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

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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!

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[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.

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He then shared this text from Wikipedia:

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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.)

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[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)

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[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

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:

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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?


#1

benji 1

#2

benji 2

#3

benji 3

#4

benji 4

#5

benji 5

#6

benji 6

#7

benji 7

#8

benji 8

#9

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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A Cornucopia of Clever Clues

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Last month, in the afterglow of the Crossword Tournament From Your Couch event, I waxed nostalgic about some of the clever and tricky cluing that the constructors employed to keep the solvers on their toes.

I had so much fun poring over those puzzles and highlighting the clues that caught my eye that I’ve decided to do it again.

You see, I keep track of favorite clues from constructors as I solve various crosswords. Not only are they often witty, hilarious, and/or impressive, but they inspire me as a puzzler to always try to find entertaining, engaging new angles for clues.

So here are some favorites from my personal clue vault.

(And I’m crediting the constructor listed on the byline for each clue. These clues may have been created elsewhere and reused, created by the constructor, or changed by an editor, I have no way of knowing. So I’m just doing my best to give credit where credit is due.)


I’m a sucker for delicious wordplay, and thanks to a plethora of ingenious constructors, modern crosswords are rarely lacking in linguistic legerdemain.

One of my favorite cluing tropes is the old word-form switcheroo, when a constructor makes you think the clue is one word form (a verb, for instance) when it’s really a noun, or vice versa.

Erik Agard’s clue “Leaves from a club” certainly sounds like a verb, so it’s a fun surprise when you realize the answer is LETTUCE.

Similarly, the ability to utilize the multiple meanings of words can make for some seriously elusive clues. Mike Shenk’s “Volume setting?” has you thinking music or audio, but the answer SHELF also fits neatly.

Byron Walden is a master at this sort of cluing, as evidenced by his clue “Uruguayan uncle?” for the phrase NO MAS. Given how often TIO, TIA, MADRE, and other Spanish familial terms are used in crosswords, it’s a keen example of misdirection.

keep-right-misdirection

And playing with the tropes of crossword cluing creates opportunities for more wordplay.

“Trick or treat,” a clue from Aimee Lucido, masquerades as the common Halloween phrase when it’s really two examples cluing the answer VERB.

Similarly, “Jets or chargers starter” sounds like a sports reference, but the lowercase “chargers” reveals something else is afoot. The answer to this clue (which appeared in a puzzle constructed by Craig Mazan and Jeff Chen) is TURBO.

Erin Rhode’s “Drum, for some” sounds like a simple example-style clue, but the answer RHYME reveals how she hid her wordplay in plain sight.

Yes, these clues have a lot in common with wordplay clues, but they also play with the conventions of crossword cluing.

owl

Oh, and speaking of clues that hide their trickery in plain sight, I’ve got a few examples of that as well.

Kathy Weinberg once clued ROWS as “15 things in this puzzle,” which is the sort of clue that’s simultaneously so vague and so on-the-nose that it drives me insane.

Similarly, Steve Faiella uses modern slang to hide an answer in plain sight with the clue “Has beef with somebody, say.” That sure sounds like a vernacular use of “has beef with,” so you’re less likely to read the clue as a simple description of EATS, the actual answer. Very sly.

I’m going to close out today’s post with a clue that’s not only clever, it’s economical as well. Robyn Weintraub clued HOLE with two simple words — “Darn it!” — and it’s as hilarious as it is effective.

What are some of your favorite crossword clues, fellow puzzlers and PuzzleNationers? Let us know in the comments section below! We’d love to hear from you.


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5 Questions for Twitch Streamer and YouTuber Rachel Howie

Welcome to 5 Questions, our recurring interview series where we reach out to puzzle constructors, game designers, writers, filmmakers, musicians, artists, and puzzle enthusiasts from all walks of life!

It’s all about exploring the vast and intriguing puzzle community by talking to those who make puzzles and those who enjoy them! (Click here to check out previous editions of 5 Questions!)

And I’m excited to welcome Rachel Howie as our latest 5 Questions interviewee!

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Whether she’s exploring the verdant expanses of Breath of the Wild or slaying overpowered monsters in Dark Souls, Rachel Howie is an established force in the Twitch video game community. Wielding years of experience as a YouTube presenter and a lifetime of video game fandom, Rachel entertains and informs across Twitch and YouTube under the handle “DontRachQuit.”

As both onscreen performer and video editor, Rachel is a one-woman multimedia content creator, bringing humor, enthusiasm, and some wicked button-mashing skills every time she picks up a controller and live-streams her gaming exploits.

And this month, she’s even raising money for St. Jude Children’s Research Hospital through their Play Live program!

Rachel was gracious enough to take some time out to talk to us, so without further ado, let’s get to the interview!


5 Questions for Rachel Howie

1. How did you first get into video games? What genres or styles of games most appeal to you?

Growing up, I was always obsessed with Nintendo. My older cousins had a SNES, and then later an N64, and I was just absolutely obsessed with it. Because I was far too young to play much more than Jungle Hijinx on Donkey Kong Country without screwing up all my cousins’ progress, I’d beg and beg them if they would play so that I could watch and learn all the secrets. Perhaps a prelude to my future career in streaming!

