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. D’Oh! I didn’t think of that. I tried upside-downifying it, which only needed 2 moves; or a “proper” answer, which needed six moves. i gave up too easily.

2. laconicsax says:

Wait…I actually got one? Ha!

3. Dharmaruci says:

To hold the equat up to a mirroe I have to move ALL the matches.

1. The Moron says:

Have you considered moving the mirror instead?

2. Dharmaruci says:

Move mirroe would not be Richards soln. His is “Just hold the equation up to a mirror”

4. edwardv says:

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.

5. Chris Emerson says:

I did the upside-down and change 2 matches trick too… didn’t spot this!

6. edwardv says:

There’s also a four stick move to change it to 0 2 X 001 = 002

7. Great puzzle that required lateral thinking but had no other assumed information about the actual equation or match sticks. A proper puzzle. Pity I didn’t get it.

8. Eddie says:

Not a lot for discussion on this one.

9. Paul Durrant says:

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.

10. ctj says:

an alternative 0 move solution is to read the equation as

S – 2×501 = 802

where S = 1804

1. -M- says:

hmm… If Richard would have given this answer I would complain…

2. Tw*twatch says:

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

11. -M- says:

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

12. Walter says:

You don’t even need to use ore move a mirror. Put the matchsticks on a glass table, and view it from below.

1. -M- says:

nice!

2. Berhard says:

Nice, but did`t putting the matches on a glass table require to move them all?
hehehehehe…

13. Julia says:

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. Julia says:

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!

14. SimonP says:

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…

15. Anonymous says:

16. Thomas G says:

you could also just look at it from the side and all you would see is |, which in a Boolean sense is true

17. Andrew H says:

Without mirrors and glass tables I got it in 4.
5+7X86=602

18. Andrew H says:

Oops that should be 5+2

19. 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).

1. Anonymous says:

Wouldn’t moving matches be making a new equation too?

20. Anonymous says:

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 🙂

21. Anonymous says:

Good one! I’m very glad I didn’t spend much time on this; I’d have never gotten it…

22. The other Matt says:

Move four pieces complete away to another place and build there 1=1

23. I set fire to the matches and smashed the mirror.

On an unrelated note, I rotated the equation 180 degrees and moved the two matches as mentioned above.

24. Henry says:

Ouch. Please accept my middle finger as gracious thanks, Richard.