When I am not focused on discussing mathematical concepts and puzzles, I spend my time developing my children’s book series, Football School. This series utilizes the sport of football as a means of exploring the world. During my research for the newest book in the series, the Football School Encyclopedia, I stumbled upon an interesting geometric fact. In 1891, when painted markings were first added to the pitch, the goal area was shaped like a “B.”

The distance between goal posts is 8 yards (7.3m). In 1891, players were required to take goal kicks from a spot within 6 yards (5.5m) of either post. Therefore, each curved section of the letter “B” represents the path of a point located 6 yards away from each post.

Another method for comprehending the concept of “locus” is by envisioning a dog tethered to a goal post with a 6-yard leash. In this scenario, the locus of a point 6 yards away from the post would be represented by the circular path traced by the dog as it reaches the end of the leash.

This brought to mind the initial puzzle of the day. (The remaining two were also influenced by the Football School Encyclopedia.)

1. Dogged delivery

There is a five-foot wall surrounding a house. The only way to reach the front door is by following a path that begins at the main gate. A dog is tied to a tree in the yard, but can still reach the path due to the length of its leash. When a delivery driver arrives with a package, they must find a way to safely reach the front door without being attacked by the dog. How can they successfully deliver the package?

2a. The three lions

Three lions are confined in a pen. The preferred meal of lions is zebra. If a lion consumes a zebra, it will feel sleepy and could potentially be preyed upon by another lion in close proximity. Similarly, a lion that devours another lion will also feel drowsy and could face the same fate.

A zebra is placed in a fenced area. Lions are highly rational and prioritize self-preservation. They will only consume other animals if they are certain that they will not become prey themselves. Additionally, if a zebra is consumed, it will be by a single lion and not shared among the group.

Is the zebra able to survive?

of the vector

2b. The four lions represented by the vector

Is the zebra able to survive with four lions in the pen, similar to the previous scenario?

3. Dogged defending

Is the outcome of this scenario a goal or not?

I will return with the answers at 5pm UK time.

Please refrain from sharing spoilers. Instead, let’s talk about pitch markings, heraldic animals, or stories involving dogs in sports.

The answers can be found here.

The book “The Football School Encyclopedia” by Ben Lyttleton and myself can be purchased on The Guardian Bookshop and other online retailers. It is a large, full-color hardback that covers a wide range of topics related to football, including history, geography, science, statistics, rules, psychology, quizzes, and jokes. The Daily Telegraph gave it a perfect rating of 5 stars and stated that it is the only book about football that your children will need. TalkSport also recommended it as a great stocking filler, although parents may end up taking it from their children after Christmas lunch. But enough about the book, let’s get to the point! 😉

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.

Every other Monday, I post a new puzzle here. I am constantly seeking out interesting puzzles and welcome suggestions via email.

Source: theguardian.com