CLOSE
Original image
YouTube // TED-Ed

Can You Solve the Prisoner Hat Riddle?

Original image
YouTube // TED-Ed

If you like brain teasers, we've got a doozy for you. In this TED-Ed lesson, Alex Gendler walks us through the "prisoner hat riddle," a classic puzzle. In this version, you and nine other humans have been abducted by aliens. The aliens would like to eat you all, but not if you can prove your intelligence. So they propose a test.

The aliens line you up, placing you in order of height (tallest in the back, shortest in front), and place black or white hats on each of you. You must face forward, and you mustn't look at your own hat. Starting with the person in the back, each person must say a single word: "black" or "white" to guess the color of the hat on his or her own head, despite not being able to see it. If nine of you get it right, you live. If you don't, you're lunch. The good news? You get to talk it through as a group first.

This is a classic puzzler because it requires the group to devise a way to signal hat-color information without directly saying it. I'll admit, I watched the setup, paused the video, and thought about it a bit. I did not solve this riddle. Can you? (The answer is explained after about 90 seconds of setup.)

You can read more about this lesson from TED-Ed. If you like this kind of puzzle, you need to check out their Math in Real Life video series.

arrow
fun
Can You Figure Out How Many Triangles Are in This Picture?

Time for another brain teaser. How many triangles do you see here? A Quora user posted the image above (which we spotted on MSN) for fellow brainiacs to chew on. See if you can figure it out. We’ll wait.

Ready?

So, as you can see, all the smaller triangles can combine to become bigger triangles, which is where the trick lies. If you count up every different triangle formed by the lines, you should get 24. (Don’t forget the big triangle!)

Some pedantic Quora users thought it through and realized there are even more triangles, if you really want to go there. There’s a triangle formed by the “A” in the signature in the right-hand corner, and if we’re counting the concept of triangles, the word “triangle” counts, too.

As math expert Martin Silvertant writes on Quora, “A triangle is a mathematical idea rather than something real; physical triangles are by definition not geometrically perfect, but approximations of triangles. In other words, both the pictorial triangles and the words referring to triangles are referents to the concept of a triangle.” So yes, you could technically count the word “triangle.”  (Silvertant also includes a useful graphic explaining how to find all the pictorial triangles.)

Check out the whole Quora discussion for in-depth explainers from users about their methods of figuring it out.

[h/t MSN]

Original image
iStock
arrow
video
This Puzzling Math Brain Teaser Has a Simple Solution
Original image
iStock

Fans of number-based brainteasers might find themselves pleasantly stumped by the following question, posed by TED-Ed’s Alex Gendler: Which sequence of integers comes next?

1, 11, 21, 1211, 111221, ?

Mathematicians may recognize this pattern as a specific type of number sequence—called a “look-and-say sequence"—that yields a distinct pattern. As for those who aren't number enthusiasts, they should try reading the numbers they see aloud (so that 1 becomes "one one," 11 is "two ones," 21 is "one two, one one,” and so on) to figure the answer.

Still can’t crack the code? Learn the surprisingly simple secret to solving the sequence by watching the video below.

SECTIONS

arrow
LIVE SMARTER
More from mental floss studios