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Sandy Wood
Brain Game: The Elevens Puzzle
by Sandy Wood - June 30, 2009 - 7:30 AM

bloghead_braingames.jpg

First, examine the equation below.

 the 11 puzzle

Obviously, this equation is false. There are a few ways we could alter the equation to make it true, such as removing the + from the left side and the × from the right side to make both sides read 1111. This maneuver would NOT solve today’s Brain Game, however. Too easy. Your goal:

Find a way to insert the SAME SINGLE MARK to the SAME SPOT
on both sides of the equation in order to make it true
.

Here is one ANSWER.
Comments (26)
  1. I got that you make it 111 + 11 = 11 x 11.

    Buuuuut…. I read the question wrong, so I get no points for finding another way.

  2. Yay, I finally got one!! I don’t have to start the day feeling like a dolt, woohoo!

    Captha: impede unite

  3. 11+1.1=11*1.1

  4. how about this

    -11 + 11 = 11 x 1-1

    -11 + 11 = 11 x 0

    0 = 0

    maybe???

  5. ok, so its not in the same spot

  6. sorry ian but your solution is incorrect. -11 + 11 = 11 x 1-1. you would multiply 11 by 1 before you would subtract the 1 by 1. it would come out to 0 = 11 – 1 which is false.

  7. Nice job, MG!

    And close, Ian – very close. Yoni’s right about the calculation, though. I still use the old “Please My Dear Aunt Sally” mnemonic to remember the order (Parentheses, Multiplication, Division, Addition, Subtraction).

  8. I just threw a subtraction sign in place of the (+) and (x) signs.

    11-11 = 11-11

    Obviously, that was not what you were looking for, lol.

  9. 1-1+11=1-1*11

  10. A single mark which would make this equation true, could also be to put a slash through the equals sign. Thus making the sign now (not equals).

    Then your unbalanced equation would also be true.

  11. I went with 1.1 + 11 = 1.1 x 11

    …but…

    what about putting a slash through the + and throught the x, resulting in * and *. Then, 11 * 11 = 11 * 11.

  12. 1^1+11 = 1^1*11
    1^12 = 1^11
    1 = 1

    you like it?

  13. 11 + 110 = 011 x 11
    121 = 121

    The 0 is in the same location relative to the equals sign.

  14. We always used Please Excuse My Dear Aunt Sally…well that’s what they taught us in middle school.

    (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

  15. We’re getting into semantics here, but I think you could make a good arguement this plays by the rules.

    11+1 (-) 1 = 11*1 (/) 1

    It is the same mark, and it’s in the same “spot” (meaning between the final two 1s on each side of the equation). It’s just rotated.

  16. pardon misspelling. “argument”

  17. 11=11=11=11
    or
    11-11=11-11

    Is that what you are looking for, or am I just being daft?

  18. 11 + 11 11 * 11

  19. 11 + 11 lessthan = greaterthan 11 * 11

    - comment system ate my angle brackets first time

  20. This is a bit of a stretch (and requires a font without the serif)

    adding a + sign on top of the third 1 on the left and inside either 11 on the right becomes:

    11 + +1 = 1+1 * 11

  21. I was thinking 11 + 11 =/= 11 * 11

    If it’s in the middle, it’s on both sides, technically speaking…

  22. There’s an easy anwswer if you get the point.

  23. How about a simple vertical dash down the middle of the equal sign.
    11 + 11 =|= 11 x 11

    (technically half of the vertical dash would be on the left, and the mirror other half making it a whole would be on the right. This would make the equal sign into a “not equal” sign.)

  24. I didn’t get this one – not a math person AT ALL, but all the talk of Please Excuse My Dear Aunt Sally reminded me of something. I was studying Spark Notes for the GRE Math section and they covered this and said, “Please Excuse My Dear Aunt Sally. Excuse us, but that is a supremely lame 1950s-style acronym. We prefer ‘Picking Eminem Made Dre A Star’ Whatever.”

    Loved it.

  25. Don’t worry John, I’m daft, too. I opted to just replace the ‘+’ and the ‘x’ with ‘.’.

    11.11=11.11

    :-D

  26. Jacob, 1-1 + 11 = 0 + 11 = 11
    1-1 x 11 = 0 x 11 = 0

    That argument does not make each side equal. Having said that I didn’t get the correct answer, just noticed that someone else didn’t either!

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