Puzzles & Quizzes

Can You Find Both Correct Answers to This Math Puzzle?

We love puzzles here at Curiosity: even the ones that are too hard for us. Scratch that — especially the too-hard ones. Even without getting the answer for yourself, it's satisfying to find out the one-and-only answer to the "Hardest Logic Puzzle Ever." But this puzzle is a little different: there's only one blank to fill in, but two possible answers that could go there. Can you figure out both of them?

The Setup

The puzzle consists of a series of numbers, which are all related to each other in a way that starts out clear-cut and swiftly gets murky. At the end, there's a single blank space for the last number in the sequence. Here's how it goes:

1 + 4 = 5

2 + 5 = 12

3 + 6 = 21

8 + 11 = ???

The First Answer

Okay, this looks doable. One plus four is five, so we're assuming that's how the first line works. But then there's the next line. Two plus five doesn't equal 12, but two plus five plus the five from the last line does. Okay. And then 3 plus 6 plus the 12 from the last line equals 21. Finally, eight plus 11 plus 21 equals 40. Voila — there's your answer.

The only problem is, there's another answer to this sequence. Take a minute to try and work it out. We'll give you a hint: for the second answer, the order of the lines doesn't matter, but the order of the numbers in those lines does. When you're ready, watch this video — this puzzler found the other answer more intuitive than 40. Can you work it out before he does?

The 1 + 4 = 5 Puzzle

The Second Answer

For the second answer to this puzzle, there's no interaction between the lines of numbers, so it doesn't matter what order the lines are in. The trick is that the math is a skosh more complex than simple addition. What if instead of just adding one and four to get five, you first multiplied them together, and then added the one? Well, first of all, you'd be making things more complicated than they need to be. And second, you'll have solved the other half of the puzzle.

As it turns out, the "multiply the two numbers then add the first number" strategy works all the way down the line. Two times five, plus two, equals 12. Three times six, plus three, equals 21. And eight times 11, plus eight, equals (drumroll please) ... 96. There you have it. The answer is either 40 or it's 96, but it's not a Yanny/Laurel style illusion, just good old-fashioned math-magic.

If you stumbled on that answer plus a half-dozen more, maybe it's time to turn up the heat in your mental kitchen. Try working your way through this book of math and logic puzzles from MENSA — you just might be a genius. We handpick reading recommendations we think you may like. If you choose to make a purchase through that link, Curiosity will get a share of the sale.

Written by Reuben Westmaas July 3, 2018

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