Tag Archives: puzzle analysis

Puzzle Books

The sidebar of the logic article I wrote in Imagine contains several books about puzzles. Here is an extended, annotated version of that list:

Books by and about Lewis Carroll (Charles Lutwidge Dodgson, 1832-1898):

Two books detailing his mathematical puzzles, including sections on “game of logic”:

Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life by Robin Wilson (W. W. Norton & Co., 2010)

The Universe in a Handkerchief, Lewis Carroll’s Mathematical Recreations, Games, Puzzles, and Word Plays by Martin Gardner (Copernicus, 1998)

Lewis Carroll’s two major works of logic are now published as one volume:

Symbolic Logic and the Game of Logic by Lewis Carroll (Dover Publications, 1958)

A collection of Lewis Carroll’s puzzles that remained unfinished upon his death:

Rediscovered Lewis Carroll Puzzles, Newly Compiled and Edited by Edward Wakeling (Dover Publications, 1996)

A new edition of the absolutely authoritative and exhaustive guide to both classics: Alice’s Adventures in Wonderland and Through the Looking Glass. Extensive annotations concerning the background and influences of the work, the historical context, and how the works comment on the state of mathematics:

The Annotated Alice: 150th Anniversary Deluxe Edition by Lewis Carroll, Introduction and Notes by Martin Gardner, Original Illustrations by John Tenniel (W. W. Norton & Company, 2015)

A selection of books by Raymond M. Smullyan (ordered chronologically):

What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles (Dover Publications, 1978)

The Lady or the Tiger? and Other Logic Puzzles (Random House, 1982)

Satan, Cantor and Infinity: Mind-Boggling Puzzles (Dover Publications, 1992)

The Riddle of Scheherazade and Other Amazing Puzzles (Harcourt, 1997)

King Arthur in Search of His Dog and Other Curious Puzzles (Dover Publications, 2010)

The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs (Dover Publications, 2013)

Books about Sudoku and other number logic puzzles:

A mathematical exploration of Sudoku, including how many Sudoku puzzles there are, how many clues are necessary, and different fields of mathematics that can help us better understand Sudoku:

Taking Sudoku Seriously: The Math Behind the World’s Most Popular Pencil Puzzle by Jason Rosenhouse and Laura Taalman (Oxford University Press, 2009)

For more background on Latin Squares and other mathematical concepts that Sudoku are based upon:

Before Sudoku: The World of Magic Squares by Seymour S. Block and Santiago A. Tavares (Oxford University Press, 2009)

For a thorough guide of basic and advanced solving strategies (this excellent book is unfortunately out of print):

Teach Yourself Advanced Sudoku and Kakuro by Nick Afka Thomas (McGraw-Hill, 2006)

For many, many more examples of different types of number puzzles (another excellent book that is currently out of print):

Japanese Number Puzzles by Anthony Immanuvel (Running Press, 2006)

Masters of Deduction

Imagine magazine has graciously allowed me to share with everyone the logic article I wrote for their most recent issue!

Click on the above thumbnails to open jpegs of each page, or use this link for a PDF

I mentioned some of my own puzzles in the article:

• I’ve written several logic puzzles (organized both chronologically, in the order they were published, and thematically), including a few special holiday logic puzzles.

• Two logic puzzles were specifically styled after Raymond Smullyan’s “knights and knaves” or “truth tellers and liars” puzzles. The first Castaway puzzle (based on the reality television show Survivor), adds people who sometimes lie and sometimes tell the truth. Smullyan calls these people “normals”. The second Castaway puzzle, not mentioned in the article, defines different ways in which people might lie based on whom they are speaking to. I have not found a similar Smullyan puzzle (although by no means have I read them all).

• The rubber stamp puzzles were directly influenced by battleship puzzles I had seen in Games magazine. Another example of a grid-based number puzzle, albeit one I created and not based on one of the Nikoli puzzles, are the gerrymandering puzzles. Another example of a puzzle I created that was inspired by a different puzzle are the space pods puzzles. I wrote a blog entry about how I tried to improve upon another Games magazine puzzle I had seen.

