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Can You Solve the Control Room Riddle?

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In this riddle from TED-Ed, you've got a tricky math problem to solve.

In the riddle, you're trying to infiltrate the headquarters of an enemy organization, locate a secret control panel, and shut down their death ray. There are various reasons why this isn't easy.

First off, the enemy headquarters is a ten-story pyramid. It has a regular structure, where the top level contains one room, the floor below that has two rooms, and so on—the ground floor has 10 rooms. The control panel is hidden behind a painting, on the highest floor that satisfies the conditions listed below.

Each room has exactly three doors to three other rooms on that floor...except the control panel room, which only connects to one room. (Thus, the control panel room only has one door in it.)

There are no hallways, and you can ignore stairs while figuring the layout of the building.

You have no floor plan.

You only have enough time to search a single floor before the alarm system goes off.

Given the rules above, can you figure out which floor the control room (with its associated control panel) is on? Watch this video, and pause at the one-minute mark (when instructed), for a video view of the same problem. The solution is then presented, with a step-by-step breakdown of how to get there.

To figure out the solution, it may help to start drawing room maps, starting at the highest floor. If you're interested in this kind of puzzle, read up on graph theory.

For more on this puzzle, check out this TED-Ed page, and be sure to visit the "Dig Deeper" section, which includes links to the puzzle author's website, Doctor Ecco.

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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]

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This Puzzling Math Brain Teaser Has a Simple Solution
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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.

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