The answer is 10 triangles.
This fan is built to be counted exactly — no tricks hidden in the drawing. Look at the construction: one apex point at the top, 5 straight rays fanning down from it, and every ray touches the single straight baseline at the bottom. There are no horizontal crossbar lines — and that matters, because a crossbar would chop the fan into extra little stacked shapes. Without one, every triangle in this figure has its apex at the top point and its base on the baseline.
So a triangle is completely decided the moment you pick which two rays form its sides:
- Choose any 2 of the 5 rays: 5 × 4 ÷ 2 = 10 pairs.
- Every pair makes exactly one triangle with the baseline.
Count them by width if you want to see all ten: 4 smallest triangles (between neighbouring rays) + 3 spanning two gaps + 2 spanning three gaps + 1 whole fan, using both outer rays. 4 + 3 + 2 + 1 = 10. The skinny ones count. The giant one counts. And if you found yourself hunting for small triangles stacked halfway down — there are none, because there are no crossbars to make them.
Did you land on 10, or did your eyes invent crossbars that aren’t there? Be honest in the comments — and watch our page for tomorrow’s counting game.