The article also includes a sidebar of puzzle books. I’ve listed those in a separate blog post if you’re interested in details and links.

Again, I’d like to thank Imagine and my editor, Melissa Hartman, for giving me the opportunity to write an article like this, in addition to my continued puzzle contributions. If you like the article and Knossos Games in general, please consider subscribing.

More Gerrymandering

FiveThirtyEight.com also got into the puzzle-themed election spirit with some of their own Gerrymandering puzzles (one easy, one way hard). They come from Eli Ross at Brilliant.org, which also has a small selection of gerrymandering puzzles on its site.

FiveThirtyEight’s weekly The Riddler column has an excellent variety of difficult math puzzles. Scroll to the end to also get a curated collection of new puzzles appearing in the last week.

Crossword Plagiarism Update

FiveThirtyEight continues to follow the unfolding story I summarized in an early blog post concerning a crossword puzzle plagiarism scandal.

On April 29, they reported that Universal Uclick, the syndicator of the puzzles, confirmed the allegations that the crossword puzzle themes had been copied from those found in the New York Times.

But the editor of the crosswords, Timothy Parker, would only be placed on a three-month leave, which led to an uproar in the puzzlemaking community.

Then on May 10, FiveThirtyEight reported that Parker was out as USA Today’s crossword puzzle editor, although they would retain Universal Uclick’s services, albeit with a new puzzle editor.


Crossword Plagiarism

I’m terrible at word puzzles, so I don’t spend much time with them: solving, creating, or following. But crossword puzzles are so ubiquitous that I can’t help being interested (Wordplay was a fascinating documentary). In characteristic fashion, FiveThirtyEight adeptly reports an emerging plagiarism scandal in the crossword puzzle community. Traditional puzzle “news” is rare, so this is big.

Update: Timothy Parker, the crossword puzzles editor, has stepped aside while USA Today and Universal Uclick investigate the claims detailed by FiveThirtyEight.


I recently went through a pile of newspapers that had accumulated over the past few months, only to discover this:

Compare the given numbers around the edges…


Generate puzzle, publish, then rotate 90° and reprint a few weeks later. I never would have thought of that! It’s a real time saver. I guess I’ve been doing this whole puzzlemaking thing wrong all these years.

I haven’t been able to find any indication of how popular Numbrix puzzles have been since their 2008 debut, but seeing as they have stuck around in vos Savant’s “Ask Marilyn” column and are now available as a daily online version, they must attract at least some measurable level of reader, uh, solvership.1

Numbrix puzzles are an easier variant of Hidato, which allow diagonal connections and do not restrict the grid boundary and number chain length to be, well, anything in particular. Like Sudoku and many other types of number-based puzzles, Numbrix can be generated and solved via computer algorithm, although vos Savant claims she generates every puzzle by hand:

According to vos Savant, she created Numbrix partly for her readers and partly for herself. “I developed the puzzle to offer readers an enjoyable diversion that would exercise their fluid intelligence (meaning: logic plus memory) at the same time,” she says. “But the real fun for me was constructing every puzzle by hand — no real Numbrix puzzles are generated by a computer — and proofing it the same way to create puzzles that had unique solutions.”

– Chris Warren “How to Play Numbrix” 21 July 2011.

That only makes the above revelation all the more conspicuous. But the blame may not rest solely on vos Savant, since Parade now lists Jeff Marchant as a contributor of Jadium puzzles, which claim to be harder than the similar Numbrix because they contain fewer givens. However, after researching all of these different types of number chain puzzles, it is still unclear to me what exactly the difference is between Numbrix and Jadium puzzles (both can contain 16 givens), what the division of authorship is between vos Savant and Marchant, or if the puzzles are still being generated by hand.

I’m not trying to disparage comptuer-generated puzzles in general, or vos Savant’s Numbrix in particular, since I use a lot of computerized tools while creating my own puzzles, although much of the heavy lifting in creating Knossos Games is still done on paper. Why should a computer have all the fun? Because of their hand-crafted nature, I don’t publish puzzles with great frequency. But that also means the expectations I have on my own puzzles are very high. While those aren’t always met, I’d be absolutely mortified by the above mistake.