A Conway Puzzle Solution (And Some Hints for the Other Puzzle)

Posted on May 15, 2020 by gmdirect

John_H_Conway_2005_(cropped)

Two weeks ago, in honor of mathematician and puzzly spirit John Horton Conway, we shared two of his favorite brain teasers and challenged our fellow PuzzleNationers.

So today, we happily share the solution for puzzle #1, The Miracle Builders.

I had a window in the north wall of my house. It was a perfect square, 1 meter wide and 1 meter high. But this window never let in enough light. So I hired this firm, the Miracle Builders, who performed the impossible. They remodeled the window so it let in more light. When when they’d finished the window was a perfect square, 1 meter high and 1 meter wide.

How did they do it?

Both windows are perfect squares, 1 meter wide and 1 meter high. So how can there be a difference in the amount of light?

The trick of this puzzle is in the description. Although the original window was a perfect square, the dimensions of the square aren’t 1 meter by 1 meter. No, it was a square placed like a diamond, with one corner directly above its opposite. So the 1 meter dimensions were the diagonals, not the sides.

All the Miracle Builders had to do was build a square window in the usual arrangement (two sides horizontal, two sides vertical) with dimensions of 1 meter by 1 meter. That creates a larger window (with a diagonal of √2m) and allows more light.

Very tricky indeed.

We had several solvers who successfully cracked the Miracle Builders puzzle, but there was less success with puzzle #2, The Ten Divisibilities.

So, in addition to the original puzzle, we’re going to post some solving hints for those intrepid solvers who want another crack at the puzzle.

The Ten Divisibilities

I have a ten digit number, abcdefghij. Each of the digits is different, and:

a is divisible by 1
ab is divisible by 2
abc is divisible by 3
abcd is divisible by 4
abcde is divisible by 5
abcdef is divisible by 6
abcdefg is divisible by 7
abcdefgh is divisible by 8
abcdefghi is divisible by 9
abcdefghij is divisible by 10

What’s my number?

[To clarify: a, b, c, d, e, f, g, h, i, and j are all single digits. Each digit from 0 to 9 is represented by exactly one letter. The number abcdefghij is a ten-digit number whose first digit is a, second digit is b, and so on. It does not mean that you multiply a x b x c x…]

Here’s a few hints that should help whittle down the possibilities for any frustrated solvers:

-If you add all the digits in a number, and the total is divisible by 3, then that number is also divisible by 3.
-If the last two digits of a number are divisible by 4, then that number is divisible by 4.
-If the last three digits of a number are divisible by 8, then that number is divisible by 8.

Good luck, and happy puzzling!

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Famous Director Stumbles Into Trivia Trap!

Posted on May 14, 2020 by gmdirect

[Image courtesy of Buzztime.]

It’s no secret that I love trivia. I enjoy bar and pub trivia nights, I compete in an online trivia league (Learned League), and I’ve served as a quizmaster myself. I delight in slipping trivia into puzzles — from encrypted content to tricky crossword clues — and I happily peruse trivia books whenever I find them.

Recently I was reminded of one of my favorite trivia stories, and I thought I’d share that story with you today.

It all starts with a few tweets by filmmaker Rian Johnson, director of Brick, Looper, Star Wars: The Last Jedi, and Knives Out.

He then shared this text from Wikipedia:

Yes, as many fans and readers had commented, keen-eyed Columbo viewers had discovered the name “Frank” on Columbo’s ID, but the famous detective’s first name was never spoken or mentioned onscreen.

I had encountered a similar problem with a trivia game years ago that asked for the first name of the character Gilligan from the TV show Gilligan’s Island. I had no idea, and got the question wrong.

But as it turns out, Willy, Gilligan’s first name, was never mentioned on the show. The show’s creator always envisioned the character with that name, but it was never officially canon. (Bob Denver, who played Gilligan on the show, often joked that the character’s name was actually Gil Egan, but it ran together when yelled, as it so often was.)

[Image courtesy of Gilligan’s Island Wiki.]

As far as I know, the Gilligan error was simply that, a mistake. But the Columbo error, as mentioned in the Wikipedia article, is an example of a copyright trap.

A copyright trap is an intentionally false, seemingly trivial piece of information in a larger work, intended to help demonstrate plagiarism if the larger work is ever stolen or copied. (After all, anyone who had done their own research would have discovered it was incorrect and left it out, or at the very least, not included it as part of a wholesale act of plagiarism.)

And the more you learn about copyright traps, the more ridiculous and intricate they become.

