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Mathematical Brain Teasers and Logic Puzzles

An award-winning author, mathematician, and puzzle enthusiast shows you how to master tricky brain teasers, solve challenging riddles, and increase your chances of winning games.
Mathematical Brain Teasers and Logic Puzzles is rated 4.5 out of 5 by 15.
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Rated 5 out of 5 by from Very good Pushes the mind to think outside the box Learn to think differently with better results.
Date published: 2021-11-27
Rated 5 out of 5 by from Terrific course, informative, intriguing If you like puzzles of any kind this course is ideal. Your inner nerd will befriend your inner geek and the two of you will have a good time. Wonderful teacher/ great subject.
Date published: 2021-09-23
Rated 5 out of 5 by from Fun Games & Stories with and without formal Math It's pretty cool - for Math. I was really surprised at how articulate the professor spoke when explaining everything. He wasn't boring and dull or spoken too quickly either. There were nice visual aids used to help understand what was happening. The stories and games and mathematical riddles were a pleasure to learn about. I'm glad I bought it.
Date published: 2021-08-26
Rated 1 out of 5 by from Save your $$$! Terrible, seems like the author was stuck on a deserted Island with nothing to do, so spent his time playing with match sticks making triangles seeing how few sticks he could use. Glade I checked it out of the library and saved my money.
Date published: 2021-07-04
Rated 5 out of 5 by from Great fun! The professor is engaging, and his presentation and explanation of the puzzles is crystal clear. I also had fun dreaming up some alternate ("out of the box") solutions. Some of the puzzles seemed to difficult, so I just sat back and watched the solution. But most of them were too tempting not to try solving. Either way, it was all very enjoyable.
Date published: 2021-04-05
Rated 5 out of 5 by from fun and informative An excellent course for those interested in the subject matter. Lots of tricky puzzles to get your mind working. I enjoyed it a lot! I noted one error in the Muddy Children puzzle in Lesson 8 (p113-144 in the Course Guide). Without spoilers, there are two other possibilities where the product is greater than what is presented to be the highest possible product for sequences starting with one. It derails the reasoning that follows somewhat, but doesn't change the veracity of the answer.
Date published: 2021-02-20
Rated 5 out of 5 by from Interesting and fun to watch together. Well worth a watch, however, as always, mathematical logic breaks down when humans are involved. When working in a café' I'd have been fired for serving coffee to customers who hadn't explicitly asked for one. A real life solution to that problem would go as follows; "Do you want coffee?" "Don't know," "Don't know, "Don't know, "No." "Hang on a minuet I'll have a cup of tea," "well if she's having tea I'll have a hot chocolate," "I'd like tea too, no wait I'll get a coffee." etc. etc. etc.
Date published: 2021-01-06
Rated 5 out of 5 by from Fun exercise for the brain! Highly recommend! Very fun course and makes you exercise your brain and think outside the box.
Date published: 2020-12-27
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Professor Jason Rosenhouse presents his favorite brain teasers and logic puzzles. Each lesson starts with a relatively simple puzzle that illustrates a mathematical idea or problem-solving strategy. From there, you progress to more challenging problems that will provide hours of amusement. Puzzles include the Bridges of K≈nigsberg, the Monty Hall problem, the Hardest Logic Puzzle Ever," and many more."


Jason Rosenhouse
Jason Rosenhouse

For centuries, people have used brain teasers as a way to keep their minds sharp, increase critical thinking skills, and boost creativity.


James Madison University

Jason Rosenhouse is a Professor of Pure Mathematics at James Madison University. He holds a PhD in Mathematics from Dartmouth College. He is the author or editor of several books on topics ranging from recreational mathematics to evolutionary biology, and he has published more than a dozen research papers on number theory and combinatorics. His books include Taking Sudoku Seriously: The Math behind the World’s Most Popular Pencil Puzzle, which received the 2012 PROSE Award for Popular Science and Popular Mathematics from the Association of American Publishers, and he is the editor of Mathematics Magazine, published by the Mathematical Association of America.

By This Professor

Mathematical Brain Teasers and Logic Puzzles
Mathematical Brain Teasers and Logic Puzzles


Why We Love Puzzles

01: Why We Love Puzzles

Why do we create puzzles simply for the pleasure of solving them? After proposing a few theories, Professor Rosenhouse notes that mathematicians love puzzles, especially those that lead to deep mathematical insights. Get warmed up for the course with six brain teasers involving hourglasses, a restaurant order, a biased coin, the numbers on a clock face, and two chessboard scenarios.

