Can you solve it? Are you a lion of logic? | Mathematics

When I’m not writing about maths and puzzles, I’m working on my children’s book series, Football School, which uses the sport as a lens to the world. Researching the Football School Encyclopedia, the latest book in the series, I discovered the following geometrical curiosity. When painted pitch markings were introduced in 1891, the goal area was in the shape of a “B”.

1901 FA cup final. Tottenham Hotspur 3 Sheffield United 1. Played at Crystal Palace, London in front of a then world record crowd of 110,820 . Photograph: Chronicle/Alamy

Goal posts are 8 yards (7.3m) apart. In 1891, goal kicks had to be taken from within 6 yards (5.5m) of either post, so each curved part of the “B” is a segment of the locus of a point 6 yards from each post.

One way to understand the term “locus” is to imagine a dog on a 6 yard leash tied to a (goal)post. The locus of a point 6 yards from the post is the circle made by the dog when the leash is taut.

Which reminded me of today’s first puzzle. (The other two are also inspired by the Football School Encyclopedia.)

1. Dogged delivery

A house is surrounded by a five-foot-high wall. Its front door can only be reached by a path, which you enter from the main gate. An attack dog is leashed to a tree in the garden, with enough slack in the leash for the dog to reach the path. A delivery driver arrives with a package. The delivery driver is going to have to walk down the path, but cannot risk getting attacked by the dog. How do they deliver the package to the front door safely?

2a. The three lions

Three lions are in a pen. Lions’ favourite food is zebra. If a lion eats a zebra, however, the lion will become drowsy and may be eaten by another lion if one is nearby. A lion that eats a lion will also become drowsy and risks being eaten by another lion.

A zebra is put in the pen. Lions are very logical, and also self-preserving. They will only eat other animals if they are sure they will not be eaten themselves. Also, if a zebra is eaten, it is eaten by one lion only, not shared by the pack.

Does the zebra survive?

2b. The four lions

The same as above but with four lions in the pen to start. Now does the zebra survive?

3. Dogged defending

Does the following situation result in a goal, or no goal?

Football School still
From The Football School Encyclopedia Illustration: Spike Gerrell/Walker Books

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

PLEASE NO SPOILERS. Instead discuss pitch markings, heraldic animals or stories about dogs in sport.

UPDATE: The solutions can be read here.

Football School Encyclopedia
Photograph: Walker Books

The Football School Encyclopedia by Ben Lyttleton and me is available on The Guardian Bookshop and other online retailers. It’s a large-sized hardback, full-colour and gives 110 per cent: you will find lots of history, geography, science, statistics, rules, psychology, quizzes, jokes and more. The Daily Telegraph gave it 5 stars, saying: “If your children like football, there’s only one book you need.” TalkSport said it was the perfect stocking filler, even though parents would be stealing it from their children after Christmas lunch. Okay, enough self-promotion. You know what to do! 😉

Puzzle 1 adapted from Hall of Fame Lateral Thinking Puzzles by Des MacHale and Paul Sloane, Puzzle 2 adapted from Math Puzzles for the Clever Mind by Derrick Niederman.

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.

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