There have been:

false cities (aka paper towns) on maps, like Agloe, New York, and the paired cities of Beatosu and Goblu in Ohio, as well as trap streets, fake mountain peaks, and more
false dictionary entries (like esquivaliance in the second edition New Oxford American Dictionary)
false encyclopedia entries (like the story of a photographer named Lillian Mountweazel who exploded on a shoot for Combustibles magazine)
false movies (like Dog of Norway, a fictional film mentioned in The Golden Turkey Awards, a book I actually own, alongside its sequel, Son of Golden Turkey Awards)
a false member of the German parliament
false Google searches (which were used to purposely expose the search engine Bing for copying Google’s search results)

[Image courtesy of RadioTimes.]

Although Mr. Worth’s Columbo trap did reveal the thieving nature of the designers of the original Trivial Pursuit, it failed to protect him. It also failed to protect trivia fans, as this and other spurious bits of trivia continue to percolate throughout trivia books, webpages, and other sources. (I’ve found easily misproven false trivia everywhere from IMDB to Ripley’s Believe It or Not books.)

So enjoy your trivia, but keep your eyes peeled, fellow puzzlers and trivia-hounds. You might just get tripped up by a copyright trap one of these days.

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A Two-For-One Visual Puzzle

Posted on May 12, 2020 by gmdirect

Given the technology available to us — be it Photoshop or other visual manipulation software — there is truly no end to what we can create.

An Instagram account called morphy_me is doing something interesting with celebrity photos. The artist, credited only as Benji, merges elements of both celebrities, somehow creating an image that is reminiscent of both, and yet feels strangely new.

For example, this is a combination of Johnny Depp and Brad Pitt:

benji 0

It’s an intriguing approach that has garnered the account over 100,000 followers. It’s also something of a puzzly challenge sometimes to figure out who the two celebrities are that have been merged.

Can you puzzle out the 15 pairs of celebrities that have been combined in these images by Benji?

benji 1

benji 2

benji 3

benji 4

benji 5

benji 6

benji 7

benji 8

benji 9

#10

benji 10

#11

benji 11

#12

benji 12

#13

benji 13

#14

benji 14

#15

benji 15

How many did you get, fellow puzzlers and PuzzleNationers? Let us know in the comments section below! We’d love to hear from you!

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Two Brain Teasers, Courtesy of Conway

Posted on May 1, 2020 by gmdirect

John_H_Conway_2005_(cropped)

Last week, we penned a post celebrating the life and puzzly legacy of mathematician John Horton Conway, and several of our fellow PuzzleNationers reached out with their own thoughts or questions about Conway.

One recurring subject was about his love of puzzles and what kind of puzzles he enjoyed solving. So, naturally, I went hunting for some of Conway’s favorite puzzles.

As it turns out, Alex Bellos of The Guardian had me covered. Alex has a recurring puzzle feature on The Guardian‘s website where brain teasers and other mental trickery awaits intrepid solvers.

Years ago, Alex had asked Conway for suggestions for his column, and Conway offered up two tricky puzzles.

And now, I happily share them with you.

#1: The Miracle Builders

How did they do it?

#2: The Ten Divisibilities

I have a ten digit number, abcdefghij. Each of the digits is different.

The following is also true:

a is divisible by 1
ab is divisible by 2
abc is divisible by 3
abcd is divisible by 4
abcde is divisible by 5
abcdef is divisible by 6
abcdefg is divisible by 7
abcdefgh is divisible by 8
abcdefghi is divisible by 9
abcdefghij is divisible by 10

What’s my number?

Did you solve one or both of these fiendish mind ticklers? Let us know in the comments section below! We’d love to hear from you.

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Cultural Sensitivity and Crosswords: Where Is The Line?

Posted on April 30, 2020 by gmdirect

A few days ago, an entry in The New York Times Crossword caught the eye of a solver. That solver posted about it in the Facebook group “The Crossword Puzzle Collaboration Directory,” which is dedicated to encouraging new constructors to make and submit puzzles.

That post kicked off an intense debate about problematic entries and how to handle them. Not only is this topic far from settled, but it’s emblematic of a larger question: where is the line?

You see, one of the advantages of our modern Internet-savvy culture is that feedback is virtually instantaneous now. If someone is offended or troubled by an entry or clue in the Monday crossword, it doesn’t take days for a letter to the editor to arrive at the paper. It takes seconds to post online and reach a potential audience.

Of course, that rapid response is a double-edged sword, because hot takes and rush-to-judgment commentary are just as quick to spread.

Both sides of that double-edged sword were in full effect as the replies piled up on that original Facebook post. As those in agreement with the original poster offered their support, counterpoints rolled in, either in defense of the entry or the clue.

