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Wiseman’s Friday Challenge – Anatomy of a Puzzle

March 12, 2010

9 - 3 = 6 - move one line to make other valid equationsRichard Wiseman’s Blog has a weekly challenge. It is usually entertaining and I thought I would Highlight it in my blog.

This week’s challenge is based on the above graphic.  The challenge is as follows:

Can you move one matchstick and still have an equation that is correct?  I think there are at least three answers – can you find all three?

The nice thing about this puzzle is it has multiple levels – each of which stretch your imagination to varying degree.

The rest of this post has spoilers, so you might want to check out the original puzzle before going on (and no, I’m not worried about other readers of Wiseman’s blog finding this – my average readership has yet to get into the double digits).

On the first level, this puzzle stretches your visual manipulation skills – you mentally take lines away and add them in to make new numbers.  This is how you get the first solution:

Of course, the numbers are the most obvious things to manipulate – you have to start thinking outside the box to go further – for instance, a line crossing that minus sign can give you this:

With a little more exploration, we realize that that equals sign does not necessarily have to be exactly equals – this gives you the following:
And while we’re at it, equations don’t necessarily need to just be numbers – that’s what variables are for:

Of course, there may be more solutions – but that’s the beauty of this kind of puzzle – it’s exactly as hard as you want it to be!

Update: I forgot an easy one!

That makes 21 – unless you don’t count inequalities (apparently “equation” strictly means both sides are equal) in which case, I have 9

update 2: make that 10:

I think I’ll stop there.

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