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Can You Solve the Counterfeit Coin Puzzle?

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Mathematicians have long plagued humankind with a style of puzzle in which you must weigh a series of items on a balance scale to find one oddball item that weighs more or less than the others. They're known collectively as balance puzzles, and they can be maddening...until someone comes along and trots out the answer.

Within the world of balance puzzles, the 12-coin problem is well-known (there's also a nine-coin variant, and a horrendous 39-coin variant). There is in fact a generalized solution for such puzzles [PDF], though it involves serious math knowledge.

In the video below, we are presented with a version of the 12-coin problem in which we must determine a single counterfeit coin in a dozen candidates. The problem is, we're only allowed the use of a marker (to make notes on the coins) and three uses of a balance scale. Here are the detailed conditions:

1) All 12 coins look identical.

2) Eleven of the coins weigh exactly the same. The twelfth is very slightly heavier or lighter.

3) The only available weighing method is the balance scale. It can only tell you if both sides are equal, or if one side is heavier than the other.

4) You may use the scale no more than three times.

5) You may write things on the coins with your marker, and this will not change their weight.

6) There's no bribing the guards or any other trick.

So how do we solve this specific case? Watch the video to find out.

For a bit more on this puzzle, check out this TED-Ed page.

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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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