The Puzzler's Dilemma: From the Lighthouse of Alexandria to Monty Hall, a Fresh Look at Classic Conundrums of Logic, Mathematics, and Life

by Derrick Niederman

Calling all puzzlers... From mathematics to word puzzles, from logic to lateral thinking, veteran puzzle maker Derrick Niederman delights in tackling the trickiest brainteasers in a new way. Among the old chestnuts he cracks wide open are the following Knights and knaves The monk and the mountain The dominoes and the chessboard The unexpected hanging The Tower of Hanoi

Using real-world analogies, infectious humor, and a fresh approach, this deceptively simple volume will challenge, amuse, enlighten, and surprise even the most experienced puzzle solver.

Genres: Nonfiction, Mathematics, Humor, Popular Science, Psychology

223 pages, Kindle Edition

First published February 1, 2012

Reviews

[Jonathan Terrington · Rating 4 out of 5]

Derrick Niederman has a Phd in mathematics and was an economist for a few decades. He now makes puzzles for companies, as well as writing some of the New York Times crossword puzzles. Which all on its own is impressive but not nearly as interesting as this little gem of a book.

While I've read many different opinions about puzzles and have attempted to solve many more this book was different from other puzzle books Some of the puzzles I may have solved before or failed at (for instance the infamous Monty Hall problem) but the way Niederman explains opened up insights for me that I'd missed - although I'm not sure he explains the Monty Hall problem particularly well, but he does explain why so many people get it wrong. In essence this book is not just a puzzle solver's aide but rather is a look at the psychology, the mathematics and the history of puzzles. It therefore has some real life applications.

The way the book is set up is brilliant. Niederman breaks everything down into different topics per chapter. To provide a brief oversight of the novel I'll list the chapters and what they focus on.

1. In the Beginning
This chapter focused briefly on one ancient conundrum and was a basic introduction to the enigma of puzzles. It was an entertaining but less informative chapter that set the tone for the rest of the book.

2. Kangaroo Puzzles
Explored the nature of 'Kangaroo Puzzles' or puzzles that provide you the answer in the clue or question. For instance crycptic clues like: contaminate where the answer is taint. Or even a question like 'See that bloke? Can you guess how old he is?' The answer is in the clue in a way because you instantly are informed that the individual is likely older than expected.

3. The Human Element
A kind of interlude which discussed human behavior, strategy stealing and how they interact with conundrums and logic.

4. Try Lateral Thinking
As the name suggests this chapter was about lateral thinking. It was less interesting than pure lateral thinking books alone but it did challenge the idea of applying lateral thinking to everyday life to solve problems.

5. Keeping it Simple
Focused on the idea of Occam's Razor, using this idea in relation to puzzle solving to say that the simplest solution is the solution that should be looked at first. However the catch is that this is not always the case.

6. Parabolic Parables
This was a chapter that confused my brain in varying degrees. Because I am not very good at adjusting to complex mathematical principles I found the information challenging. However as the name suggests it was a chapter about parabolas and puzzle solving applications.

7. Little Big Jump
A chapter about the substitution of ideas in order to allow for better puzzle solving. It was also about breaking things down into smaller 'jumps' in order to complete one larger 'jump'. In other words break puzzles down into smaller steps to complete the overall puzzle.

8. It Can't Be Done
This was all about the unsolvable puzzles that exist or even the puzzles that seem like they cannot be solved but can.

9. Solved According to Doyle
Puzzle solving using the Sherlock Holmes' principle of elimination. Also discussed the curious effect known as learned helplessness. If you learn you cannot solve something earlier then you will believe you cannot solve it later even if you can unless told otherwise by someone intervening.

10. When Induction Goes Bad
Again this was a mathematics section that focused on induction which I somewhat get. It's possible to induce the answer based on observable patterns. However things become complicated when paradoxes are introduced which is another component that was introduced.

