Love Mathematical Puzzles? Readers share 49 books like Mathematical Puzzles...

Raymond Smullyan is a riddler, a puzzler, well-known for various Knights and Knaves puzzles, a type of logic game where some characters can only answer questions truthfully, and others only falsely. However, I recommend this book as here he offers not only logical tricks but many insights too. One section offers the World's shortest explanation of Gödel's theorem which is a magnificent achievement but frankly, reminds me why I like long explanations sometimes.

Basically, this is an examination of boolean logic, which is (rather boringly) a branch of algebra in which all operations are either true or false, and relationships are expressed with logical operators such as and, or, or not. So it’s serious stuff, but also pretty funny along the way.

Abraham Lincoln famously had little formal education but was capable of sophisticated logical thinking in his arguments. He credits his ability to form his arguments to his encounter with Euclid’s writings about geometry. He felt in awe by the notion of “demonstration” and went on to apply that notion to his compelling arguments about the injustice and hypocrisy of slavery. 

Polya was a great mathematician who knew what counted (after all, he made major contributions to combinatorics, the mathematics of counting). He thought hard about what he was doing when working on problems in mathematics, developing a mental process that lead to creative breakthroughs and solutions. Polya’s problem-solving method is broadly applicable to domains other than mathematics, and this book features many nice puzzles to improve your thinking.

Algorithm design is challenging because it often requires flashes of sudden insight which seem to come out of the blue. But there is a way of thinking about problems that make such flashes more likely to happen. I try to teach this thought process in my books, but Polya got there first.

In the history of science, fields of studies have evolved from empirical to principled. In linguistics, field linguists had understood the need to construct grammars of languages they encountered. Noam Chomsky understood the need to place grammars into a mathematical hierarchy of formalisms, showing through brilliant counter-examples which grammatical constructs could be handled by each formalism. For example, Chomsky showed that finite state automata model noun phrases beautifully but fail with if-then sentences. He showed that context-free grammars handle if-then, but fail at passive constructions. The book offered a new way to think about language.

Peter Winkler is famous for his collections of counterintuitive puzzles. Thousands of people, including me, have spent many sleepless nights trying to understand the mysteries in these puzzles, for which, I am forever grateful.

Haunting puzzles in the book include hats and infinity, all right or all wrong, comparing numbers version 1/2, wild guess, laser gun, precarious picture, names in boxes, sleeping beauty, and dot-town exodus.

Most puzzle books exclude counterintuitive puzzles for unknown reasons. So, many people incorrectly assume that counterintuitive puzzles are majorly found in paradoxes. Peter Winkler in this book shows that counterintuition can come from either puzzles or solutions or both, and they need not come from paradoxes alone.

Finally, reading Winkler's statements is an absolute delight due to its enjoyable and entertaining nature.

I have always liked the classical geometry of triangles and circles, but Matt Parker's book helped me go way beyond that and broaden my whole outlook. And the attractively hand-drawn diagrams and zany humour just added to the whole experience. After all, how many maths authors do you know who decide to build a computer out of 10,000 dominoes, just to calculate 6 + 4? 

Anany Levitin introduced me to algorithmics – my second love (my first love is mathematics), through his legendary algorithmics textbook. He was one of my superheroes in my young adult life and he got me addicted to algorithms. His book is my favorite because it is beautifully organized based on design techniques, well-written, and uses nice puzzles to teach algorithms.

Levitin went much deeper and wrote this book on algorithmic puzzles. This book is the first mainstream book in the puzzle literature that taught beautiful algorithmic puzzles via various algorithm technique techniques. Levitin claimed several mathematical puzzles as algorithmic focusing on aspects of the solutions that are automatable.

Elegant puzzles (with extensive references) in this book that I have enjoyed include missionaries and cannibals, bridge crossing, circle of lights, MU puzzle, turning on a light bulb, chameleons, poisoned wine, game of life, twelve coins, fifteen puzzle, hats with numbers, and… show more.

The Scientific American columns of Martin Gardner ran for 24 years and were read by amateurs, semi-amateurs, professionals, and major mathematicians (Conway, Knuth, Diaconis...). It was the interaction with this audience (recorded in addenda) which gave these essays their special quality and will give the interested outsider a real feel for what interests mathematicians. The collected columns are being reissued by the AMA and CUP but my view that anything by Martin Gardner is worth reading is reflected in my personal library.

I was given this book when I was about 15, and devoured it. It is an eclectic collection of mathematical paradoxes, fallacies, and curiosities so strange that they seem impossible. Mathematical magic tricks, a proof that all numbers are equal, a proof that all triangles are isosceles, a curve whose length is infinite but whose area is finite, a curve that crosses itself at every point, a curve that fills the interior of a square. Infinities that are bigger than other infinities. The Saint Petersburg Paradox in probability, a calculation that you should pay the bank an infinite amount of money to play one fair coin-tossing game. The smallest number that cannot be named in fewer than thirteen words (which I’ve just named in twelve words).

The Four Color Problem was one of the most baffling questions in mathematics for over 120 years. First posed in 1852, it asks whether every map can be colored with four colors, or fewer, so that regions adjacent along a boundary have different colors. The answer (yes) was finally obtained in 1976, with massive computer assistance. This method was initially controversial, but the result is now firmly established. This highly readable account, with full-color illustrations, opens up the history and the personalities who tackled this topological enigma, as well as making the mathematics comprehensible. The path to the final solution is littered with blunders and mistakes, but also illustrates how mathematicians can join forces across the generations to chip away at a problem until it cracks wide open.