(Naturally, given that this is the Internet, some chose to expand on the topic in general disagreement with a culture they claimed was too sensitive and quick to condemn every little thing that offended them. But since those people are an incredible waste of time and energy and have little interest in genuine discussion, this will be my last mention of them.)

Other posters focused on the mechanics of the puzzle itself, pointing out easy fixes that would have prevented the potentially problematic word from appearing at all. Some of these folks sided with the original poster, pointing out that a word that is potentially problematic should be edited out, and it’s part of a constructor’s job to think of these things.

And that’s the question. How much should constructors and editors be taking the potentially problematic aspects of words into consideration when constructing?

True, it’s not always possible to anticipate every negative response to the words filling your grid or the accompanying clues. (Heck, we have numerous examples of words and clues slipping through that catch fire with part of the audience in the worst possible way.)

But is that part of a constructor’s job?

In my opinion, yes, it is.

Crosswords should be inclusive. They should be an engaging activity that evokes occasional frustration but eventual satisfaction, whether you’re completing a grid, unraveling a particularly tricky theme, or besting your previous solving time. It should be fun. It should be entertainment, a distraction.

It should NOT be a place where people feel excluded, or where personal or historical traumas surface because of cluing or grid fill.

For example, I don’t believe CHINK should appear in crosswords, even as “flaw in one’s armor,” because anyone casually glancing at the grid will only see that word, not necessarily the context.

We can do better.

[Image courtesy of Bogoreducare.org.]

Originally, I wasn’t going to mention the specific clue/entry at all, because the issue is larger than this one example. But knowing the word that offended our original poster adds context.

The entry was NOOSE, and the clue was “End of a hangman’s rope.”

For the poster, the associations surrounding both clue and entry were troubling. But, for the most part, the main reason for posting appeared to be twofold:

1. Pointing out that the word’s inclusion in the grid was easily avoidable
2. Asking if other constructors/aspiring constructors found the entry as problematic as she did

She wasn’t calling for peoples’ heads. She was opening a dialogue and inviting discussion. She made her personal feelings clear — by using the word “appalled” — but made the discussion about something larger than her individual reaction.

Some replies concerned the clue more than the entry, pointing out that the noose was used for many other, non-negative uses. The general association of nooses with lynching was brought up, with some instantly making the connection while others felt it was unfair or hypersensitive to make that association. Others brought up the word LYNCH, asking if the entry was problematic even if the cluing was about director David or actress Evanna.

These aren’t easy questions to answer. This is obviously not a debate that will be concluded anytime soon. But it’s one worth having.

And when it comes to conclusions to draw from all this, I think the original poster said it best in one of her replies: “In my opinion, it’s better to err on the side of empathy.”

Amen.

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The Best Puzzle Solvers in Young Adult Fiction

Posted on April 28, 2020 by gmdirect

In the past, we have assembled super-teams of the best puzzle solvers in horror films, television, and literature. The goal was to highlight characters who stand out, the ones you’d want on your side, because they’re clever, decisive, and immensely capable.

In the fourth installment in this delightful series, we turn our attention to books for young adult readers, seeking out the quickest minds and the deftest problem solvers from the printed page.

So let’s meet (or revisit) some wickedly bright minds from teen-centric reads.

nancy drew

[Image courtesy of Amazon.]

Nancy Drew

Originally created as a female counterpart to the Hardy Boys, detective Nancy Drew has largely eclipsed them at this point, cementing her reputation as one of the most prominent teen detectives in literature. Nancy’s interest in numerous fields — psychology, language, and many others — served her well as she dove headlong into each case.

Her gift for association — making connections others miss — gave her a leg-up in locating clues and building cases before her lawyer father and the local police could do so. The criminal element in River Heights never left a puzzle that the diligent and outspoken Nancy couldn’t solve.

hermione-granger

[Image courtesy of Claire Fox Writes.]

Hermione Granger, Harry Potter series

When you’re a student of magic at one of the most dangerous schools in the world, you need to be sharp and ready. And Hermione Granger has those qualities in abundance. As studious as they come, Hermione is one of the puzzliest characters in modern literature. She brewed the notoriously difficult Polyjuice Potion, solved Professor Snape’s potion riddle, and deduced that Remus Lupin was a werewolf.

She’s as comfortable bending time to enhance her coursework (and save a few lives) as she is battling the gossip and lies of the treacherous Rita Skeeter. Numerous mysteries surrounding Hogwarts and Voldemort are solved by the trio of Ron, Harry, and Hermione, but without the stalwart and clever Miss Granger, Ron and Harry would’ve been out of luck.

wide window

[Image courtesy of Thrifty Teachers.]