11. You Are Here: The Search for a Fixed Point
This was a very interesting chapter. It talked about puzzle solving in relation to the idea of a fixed point which is basically a point of reference. Apparently humans rely upon various fixed points as references for how to live life in order to help accomplish tasks properly. If you've seen the film Bug's Life where a leaf interrupts the movement of ants that's what interruption to these fixed points can do to people. Fixed points are also the reason why individuals find it so difficult to solve problems like: attach a candle to a wall with thumbtacks in a box and matches. The solution being to thumbtack the box to a wall and then set up the candle. But due to fixed points we find ourselves unable to think of the box as anything but a thumbtack holder. (Fixed points also allow for magicians and assassins (who poison drinks with sleight of hand) to trick us right before our very eyes. We really are 'creatures of habit' when it comes to puzzling ideas.

12. The Full Monty Hall
To finish the famous Month Hall problem was discussed along with probability and similar circumstances where choices and probability interact. The author briefly discussed why errors occur with individuals and probability so often.

There were elements of this book that I simply understood straight away. There were elements that went over my head. There were elements that taught me something new - yes I admit that I don't know everything (not yet anyway) and actually learnt from a book! In the end this was a book that was comfortable to read due to the author's style and approach to using tangents and anecdotes to break everything down at times into layman's terms. I must say however that this is not a book for casual reading necessarily, it is a book of puzzles after all, but that it is an accessible book when time can be spared. Very recommended for anyone interested in puzzle solving or psychological ideas.

[Mirek Kukla · Rating 2 out of 5]

Partly awesome, partly lame, and aside from some really cool puzzles, mostly forgettable. As one might guess, this book is about puzzles. Beyond that, here's very little in the way of thoughtful organization - each chapter feels like a stream of consciousness monologue, and the ordering of chapter might as well have been random.

That said, some of the puzzle are cool, and you'll come across some occasional insights. I enjoyed the chapter on 'kangaroo puzzles' - puzzles that give you a hint by their very formulation (for instance, if counting the number of letters in a fill-in-the-blank sequence yields 26, it's a good indicator that the sequence has something to do with the alphabet). A chapter on induction (and 'erroneous' induction proofs) is great, and the discussion of the Monty Hall problem is pretty well done.

On the other hand, the chapter on 'lateral thinking' is just shy of retarded. (Q: "Deep in the forest was found the body of a man who was wearing only swimming trunks, a snorkel, and a face mask. The nearest lake was 8 miles away, and the see was 100 miles away. How did he die?" A:"During a forest fire, a plane had scooped up some water from the lake and dropped the water, swimmer and all, into the forest." WTF?) At some point, the author goes on a chapter-long rant about the Laffer Curve from economics; the only puzzle here is trying to figure out what this chapter might possibly have to do with puzzles.

Anyways, I claimed there were some fun puzzles, so here's a nice one that stumped me for some time:

"Four people come to a river in the night. The only way to cross is a narrow bridge that can hold only two people at a time. Because it is nighttime, a lantern has to be used when crossing the bridge. A can cross the bridge in 1 minute, B in 2 minutes, C in 5 minutes, and D in 10 minutes. When two people cross the bridge together, they must move at the slower person's pace. How can they get across the bridge in 17 minutes?"

Getting across in 19 minutes is trivial. Doing it in 17 is tricky - and note that there's no trickery involved. Enjoy!

[Maurizio Codogno · Rating 5 out of 5]

Uno sguardo generalista sui quizzini matematici

Ho letto decine di libri di quizzini matematici (e ne ho scritto anche qualcuno...). Ciascuno di essi ha uno stile diverso, sia per la scelta dei problemi che per la loro esposizione e per come si passa alle soluzioni. Non mi era ancora capitato di vedere pero l'approccio usato da Niederman. In pratica i problemi - non ce ne sono tantissimi, anche se qualcuno mi era comunque nuovo - sono solo la ciliegina sulla torta di un discorso molto più generale, che parla dei problemi matematici come un modo di vedere il mondo. E il bello è che il discorso fila anche senza cercare di risolvere i problemi! In pratica è possibile divertirsi nella lettura senza impazzire nel risolvere questi problemi. Dite niente...

[John Fredrickson · Rating 2 out of 5]

I never really figured out what the theme of this book was. There was some very interesting material scattered throughout the book, but through much of the book I found myself wondering when it would get interesting again. The author talks about different kinds of puzzles, and different kinds of strategies for working on them, and explores some puzzles that he himself tried to (or did) bring to market.

