Imagine 24.4 puzzle…

Work has kept me very busy this spring, so I’m still working on updates for the If Then City Blocks and Cell Wall Transport System puzzles. But it was long overdue to switch off the winter theme and remove the direct link to the holiday puzzles, although they can still be found here.

Site Updates: Fall 2016

An ongoing catalogue of Knossos Games website issues and minor updates.

Updated through WordPress 4.7

As part of the holiday-themed update at Thanksgiving, I created a new Knossos Games banner for all pages.

This fall included several big content updates: a new Neuron Activation Level puzzle and website update, a new Gerrymandering puzzle, the return of the holiday logic problems, and a feature article about logic and puzzlemaking in Imagine magazine.

More updates are on their way in the new year!

Origin Stories: Christmas Trees

My mom loves Christmas decorations. She decorates every available space in the house with garlands, greens, candles, wreaths, and lights. Her navity scene was hand-carved in Germany and was a gift from my dad on their honeymoon. But nothing compares to her collection of Christmas tree ornaments.

Every Thanksgiving, dozens and dozens of boxes descend from the attic to decorate the Christmas trees. Yes, trees. We started with one in the living room, but with so many ornaments, she became a museum curator, only able to display a small fraction of the continuously growing collection on any one holiday. For years, my dad refused to put up a second tree, knowing this would be the path to extreme self-indulgent holiday cheer.

And he was right. When a neighbor brought over a used artificial tree one year, the barrier holding back unrelenting twinkle and sparkle had been breeched. She’s now up to four trees: a live tree we get every year from a local Christmas tree farm, a small driftwood tree for displaying ornaments made from natural materials, a half-size artificial tree for the small ornaments, and the aforementioned full-size artificial tree that stays up all year. (The excuse: it’s too difficult to take apart and haul into the attic. Sure.)

In the sprit of her unrelenting passion for Christmas tree ornaments, the latest holiday logic problem celebrates the yearly chaos of choosing which ornaments should go where. This puzzle was modified from one originally posted in 2005. It is an homage to the holiday-themed grid-based logic problems I made as a kid, but which have been entirely lost. I updated the puzzle text and clues (including changing some of the ornaments and tree locations), added new graphics and a detailed solution.

Origin Stories: Reindeer Games

I started writing holiday-themed logic problems as a kid. I really liked solving grid-based logic problems, and once I figured out how they worked, I started creating my own. Unfortunately, I can’t find any copies of those original puzzles I made. But those early puzzles inspired me to start writing holiday-themed logic problems again once I got serious about the Knossos Games website in the mid-2000’s. As these puzzles aren’t published in the magazine (or anywhere else), they are a special bonus to my website visitors.

Even though my earliest logic problems were of the grid-based variety (both solving and creating), I have avoided that type of puzzle when writing for the magazine. In fact, I refrained from writing logic problems for the magazine altogether for the first five years. It was only when I found an interesting though flawed logic problem that I published my own improved version in the magazine. The following year I wrote the two-year garden logic problem and have written about one per year every year since.

When writing a logic problem, you want to situate or structure the puzzle using a natural order or pre-existing rules. This helps solvers initially engage with the puzzle, as they can utilize their prior knowledge to gain an entry point and start solving. The order of Santa’s reindeer, memorialized in story and song, made for an obvious choice. I used the L-shaped arrangements of the two-year garden logic problem as the basic structure for this new puzzle.

Top: L-shaped example from two-year garden logic problem.  Bottom: L-shaped example from reindeer games holiday logic problem.

This puzzle was originally posted to an older version of the website in 2004, then resurrected as part of the newest version of the website in 2015. When I decided I wanted to restart the holiday logic problem tradition, I found a copy of the clues to this puzzle, but no solution! I had to go back and solve the puzzle myself to remember how it worked. I rewrote the entire prologue to the puzzle, utilizing actual proclamations found on the internet as a basis for the language used. The new version of the puzzle added graphics and a detailed solution.

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. If you’re thinking of buying one of these books, please consider clicking the Amazon affiliate links below:

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.

Welcome Logic Fans

If you’re here because you read the article I wrote on logic and puzzlemaking in the recent issue of Imagine, you might want to check out the following:

There are “origin story” blog entries for some of the logic puzzles I’ve written: the Coin Box problem, the Two-Year Garden problem, and the Castaway (Part 1) problem. I’m working on more.

I also wrote about the updates (part 1, part 2) of the logic puzzles for the most recent version of the web site.

Finally, here’s the blog entry that started it all, where I discuss how making puzzles and my job as an educational psychologist are really two sides to the same coin.

More Gerrymandering 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, 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.