Violet Baudelaire, Lemony Snicket’s A Series of Unfortunate Events

The eldest of the three Baudelaire orphans, Violet has the most mechanical mind of the trio. She is a prolific inventor, making marvelous contraptions out of whatever’s handy, and often getting her and her siblings out of dangerous situations in the process. Pursued by the malevolent and greedy Count Olaf, Violet outwits Olaf on more than one occasion, paying close attention to him and tailoring her behavior accordingly.

Whether she’s inventing a grappling hook to save her sister or picking a lock to find evidence against Count Olaf, Violet has a mind made for puzzles, whether she’s putting things together or taking them apart. As imaginative as she is capable, no mechanical brain teaser could stymie her for long.

ender game

[Image courtesy of Heritage Auctions.]

Ender Wiggin, Ender’s Game series

Although Ender’s story is not as happy as some of the others in this list, as mistreated and manipulated as he is throughout the first book, he should absolutely be counted among the best puzzlers in young adult literature. He is a phenomenal tactician, first in laser tag competitions in zero gravity, then later in simulated interstellar combat scenarios as part of his command training.

Ender uses his cleverness to circumvent the final test and win an unwinnable battle. And when he discovers that the battle was NOT simulated, and he had in fact won a war through his clever ruthlessness, he turns his puzzly mind to figuring out the mistakes that led to the war in the first place. As his adventures continue, he unravels numerous mysteries, often saving lives in the process.

ready player one

[Image courtesy of Goodreads.]

Parzival, Aech, and Art3mis, Ready Player One

In a virtual world known as the OASIS — a fully immersive Internet where work, school, and recreation are conducted — the characters of Ready Player One are on the ultimate puzzle hunt. For five years, the prize has remained unclaimed, no matter how expansive or expensive the methods employed to find it. Entire corporations are dedicated to solving it, because the prize is nothing less than control of the OASIS itself.

Which makes it all the more impressive that game and puzzle-loving teenagers are the ones to uncover several of the keys needed to complete the hunt. They are clever, determined, and resourceful puzzlers who combine a thirst for knowledge, top-notch gaming skills, and impressive deductive reasoning to accomplish the seemingly impossible.

westing game

[Image courtesy of Amazon.]

Turtle Wexler, The Westing Game

When you find yourself — and everyone else in your apartment building — on the list of possible heirs for a dead millionaire’s fortune, you know something strange is going on. And if it’s a race to a fortune predicated on solving an intricate puzzle, solving a murder, and uncovering a mysterious secret, then Turtle Wexler is the person you want on your side.

Possessing a keen mind and some serious analytical chops — after all, she plays the stock market at 13 years old — Turtle’s intellect is nearly as quick as her shin-kicking feet. Another strong tactician, Turtle takes advantage of opportunities (and creating a few of her own), eventually winning the Westing Game.

queen's thief

[Image courtesy of Christina Reads YA.]

Eugenides, The Queen’s Thief Series

The puzzles that Eugenides concerns himself with are far different than the ones tackled by other characters on this list. Eugenides is a master strategist, a chess player who must treat entire countries as his gameboard. Eugenides is observant and patient, playing out slow-burn tactics that can take months or years to come to fruition, all in the hopes of protecting those he serves.

It’s quite something to solve a puzzle in front of you, but it’s something else entirely to solve the next five puzzles before they’ve even shown themselves. Over the course of The Queen’s Thief series, Eugenides shows a tremendous understanding of how others think, what motivates them, and who can be trusted. There’s not a logic problem or a brain teaser around that Eugenides couldn’t plot his way past.

benedict

[Image courtesy of Amazon.]

Sticky, Constance, Kate, and Reynie, The Mysterious Benedict Society

If you’re looking for the most overtly puzzly quartet in young adult lit, this should be your first stop. These books are loaded to the brim with puzzles and mysteries, and this fearsomely brilliant foursome is equipped to handle any riddle, cipher, or brain teaser in their way.

Whether it’s Reynie’s logical deduction skills, Kate’s incisive ability to find shortcuts, Sticky’s memory and recall, or Constance’s penchant for finding patterns in plain sight, the sinister plans of Mr. Curtain (and any other puzzly evildoer out there) don’t stand a chance.

Did I miss any world-class puzzlers from famous (or obscure) works of young adult lit? Let me know in the comments section below! I’d love to hear from you!

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Tag Archives: Puzzlin’ fool

A Conway Puzzle Solution (And Some Hints for the Other Puzzle)

Famous Director Stumbles Into Trivia Trap!

A Two-For-One Visual Puzzle

Two Brain Teasers, Courtesy of Conway

Cultural Sensitivity and Crosswords: Where Is The Line?

The Best Puzzle Solvers in Young Adult Fiction

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