On Friday I set this puzzle…

Imagine that the following equation (5 – 2 x 501=802) has been made from matchsticks….


What is the smallest number of matchsticks that can be moved to make it correct? Oh, and you are not allowed to move one to the equation sign to create a ‘not equals to’ sign.

If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.

In fact, you don’t have to move any matches.  Just hold the equation up to a mirror…..



Did you solve it? Any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UKhere and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.


  1. The first one I found was two match stick moves. Turn it upside-down and the change -5 to -2. Another two stick move is change the equals into <, but that is probably not intended to count like making a "not equal to" doesn't count.

  2. I missed that completely. There are a couple of three stick moves though, if you evaluate left to right instead of evaluating the multiplication first.

    1. We will be keeping an eye out for you ctj.
      You are the sort of person that is of interest to our organisation.

  3. I did not do the mirror thing. I did the upside down thing:
    208 = 105 x 2 – 5
    2 matchsticks shifting make it change into:
    208 = 105 x 2 – 2

  4. I moved a couple of matchsticks for 2 x 401 etc and covered the ‘5 -‘ up with a piece of paper. The solution with the mirror (or glass table) is much better…

    1. I said on Friday that I liked the fact that the puzzle asked for the minimum number of matches instead of giving a target (can you solve the puzzle by moving x matches). I should have realised that the unusual way in which the question was phrased was a clue towards the answer. There is almost always a clue in the question!

  5. Hmmm. Holding up to a mirror doesn’t actually make it correct, it just gives the appearance of being correct. I guess it would be tricky to word this question without giving away the solution though…

  6. I don’t know, I’m not really satisfied with this canonical answer – to me, using a mirror doesn’t fulfill “make [this equation] correct”, because you left it unchanged and incorrect – instead, the NEW equation now visible in the mirror is correct.

    I stand by invert and move two (which was my original answer as well).

  7. Move the two to a 3 (1 stick) so that the left side is 1002
    Transform the right side into 1002 by picking up the center match of the 8 and making a (small!) 1 out of it

    .. not as elegant as the mirror, ok 🙂

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