Friday, 29 August 2014

The answer to the chain problem

The other day I posited a problem regarding linking a chain.

A woman has four pieces of chain.  Each piece is made up of three links.  She wants to join the pieces into a single closed ring of chain.  To open a link costs 2 cents and to close a link costs 3 cents.  She has only 15 cents.  How does she do it?

Most likely you drew it like this?

If so, you are totally normal.  Normal but wrong.

Drawing it like this means you start thinking about how to join the links at FOUR points.  Your brain gets stuck on four... you do the math and you are over the 15 cent limit.  Now perhaps you suspect a trick, so you begin to think about that perhaps you don't have to join them all.  Wrong.  These are all avenues your brain runs down but essentially lead you astray.

Rule number three for getting smarter is to practice and learn to change the representation.  That is, look at things differently.  The easiest way to do this is to draw or model it differently.

So here you go - I've represented it differently.  Think about opening the three bottom links and using them to join the other pieces.

Hope you got this.

To recap:  The ways to get smarter:

  • Increase your world knowledge
  • Automatize your thinking as much as possible
  • Change the way you represent things
If you follow the link above, I highly recommend you click through to the Hanoi tower.  Like steroids for the brain.


  1. Hang on I'm not sure I understand...did I simply assume all links of chain must be used rather than think laterally and allow myself to only use three links to make a joined chained?

  2. To solve it you take the separated three links (the three at the bottom) open them and then use them to join the other three parts. Most people won't think about distributing one of the groups of three, once they see the groupings, their brain just locks it in. Maybe I'll draw a picture to explain it.

  3. Excellent! I'm in the 'most' people group cause it never occurred to me to separate the group as you say. I wonder if this means I don't think outside the box - and I don't, very structured in my thinking!

  4. Well this problem is the classic in terms of trapping people into a one solution strategy. Unless you possess the KNOWLEDGE of how to re-represent then you will have a tough time solving it. The reason I say knowledge is because it's not a born ability, it's a learned strategy. You learn to think outside the box by developing those skills. You can be structured but also develop some skills that will help you look at things in new ways. So you are not stuck with a brain that is super structured, the brain will do what you teach it.

  5. Fascinating, makes me wonder what million other strategies for problem solving I haven't learned and many trillion I have!

  6. Funny thing is there are not that many strategies. And by the time you have done about twenty of these puzzles you start to see the patterns, pretty soon you can predict what the trick is. The really cool part is then taking those strategies to the real world and using them to solve real world problems.