As an example of the my own frustration with this book, the book's title includes in its cover "a Fresh Look at Classic Conundrums" and "Monty Hall", so one of my expectations was that the Monty Hall problem would be explicated in a way that would resonate. While the author does talk about the confusion generated about this, even amongst mathematicians, the crux of what the text on this says about the switch is that the selected door's odds (1/3) never change, so therefore the remaining door inherits all the remaining odds (2/3). This may be exactly correct, but as explanations go, it falls kind of flat.

[Joe · Rating 4 out of 5]

Excellent! Maybe the most enjoyable book about high level math theory I’ve ever read. Also a lot of fun, especially if you like word puzzles, mysteries, riddles, number puzzles, and so on...

[Max · Rating 3 out of 5]

Fans of Douglas Hofstadter will enjoy it. It has a similar passionate rambling nature to GEB. There are, however, sections that are hard to understand, because if you don't already have a background in what he's suddenly started talking about, he won't get you up to speed, unlike in GEB. And I don't think it's worth slowing down and rereading a section 'till you understand it, just because it is a person rambling. That said, the parts that you do understand will have amazing nuggets of cool info and insights. The puzzles discussed are sometimes silly distractions but often move into the realm of the deeply philosophical.

Also, if you would like, check out a puzzle computer game I made here: https://maximilian.itch.io/inertia. Designing this game was my reason for reading this book.

[Alison · Rating 3 out of 5]

The book introduces conundrums I have never heard of but that are super interesting, and puzzles I have heard of but that have more background information that I didn't know. Yay puzzles! I had some issues with the non-puzzle writing and a few very confusing puzzles, but overall it's a decent book.
read more...

[Jason · Rating 3 out of 5]

The book was a bit over my head with the math it presented, but those puzzles that didn't involve math (which was the majority the book) I found interesting. Solving along with the author, or seeing how he approached puzzles was definitely interesting.

I saw a puzzle recently I'd love to know how to solve. I tried using the techniques in the book - nothing seemed to work. Ah well, not every book is useful...still, it was entertaining enough.

[Sam Colton · Rating 4 out of 5]

Talks about the methods people use to solve puzzles and how puzzle solving can be applied to life. The author bounces all over the place, so it rarely gets boring. Includes quirky puzzles, anecdotes from history, some higher level math--which were the hardest parts to get through. Only the last two chapters felt like filler; with twelve altogether that isn't so bad.

[Metta · Rating 4 out of 5]

Great introduction to the world of puzzles, especially appropriate for the curious minds who find that the world no longer titilates them anymore, except the possibility of a puzzle so unique, so weird that it no longer makes the world boring anymore.

[FranklinTV · Rating 5 out of 5]

I really liked this - the type of puzzle book where the emphasis is on the puzzle to highlight the discussion, rather the other way around. Sure, the structure is a bit lose, but the conversation style of writing is engaging. A book I'm glad I read I will probably read again sometime.

[Jeff · Rating 3 out of 5]

Bumped up from 2 to 3 stars, due to the inclusion of the game show-related chapter at the end of the book. ;-)

[Christine · Rating 3 out of 5]

interesting about how puzzles work and constructed but the some of the math was a bit hard.

[John Orman · Rating 3 out of 5]

Mighty tricky puzzles, though some seem trivial when the answer is revealed.
Kangaroo puzzles? They are here.
I liked the chapter "When Induction Goes Bad." I could not deduce the outcome!

[Sophie · Rating 3 out of 5]

Curious and quirky, full of facts and puzzles.

[Barry Mann · Rating 4 out of 5]

Enjoyable and short!

[Chet · Rating 4 out of 5]

A nice collection of descriptive puzzles.

[Derek · Rating 2 out of 5]

More a book about puzzles and less of book of puzzles. An interesting concept for sure, but the writing doesn’t come across as academic and more just a fan’s rambling on their favorite riddles.

[Andrea · Rating 3 out of 5]

Logic is awesome! A really fun read for someone who thinks way too much about probability. :)