Mindbenders

Giving Puzzles a Punchline

Developing puzzles can be like developing jokes


Here's a joke that is told by the comedian Richard Lindesay.

   My doctor told me that the average daily energy intake for a man is 2500 calories......So that's good.....It's not every day you find out you’re officially above average. 

Part of what makes audiences laugh out loud at that joke is that Lindesay is known for being a bit overweight.  The same joke told by (say) me would barely raise a smile.

But there is more to it than who tells the joke.  Jokes themselves are often the result of careful crafting, having been through several iterations before they become the finished article.

According to comedy director Chris Head, the 2500 calorie joke began its life as this:

  The average daily energy intake for a man is 2500 calories, which makes me above average.

This version is much flatter.  There's less of a build-up before the punchline, and there's no context to the story.  We might wonder: 'Why is the comedian telling us this?'.  The joke needed to go through a couple more stages of refinement before it became the version that started this blog.

In many ways, puzzles can be like jokes.  The very best puzzles create reactions of surprise or laughter, but a good puzzle might have started life as a simple mathematical idea that then needed to be honed into something that would grab the attention of its audience.

Let's see this in action.  Here is a routine maths-problem:

    A+B = 78

    B+C = 69, 

    A+C = 137

    Work out A+B+C.

How can we make this problem more engaging?  We could try making A, B and C represent something physical in the real world.  How about this:

Alf and Bert together weigh 78kg.  Bert and Charlie weigh 69kg.  And Alf and Charlie weigh 137kg.  What is the combined weight of Alf, Bert and Charlie?

Hmm.  Even though A, B and C now represent people, the problem isn't much more engaging in this form. Who are Alf, Bert and Charlie, and why should we be interested in their combined weights?  And how is it that we know the weights of them in pairs yet we don't already know their individual weights?  For many people, the reaction to this puzzle would be: Who Cares?

About 30 years ago, this Alf, Bert and Charlie problem was re-worded to become a UKMT challenge question.  The UKMT's version has become a classic:

Weighing the baby at the clinic was a problem. The baby would not keep still and caused the scales to wobble. So I held the baby and stood on the scales while the nurse read off 78kg. Then the nurse held the baby while I read off 69kg. Finally I held the nurse while the baby read off 137kg. What is the combined weight of all three?

This time there is a reason why we don't know the individual weights - it's because babies can't weigh themselves.  And the laugh that comes from the absurdity of the final weighing makes us much more motivated to tackle the problem.

Like jokes, the best puzzles have an engaging storyline and a good punchline.