Brainteasers: Missing Things

April 29, 2011 By: erik Category: Funny, Geeky, Musings, Stuff I Found 985 views

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Missing SquareToday I wanted to share two of my favorite brainteasers. It’s just by chance that they are so similar, both tricking you into thinking something is missing. Every few years, I forget the trick to the first one – because I’m smart like that – and it stumps me again. The latter puzzle is more of an optical illusion than anything else. Like all good optical illusions, understanding how it works doesn’t ruin your ability to see it.

The Missing Dollar

Three men go to a restaurant for dinner and spend $25. Each man gives the waiter $10. The waiter keeps $2 as a tip and gives $1 back to each man. Thus each man pays $9, and so the group pay $9 x 3 = $27. The waiter keeps $2, making a total of $29. Where did the missing dollar go?

The Missing Square

Both triangles are made up of the same pieces, but one has a missing square. Why?

Missing Square

If you’re stumped, click on the image to go to Wikipedia for the mathematical solution, or watch this excellent video that my friend, Ray, made, which demonstrates the solution.

  • I’m interested in the missing $1. If you figure it out let me know.
    Only thing I can come up with is, the waiter gave the dollar to somebody else(bus boy or cook) or it went towards taxes on the meal that the three gentlemen ate, but I doubt either of those are right.

    • erik

      Oh, I know the answer. The answer is the same as the answer to the second puzzle: It isn’t missing. There are no other parties involved.

      The one surefire way to understanding the missing dollar is to actually break out some money and role play it.

      It’s also recommended that you wear padded gloves so as not to leave a mark on your forehead when you finally get it. 🙂

    • Luagnkid

      Its not missing. They pay 25 total for the meal +2 tip for the waitress. So thats $27 for the total meal+$3 back in change. They pay 9 each for the meal+tip.

  • ac

    The reason these are so confusing is that they are BS questions.
    We go through 16 years of school answering however many thousands of questions on tests which are always (well, almost) legitimate questions with actual answers.
    So we are we assume this is a legitimate problem that has an answer.
    These are not really logic puzzles, but social psychology puzzles.

    The missing dollar is a matter of trust. You assume there is a reason they are adding 27+2.

    The “triangles” are one of those good illusions. You assume they are triangles, so they look like perfect triangles, until you realize they are not. Then it is easy to see the dip and the bulge.

    • erik

      Indeed. Both questions are based on false assumptions that are easily accepted by the listener. But all magic tricks are.