Can you solve it? The art of the puzzle

Thinking in and out of the box

UPDATE: The solutions are now up here

Photograph: DrAfter123/Getty Images
Photograph: DrAfter123/Getty Images

Last modified on Mon 22 Feb 2021 12.02 EST

What makes for a great puzzle? Here’s a golden oldie that certainly qualifies.

The nine dots

Join the nine dots using four straight lines without your pen ever leaving the paper.


The nine dots puzzle is a classic because anyone can have a go without any specialist knowledge, it’s easy to understand what to do, and not too hard to crack. I find it like a story in three acts. You start off with great confidence, are plunged into despair, and finally make the breakthrough. When the solution comes, it is very satisfying.

Supposedly, the nine dots puzzle is the source of the phrase ‘thinking outside the box.’ For a further challenge, can you join the 25 dots of a 5x5 grid with only eight straight lines? Again, you must not take your pen off the paper, but this time you must not let any line go beyond the grid. It requires some crucial, if under-rated, inside-the-box thinking.

I have been pondering what makes for a good puzzle after reading this short essay by Rob Eastaway, New Scientist’s puzzle adviser and a former president of the Mathematical Association. He makes the point that puzzles (which must be fun) are different from maths problems (which often aren’t). What is it that can transform a maths problem into a puzzle? Here’s an incomplete list:

  • An ‘aha’ moment

  • A surprising, counter-intuitive outcome

  • Visually appealing

  • Whimsically written

  • Requires little background expertise

  • Concisely stated

  • Pleasurably teasing: looks very simple but isn’t

  • Easy entry point

I asked Rob to select three of his favourite puzzles for today’s column. Each includes at least one of the points above.

1. Bunting 101

A football pitch is 100 metres long. A piece of bunting 101 metres long is tied to the bases of the two corner flags along one side of the pitch. When the bunting is lifted at the middle of the pitch, the players will be able to:

  1. a) Barely get their fingers underneath.

  2. b) Crawl under.

  3. c) Get under if they crouch.

  4. d) Comfortably walk under.

[note: the bunting is non-elastic, and is raised until it is taut.]

2. My neighbours are squares

Arrange the numbers 1 to 15 in order so that each pair of neighbours adds up to a square number (for example 11+5=16).

3. A bitch of a puzzle

Goldie has just had four puppies, but her sister Princess has had five. However it’s not the litter size that their owners care about, it’s the premium that they get for female puppies. What’s the chance that Princess has had more female puppies than Goldie?

I’ll be back with the answers at 5pm UK.

Meanwhile, NO SPOILERS. Please discuss what makes for a good puzzle in the comments below.

UPDATE: You can read the solutions here.

If you are interested in the art of the puzzle, Rob Eastaway and Ben Sparks are hosting an online talk on this subject on Thursday March 4 at 4.30pm UK time. For more details and to get tickets click here.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I’m the author of several books of puzzles, most recently the Language Lover’s Puzzle Book.

Thanks to Rob Eastaway. You can follow him @robeastaway on Twitter. His latest book is Maths on the Back of an Envelope.

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