How Many Triangles Are In This Photo?

(Popular Mechanics) We Spent All Day Arguing About This Triangle Brain Teaser. Can You Solve It?

By Jan 31, 2020

Mathematicians reveal the real answer. See if you’re right.

There’s nothing quite like a maddening math problemmind-bending optical illusion, or twisty logic puzzle to halt all productivity in the Popular Mechanics office. We’re curious people by nature, but we also collectively share a stubborn insistence that we’re right, dammit, and so we tend to throw work by the wayside whenever we come upon a problem with several seemingly possible solutions.

This triangle brain teaser isn’t new—shoutout to Popsugar for unearthing it a couple years ago—but based on some shady Internet magic, the tweet below reappeared in my feed today and kick-started a new debate on our staff-wide Slack channel, a place traditionally reserved for workshopping ideas, but instead mostly used for yelling about other stuff that we occasionally turn into content.

Because I’m a masochist, I drew the triangle again and asked everyone on staff to promptly drop what they were doing and attempt to solve the simple question: How many triangles can you find?

I’ll spare you the full conversation—trust me, nobody wants to see that—but the team’s responses ranged all over the place. Some editors saw four triangles. Others saw 12. A few saw 6, 16, 22. Even more saw 18. One wiseguy counted the triangles in the A’s in the question itself, while another seemed to be having an existential crisis: “None of these lines are truly straight, just curves—thus you cannot define any of them as a triangle,” he said. “There are no triangles in this photo. Life has no meaning.”

We then posed the problem to our Instagram followers, whose replies also ran the gamut, from 5 to 14 to 37. While we acknowledge the high probability of trolling here, it’s clear that people respond to the problem many different ways.

I could’ve listened to my colleagues explain their questionable processes all day, but instead, I reached out to several geometry experts to see if we could arrive at a consensus answer. Turns out virtually all of the mathematicians I contacted found the same solution—but not all of them figured it out in the same way.

If you don’t want to know the answer just yet, stop reading and try to solve the problem first. I’ll meet you back here when you’re done.

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