Mathematical Brain Teasers and Logic Puzzles

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
Rated 5 out of 5 by from Fun Puzzles - and challenging Puzzles are a great way to learn math and this course delivers. Lots of great examples and subtle math in the answers.
Date published: 2020-12-11
Rated 5 out of 5 by from A fun participatory course in problem solving A highly intelligible and straightforward presentation of math and logic problems. The professor demonstrates ways to "think outside the box" before unnecessarily resorting to math to solve a word problem. The hints and explanations are clear and precise, with sample problems borrowed from famous puzzle lovers, including Raymond Smullyan and Lewis Carroll. The format allows you to solve the puzzles yourself by pausing the video at indicated moments, so have some paper or a chalkboard handy. This is definitely a participatory course. With this series, Professor Rosenhouse joins my list of favorite Great Courses math teachers, including David Kung, Arthur T. Benjamin, and James Tanton.
Date published: 2020-12-10
Rated 5 out of 5 by from Watch to learn how to work through a problem If you want someone to help you think through the process of puzzles and problems, this is the lecture series to watch. Multiple types of problems are presented and solved with clear explanations given to the viewer. No background in math, logic, or other academic area is needed to understand and follow along with the presenter. The camera angles were not jittery or annoying.
Date published: 2020-12-04
Rated 1 out of 5 by from Stop jittering around & be more precise Camera angles on this are pointless, ill-timed and just flat out annoying. Is the presenter on a swivel board & desperately aiming for his 10,000 a day swivels? As is the logic the presenter uses - if we ignore the rules of chess - except for board, movement & capture - what is my answer....
Date published: 2020-12-01
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Mathematical Brain Teasers and Logic Puzzles
Course Trailer
Why We Love Puzzles
1: 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
2: 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!
3: 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
4: 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
5: 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
6: 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
7: 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
8: 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
9: 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
Jason Rosenhouse

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

ALMA MATER

Dartmouth College

INSTITUTION

James Madison University

About Jason Rosenhouse

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.

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