Reviewing good puzzle books is frustrating, because you get to page one of the introduction, find a curious puzzle, become engrossed for 20 minutes, miss your stop and then fail to get home in time to say goodnight to the kids. Be warned, Alex Bellos’s new book could put a strain on your personal life, particularly if you are willing to go through the joyful ordeal and gleeful torment of solving every single one of his 125 puzzles.

I should stress, the prosaically titled Can You Solve My Problems? is not just a random list of skull-warping brain-teasers, but rather a skilfully curated anthology of puzzles, most of them straddling that tricky zone between trivial and impossible, and at least half of them guaranteed to make you kick yourself. This is a book that should be accompanied with a free shin pad.

In between the puzzles, Bellos takes us back to the origins of various types of puzzle and explains their historical development. Although this will be familiar material for metagrobologists, normal people might not realise that, for example, it was Alcuin of York who published one of the earliest collections of recreational mathematics (an apparent oxymoron that serves as an umbrella term for all types of number puzzles).

Propositiones ad Acuendos Juvenes (or Problems to Sharpen the Young) was written in the 8th century and contains 53 (or 56, depending on the edition) problems, including the first example of a river-crossing problem. Bellos’s version of the problem is:

A man arrives at a riverboat with a wolf, a goat and a bunch of cabbages. He needs to cross the river, but the one 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?

Alcuin is a forgotten hero in the history of mathematics. Prior to Bellos’s book, the most important recognition of his contribution to the history of puzzles had been in Gone Maggie Gone, a 2009 episode of The Simpsons in which Homer wants to cross a river, taking Maggie, poison capsules and his dog with him.

If you are struggling with this puzzle, here is a hint. Work out which London Underground station has six consecutive consonants within a single word. The first of these is the first letter of the first item that you need to transport across the river in Alcuin’s original version of the problem.

Once you solve that puzzle, then you can try Alcuin’s saucier variation, in which you have to find a way for three men and their wives to cross a river in a boat that can carry only two people, so that no wife is left alone with a man who is not her husband.

By mixing history with puzzles in this way, we also learn that Lewis Carroll (also known as Charles Dodgson, an Oxford mathematician) authored three puzzle books and along the way invented the classic liar truth-teller conundrums. For example, meet Berta, Greta and Rosa:

Berta says that Greta tells lies. Greta says that Rosa tells lies. Rosa says that both Berta and Greta tell lies. Who is telling the truth?

Such problems might seem frivolous, but the fact that an Oxford don would dedicate so much of his life to solving and creating puzzles is a clue that we should not dismiss curious conundrums. If more evidence is required, then please bear in mind that in 2007 in Doctor Who episode 42, the Doctor bemoans the fact that recreational mathematics is not studied in schools. Fortunately, the Doctor has been well schooled in solving mathematical puzzles, and his knowledge of happy primes enables him to fire up the back-up engines, thereby preventing the SS Pentallian from crashing into the Torajii sun. By the way, to find out if a prime number (eg 79) is happy, then take the digits (7 and 9), square each one and add the results (49 + 81 = 130). Take the new number, square each digit again and add them (1 + 9 + 0 = 10), and so on (1 + 0 = 1). If you eventually end up at 1, then your number is happy. If not, then it is sad.

Moreover, Bellos reveals how intellectual giants, such as the mathematician John Conway, the Bletchley Park codebreaker Max Newman, the Nobel physicist George Gamow and many other smart cookies, devoted a significant amount of their time to playing with puzzles.

At first, hearing that a Nobel laureate spends time inventing puzzles seems like the nerdy equivalent of learning that the poet laureate enjoys writing dirty limericks. But Bellos is correct to view puzzles as wonderful poems rather than crass doggerel: “With elegance and brevity, they pique our interest, kindle our competitive spirit, test our ingenuity, and in some cases reveal universal truth.”

One of the great puzzle poets was Martin Gardner, a remarkable polymath whose life is only briefly covered by Bellos. Hopefully, readers of Bellos will be sufficiently intrigued that they will go on to read Gardner’s autobiography, Undiluted Hocus-Pocus, which describes his incredible life as a recreational mathematician, magician and rationalist.

For example, Gardner was one of the few rationalists who believed in a personal God and an afterlife. He defended his theological views in The Whys of a Philosophical Scrivener, one of his hundred or so books. Unfortunately, the 500-page tome was torn to shreds when it was reviewed in the New York Review of Books by a critic named George Groth. Groth, it turned out, was Gardner himself, destroying his own book.

Perhaps the greatest compliment I can give to this book is that when my son spotted it on my desk, he started flicking through it, furrowing his brow and asking me questions. He had remembered that we had already discussed wolves, goats and cabbages, he answered a dice question correctly (but for the wrong reason) and he had fun exploring some of the simpler arithmetic puzzles. There is a small chance that perhaps one day he will be a mathematician, but whenever I sit with him thinking about the same questions, I am certainly transported back to my mini-geek self, picking up my first Martin Gardner compendium of puzzles.

Can You Solve My Problems? is published by Guardian Faber (£14.99). Click here to buy it for £10.99