Viral Fraction Puzzle Stumps the Internet

We love a good riddle or puzzle around here, so when we heard about the latest viral brainteaser making the rounds on the internet, we were instantly intrigued. This time, the popular head-scratcher is a math problem that focuses on fractions (remember those?).

Originally posted on Twitter by Ed Southall, an author and math enthusiast, the problem involves a square with one triangular portion of it colored in a friendly shade of pink. In the caption, Southall asks his followers a seemingly simple question about the picture: “What fraction is shaded?” Take one look at the image and you’ll know why so many folks kept guessing and second-guessing themselves!

What fraction is shaded? pic.twitter.com/f4kAjoX4C7
— Ed Southall (@solvemymaths) April 23, 2018

Considering this question was asked on social media and (fortunately) not on an actual test, many users had some pretty humorous responses. One user replied, “The pink shaded region is.” Another person wrote, “5 out of 4 people struggle with math.”

That said, other folks seemed to make it their mission to find the solution, even if it meant drawing elaborate recreations of the shape and writing out rows upon rows of numbers that made our heads hurt.

Ready to hear the real answer?

If you guessed 1/3, give yourself a round of applause because you got it right! If you’re still confused, reporter Andy Kiersz at Business Insider breaks it down perfectly: A basic rule of math tells us the area of a triangle is 1/2 (base x height), so if we assume the square is 1 x 1, the base of the pink triangle is 1, the length of the square. Then comes the trickier part — figuring out the height.

“The key trick is that the little triangle up top is similar to the pink triangle, which means that the little triangle is just a smaller version of the pink triangle,” Kiersz said. “A property of similar triangles is that the ratio of the triangles’ heights will be the same as the ratio of their bases. Since the pink triangle’s base is twice the little triangle’s base, its height is also twice the little triangle’s height. But we know that the little triangle’s height plus the pink triangle’s height is 1, so that means the pink triangle’s height is 2/3. Plug that on in and we get our area = 1/2 x base x height = 1/2 x 1 x 2/3 = 1/3.”

Phew! Talk about a brain workout. If you’re in the mood for more puzzles like this one — or simply want to improve your math skills — you can check out Southall’s book, Geometry Snacks ($12.24, Amazon).