
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