Puzzle: solve this equation!

You have the following false “equation”, made with six toothpicks arranged on a table in the following way:

XI = I

You have to re-establish the equality by changing the position of a single toothpick. Common-sense rules apply: you are not allowed to bend, break, or remove any toothpicks.

Comments (34)

  1. Re-establish the equality? As in I need an equals sign?

    One could move the "I" in "XI" and make a != sign (in math, the = sign with a slash over it).

    Or, just make 1/1 = 1.

  2. Well, technically, I suppose the != (I can’t remember the ASCII for a not equals sign, if there even is one…) is an equality operator.

    You could make a V = V (lopsided V’s: | = |/)

  3. Adi Oltean says:

    1/1 = 1 is a good solution, but not the only one 🙂

    The final solution must be stil an equality: != is not a good answer…

  4. Well, the one X would look funny. Kind of like my V’s.

    I’m looking at it at 90 degrees and I can’t see anything yet. I think I need to have a few more beers, that seemed to make programming better today anyhow.

  5. FOX says:

    You can move the "I" in "XI" over to the other side and make it X = X.

  6. I know!

    Make // 1 = 1

    Then it would be a comment, so the compiler wouldn’t look at it anyways.

  7. Wesner Moise says:

    Move a toothpick above the X so that

    Sqrt of 1 = 1

  8. That would be a funky sqrt sign, but it works.

  9. Mike Weller says:

    Well we know XI is 11 in roman numerals. How about moving one of the ‘=’ to the right to make

    XI – 11 ?

  10. David Smith says:

    These are all good solutions. I like it.

  11. fowl says:

    it is already true



  12. __me says:

    OK, move the I pick from XI to the right hand side and get

    X = II

    this is obviously true. why, X = 10 in binary (msdn here or what?) is 2, which is the same as II in roman encoding.

  13. DWD says:

    I would go with either X = X, II = II or I/I = I

  14. And there’s always:

    /I != I

    Where the ! and = overlap – you take one of the picks from the X and move it over the = sign

  15. David Betz says:

    I have an IQ of like…uh 30? I’m like a total moron but even I know that…

    II = II

    Roman numerals.

  16. David Betz says:

    oops text didnt come out right…lemme try it another way! haha X != 1 that should be more readable…

  17. David Betz says:

    heck actually my typo is legal…. II = II by "changing the position" of one and tilting the other! That not a bend, break, or a remove…and I thik common sense states that changing the axis is not changing the position.

  18. Franz says:

    X means 10 in Roman numeral while + also means 10 in Chinese numeral 🙂

  19. BigB says:

    X is non equal to I

    So leave the number X at the right side and cross the equality sign

    the non equal sighn is when you cross the equal sign.

  20. judge bools says:

    Hey Adi, some of your maths related stuff has been pretty funky, I remember the stuff about Godel numbers

    Why not blog about Lax winning the Abel prize instead of silly puzzles (or both, if you feel that way inclined)?

  21. SwitchBL8 says:

    Move the left I over the =, so that it reads:

    X <> I (where <> is = with a dash).

    Equation is correct then.

  22. SwitchBL8 says:

    OMG. The solution was already here. Sorry ’bout that.

  23. Adi Oltean says:

    >> Move the left I over the =, so that it reads: X <> I (where <> is = with a dash). Equation is correct then.


    No, no. As mentined in the original post, you must also have the equality maintained.

    So far: 1/1=1 is a good solution. X = X is probably on the edge. (given that you don’t really have an X on the right side).

    But there is yet another solution left that nobody found it out yet…

  24. What about Wesner’s solution of sqrt(1) = 1?

    (Move the one part of the X to make the sqrt symbol)

  25. "it is already true


    X=1 "

    How so? You lose a tootpick in the second line.

    Roman numeral XI is 11 in base 10, and that does not equal 1.

  26. Luke Stevens says:

    I’ve got it!

    X’ = 1

    (x prime, the derivative of x, taken with respect to x, is one)

    Almost as good as | = |

  27. The prime symbol is too short for it to be a toothpick…

  28. __me says:

    yes, i still insist on

    X = II

    (10) = (2)

  29. Andrei Maxim says:

    Judging from the position of the toothpicks, it’s rather obvious that you can’t move the toothpicks that make up the equality sign or the right side one.

    That means you could only move the three toothpicks that make up the lvalue. Unfortunatly, that X sign is rather difficult to alter (/| or | don’t really mean anything) so the only one left that could be moved is the vertical toothpick.

    Since X = II or IX = I or -X = I don’t really make sense, I believe another answer (besides 1/1 = 1) is X = T. Thinking a bit outside the box, X and T could hold the same value and therefore be equal.

  30. Wesner Moise says:

    The actual answer, derivative, is less satisfying than the other creative alternatives suggested.

    Anyway, how about square root of -1 is the imaginary number:

    /-1 = I

  31. Dan Brennan says:

    Since X1 = 1, then X = 1, so X = 1 ^^ 1 (1 raised to the first power). Or you could raise X to the first power to get the same result.

  32. Luke Stevens says:

    Here’s another one, sort of:

    1^x = 1

    where the 1 is moved so that x becomes its exponent in superscript. The positioning is a little off, and you could argue about 1^.5 having multiple values, for example, but otherwise it works.