25 min
Thinking outside the Box

02: Thinking outside the Box

Test your wits against the puzzle that likely inspired the famous expression “thinking outside the box.” Then apply this strategy to a variety of brain teasers, involving matchsticks, cards, light switches, and other objects in interesting and puzzling situations. Also ponder the legendary physics exam question: How can you find the height of a building by using a barometer?

24 min
You Don’t Need No Algebra!

03: You Don’t Need No Algebra!

First, find a shortcut solution to a classic word problem in algebra. This introduces the lesson’s theme: forget your algebra and use cleverness to solve problems without x’s and y’s. Along the way, you’ll learn that sometimes having too much information can make a problem harder. Also find out why transcontinental flights take longer in one direction than the other—not counting wind effects.

25 min
Knights, Knaves, and Normals

04: Knights, Knaves, and Normals

Now turn to logic puzzles, trying to distinguish between knights who only make true statements, and knaves who only tell falsehoods. Start with simple cases. Then introduce tricky “if–then” statements. Next, what if the knight or knave is insane and thus has false beliefs? This makes things trickier! Finally, add a third category: normal people who are sometimes truthful, sometimes not.

26 min
Lewis Carroll’s Game

05: Lewis Carroll’s Game

Lewis Carroll, author of Alice’s Adventures in Wonderland, wrote a book of logic puzzles for children. Take a crack at some of these fun exercises, which Carroll designed to illustrate the principles of Aristotelian logic. See what you can conclude from such categorical statements as “all wasps are unfriendly, and all puppies are friendly.” Carroll’s syllogisms get progressively more elaborate.

27 min
Question Puzzles and Coercive Logic

06: Question Puzzles and Coercive Logic

Return to the Island of Knights and Knaves from Lesson 4 to consider puzzles where asking the right questions is the point of the problem. Work your way up to the famous “heaven or hell” puzzle. Then close with an exercise in coercive logic, devised by noted mathematician and puzzle master Raymond Smullyan. Easy riches hinge on a very simple bargain that sounds too good to be true. Do you accept?

23 min
The Saga of the Hardest Logic Puzzle Ever

07: The Saga of the Hardest Logic Puzzle Ever

Learn about biconditional statements of the form, “p if and only if q.” Then tackle the notorious “Hardest Logic Puzzle Ever,” devised by philosopher George Boolos. You have three yes/no questions to identify three gods: the god who always answers truthfully, the god who always lies, and the god who randomly mixes true and false answers. One big problem: They answer in their own language, which you don’t speak.

26 min
The Muddy Children Puzzle

08: The Muddy Children Puzzle

Finish your study of logic with puzzles where you must draw conclusions based on what other people can infer from information they are given. Your first example is the “muddy children” puzzle, in which children with muddy faces must conclude with logical certainty—without looking in a mirror, feeling their faces, or being told—that they have muddy faces. Such puzzles are unusually subtle.

26 min
The Perils of Probability

09: The Perils of Probability

Ponder probability, starting with the chances of getting an ace of spades when you turn over the top cards on two well-shuffled decks. In probability, it’s a safe bet that your first instinct is wrong! Investigate other phenomena, including the chances that your suitcase is lost when 98 percent of the luggage has arrived at baggage claim, but yours has not. Your odds may be better than you think.

26 min
A New Look at the Monty Hall Problem

10: A New Look at the Monty Hall Problem

Study the famous Monty Hall problem from the game show Let’s Make a Deal. Your quandary: A new car is hidden behind one of three doors; after making your choice, your door is left shut and one of the doors without the car is opened. Do you care to switch to the other closed door? Find out why one expert says, “No other statistical puzzle comes so close to fooling all the people all the time.”

28 min
Arithmetic Amusements

11: Arithmetic Amusements

Discover the fun of arithmetic and other simple mathematics. Begin with the game Krypto, in which your goal is to make a given number with arithmetical operations on five other numbers. Then try out the “four fours” puzzle. Next, see how perfect squares and perfect triangles reveal algebra and geometry working together. Finally, reason out why a negative number multiplied by itself a is a positive number.

29 min
Algorithmic Puzzles

12: Algorithmic Puzzles

Take up algorithmic puzzles, which require a carefully thought-out procedure—or algorithm—to solve. Algorithms have notable applications in computer science, but they also come in handy for dividing pirate gold, transporting hungry animals to an island, and solving life-or-death riddles posed by movie villains. At least, that’s the entertaining approach you take in this final lesson.

24 min