Did you solve it? The art of the puzzle

The solutions to today’s artful problems

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Photograph: Roman___/Getty Images/iStockphoto
Photograph: Roman___/Getty Images/iStockphoto

Last modified on Mon 22 Feb 2021 12.02 EST

Earlier today I set you the following puzzles. The first is a starter problem and the other three were suggested by puzzle guru Rob Eastaway.

The nine dots

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

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Solution Yes, you needed to think outside the box.

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Photograph: alex bellos

To find the inside-the-box solution of the 5x5 grid, Rob Eastaway wrote an article about the puzzle here.

1. Bunting 101

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

Solution: d)

This is lovely because it is so counter-intuitive. That extra 1m in length provides enough to raise the bunting by 7.1m. Not only could the players comfortably walk underneath, but they could drive through in a tractor. The extra one per cent gives a surprising amount of slack.

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The bunting raised in the middle to height h gives two right-angled triangles.

The proof uses Pythagoras’s Theorem, which states that the square on the hypotenuse of a right-angled triangle is equal to the sums of the squares on the other two sides.

h2 + 502 = 50.52

h2 + 2500 = 2550.25

Rearranging, we get h2 = 2550.25 – 2500 = 50.25. So h = √50.25 = 7.1

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).

Solution: 9, 7, 2, 14, 11, 5, 4, 12, 13, 3, 6, 10, 15, 1, 8 or the reverse.

What’s nice about this one is that it looks like it’s going to be difficult, and you won’t know where to start, but there are lots of easy entry points and in the end the solution drops out. And it is lovely that there is only one solution

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?

Solution 50 per cent

This is a problem that suggests it will involve complicated probability theory, and maybe lots of working out. Yet the answer pops out with a simple bit of logic.

Princess either has more female puppies than Goldie or she has more male puppies. (It is impossible for Princess to have more female puppies and have more male puppies as Goldie.) Since males/females are equally likely, the chance of more females must be 50%.

I hope you enjoyed today’s puzzles. Thanks to Rob Eastaway for suggesting them

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.

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