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

Earlier today I set you the following three puzzles, loosely inspired by my new book, the Football School Encyclopedia. (To see why here’s the original post.)

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?

Solution

Here’s one way. Loudly walk round the house. The dog will follow you round, and end up winding the leash around the tree, thus reducing its effective length. Once the dog won’t reach the path, the delivery driver is safe to deliver the package.

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?

Solution No. The zebra dies.

We solve this by imagining a single lion in the pen, seeing what happens, and then increasing lions.

One lion, one zebra: The lion eats the zebra.

Two lions, one zebra: Neither lion eats the zebra, since if one did it would get eaten by the other.

Three lions, one zebra: One lion eats the zebra, because it has worked out that when it gets drowsy, neither of the other two lions will dare eat it. This is because when it is drowsy, the situation is analogous to the ‘two lions, one zebra’ scenario, in which neither lion eats the zebra.

2b. The four lions

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

Solution Yes! The zebra survives.

Carrying on the workings from above:

Four lions, one zebra: No logical lion will eat the zebra, since if they do, the situation will become analogous to the “three lions one zebra” scenario. With three hungry lions and drowsy lion, the drowsy lion will get eaten.

3. Dogged defending

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

Illustration: Spike Gerrell/Walker Books

Solution:

From the Football School Encyclopedia
From the Football School Encyclopedia Illustration: Spike Gerrell/Walker Books

I hope you enjoyed today’s puzzles. I’ll be back next week. Woof woof!

Football School Encyclopedia
Photograph: Walker Books

The Football School Encyclopedia 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! 😉

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.

Read original article here

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