Can you solve these knotty problems? - The Jewish Chronicle

Good, Bad and Ugly are about to take part in a three-way gunfight.

Each is positioned on one of the three points of a triangle. The rules are that Ugly will shoot first, then Bad, then Good, before returning to Ugly and continuing in the same order until only one person is left.

Ugly is the worst shot and can hit a target only one time in three. Bad is better, hitting a target two times in three, while Good is the best, never ever missing.

You can assume that everyone adopts the best strategy and no one is hit by a bullet that wasn't meant for them. Who should Ugly aim at to have the best chance of survival?

This conundrum is just one brain-teaser in Alex Bellos's latest book, Can You Solve My Problems? Readers are presented with 125 puzzles, for which they will need all their logical dexterity.

Question

A man arrives at a riverbank with a wolf, a goat and a bunch of cabbages. He needs to cross the river but the only boat available can carry only him and a single item at the same time. He cannot leave the wolf alone with the goat, or the goat alone with the cabbages, since in both cases the former will eat the latter. How does he cross the river in the shortest number of crossings?

Bellos has previously written books on Brazilian football, as well as two mathematics books for

children. But what inspired this

latest book?

"I wrote a puzzle in my blog, which is hosted by the Guardian," he explains. "It was a puzzle which I picked up off a website in Singapore. It was named 'Sheryl's birthday problem'.

"And it was the most successful story I have ever written in a 30-year career in journalism. Because within a few hours,

tens of thousands,

then hundreds of thousands, then millions of people, were clicking on to read this story.

"I was shocked," he continues, "because I wasn't expecting it.

"And I thought: 'Wouldn't it be fun to immerse myself in the world of puzzles and to try and tell the story, logic and history of mathematical puzzles, through choosing some of the best ones from the last 2000 years?'

"You write these books on mathematics. They do well, but don't get millions of people buying them. But all of a sudden you do a little maths puzzle, which was originally from a maths exam, and have millions of people fascinated by it."

The puzzles come from all over the globe, because, as Bellos says, "mathematics and logic is a universal language".

However, he does believe that recent technological shifts have affected the way puzzles are viewed.

"I think that the internet and the ease of access of everything means that we don't challenge our minds any more," he says.

"There is a perception that anything that is challenging our minds and is difficult is unhelpful and

not fun.

"But actually, using our minds is great fun.

"A good puzzle is like a piece of poetry. It has isolated some really interesting mathematical phenomenon or a piece of logic and presented to you in a really appetising way that eggs you on to solve it.

"And when you're using your wits, it gives you an achievable goal. It's like teasing you - I bet you can't do this, and so you want to prove that you can do it, and once you've done it, it's really satisfying."

Born in Oxford to Jewish parents, he says there was "not much" religion growing up.

"My father was born in Hungary in the Second World War, so the awareness of Jewish issues was pretty present in the household.

"But because we moved around a bit, we didn't really have roots in any particular Jewish community, whilst being, obviously, Jewish.

"However, my aunt Viv [Vivienne Bellos] was the head of music at North Western Reform Synagogue and recently received an MBE for services to Jewish music. So I do have relatives who are active in the Jewish community."

I put it to him that many in the religious Jewish community study the Talmud, which is believed

to sharpen the mind, and he agrees, referring to "religious textual

puzzles".

Although the puzzles in the book do not have a particularly Jewish angle to them, Bellos readily acknowledges the Jewish fascination with mathematics and brainteasers.

"If you look at maths departments and universities around the world, Jews are often there in quite large numbers," he says.

"I think we quite like abstract thinking, and also some of the playfulness to it."

Can You Solve My Problems is primarily aimed at adults, but that doesn't mean children will not be able to take on some of its thorny problems.

Indeed, one of the first puzzles in the book was being talked about as childsplay some 800 years ago.

"There's a 13th-century text that says 'this puzzle is so well-known, every five-year-old can solve it'," says Bellos.

"A couple of the puzzles are on a different sort of level, but the easiest of them are definitely accessible to seven, eight, nine, 10-year-olds."

And, on the subject of accessibility, about that question at the beginning of the piece…The answer is actually that Ugly would actually be better off aiming at neither of his two opponents with his first shot.

Why? Well, that is something you will have to work out for yourself. I could tell you, but where's the fun – or the challenge – in that?