So I have my cousins, or I suppose, my uncle, to thank for getting me interested in video games. He had a 120 star save file in Mario 64 and my little eyes just lit up with admiration every time I started it up.

When the Pokemon anime started on TV, I begged for my first console to call my own, and my parents got me a little yellow game boy pocket with Pokemon Blue. I must have been around… 6 years old? I had to ask my Dad for help because I literally couldn’t figure out how to exit Blue’s house. Good times.

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[She even named her dog after a Pokemon!]

Nowadays, the genre I am most invested in is Action/Adventure and RPG. I love anything that offers me the ability to create a custom character and just get lost in a world full of people who need my help. Throughout the past 15 years, I’ve played copious amounts of World of Warcraft, and I do enjoy MMOs, also. However it is hard just to nail myself down to one genre, as I do enjoy all sorts – Dark Souls, The Legend of Zelda, WoW, Pokemon, The Binding of Isaac, Okami, Portal, the Ori games, Kingdom Hearts, and I’ve been super into Beat Saber lately on the Oculus!

2. Puzzles are frequently an integral part of a video game, either as obstacles or as the entire focus of the game. What’s one example of a game that utilizes puzzles effectively and a game that fails to do so?

I absolutely love puzzles. The first thing that springs to mind is probably because I’ve been playing the recently released Resident Evil 3 remake, and that is last year’s Resi 2 remake. The very idea of having enjoyable puzzles inside a horror game may seem pretty strange, but in Resi it just works. It’s a great change of pace from the ‘shooty shooty zombie, run run run Mr. X is comin’, regular gameplay. So I’d definitely put the Resident Evil series as a whole forward as a game that very effectively incorporates puzzles.

If we wanna talk entire focus of the game, Portal 2 is king. Seriously. What a game.

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I find it difficult to think negatively so nothing springs to mind immediately when thinking of a game that tries puzzles but falls flat. The obvious answer I suppose might be The Legend of Zelda: Ocarina of Time‘s water temple on the N64, but this is purely linked to the Iron boots being equippable from the start menu – something fixed perfectly in the 3DS remake.

3. Visuals play a huge role in several of your endeavors, as editors are visual storytellers who help illustrate a given narrative and Twitch streamers provide a sort of visual performance art alongside their gameplay. What’s the key to accomplishing both styles of storytelling effectively?

If we take video editing first, it really is quite simple. An edited video will be made to fulfill a brief, it has a purpose – what it will be used for and whether it’s supposed to invoke a certain emotion, or response from people. The key is knowing exactly what you are making and keeping that in mind with every single cut, every title card, every sound effect or piece of music. Watching back your work is also important, and trying to visualise how it might be perceived by a third party.

Twitch streaming, I feel, is even simpler. Live content is natural, or rather, it usually is. There are plenty of streamers who put on high-production value shows or perform as a character during their streams. I honestly just wing it! I’m a naturally pretty expressive person who tends to have 150% emotions and this just seems to work so well for streaming.

I also love, and try to encourage, mascots and channel memes into things like alerts – so the visual style ends up very lighthearted and fun, full of hype to celebrate when people are kind enough to financially support. When I was creating my branding, I wanted something that people could identify with me that also described my vibe, and the kind of content I create. So I went for bright colours, and yet a strong, sharp edged font – the perfect marriage of fluffy dogs and Dark Souls!

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4. What’s next for Rachel Howie?

The tail end of last year was a bit of a roller-coaster for me. I was forced into a corner and had to give up on a job with a team I loved with all my heart, and leap into something that I wasn’t exactly ready for. I had been streaming on Twitch and creating content in my spare time for three years previously, and it was borderline sustainable income, so giving up a reliable salary was absolutely terrifying. However I have not regretted it in the slightest. My Twitch channel got partnered, my YouTube is steadily rising, supported by Patreon, and I’m exploring new avenues like podcasting. Heck, I went out and got a puppy! Life is pretty scary at the moment, but it’s also never been so exciting.

I’m going to continue working hard on my channels, and continue to try and help everyone through this uncertain time with my goofiness and relatability. I’d love to start going to more events, such as Insomnia and Comic Con, as ‘DontRachQuit’, and slowly carve my name across the industry. Also it would be really great if I could manage to finish this deathless run of Dark Souls before I grow old!

5. If you could give the readers, writers, gamers, content creators, and puzzle fans in the audience one piece of advice, what would it be?

The most important thing I’ve learned over the past 6 months, is that life is too short not to try and follow your dreams. You are the most important thing, and your happiness is paramount. It’s all fine and well putting others before yourself, but if that’s just going to make you unhappy, I’m afraid it’s not worth it. Just be yourself, treat yourself, and do what makes you happy. Never stop trying, never stop learning – failure is just another opportunity to learn. Keep trying, you can do it!


A huge thank you to Rachel for her time. You can follow her on Twitter (as well as Instagram, YouTube, and Twitch) for updates on all things “Don’t Rach Quit,” and if you enjoy her videos and streams, please consider joining her Patreon! I can’t wait to see what video game she conquers next!

Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!

Puzzles Come to Animal Crossing for May Day!

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[Image courtesy of Nintendo.]

The latest edition of the video game franchise Animal Crossing — New Horizons — has been out for a few months now. But recently, they ventured into the world of puzzles as a special promotion.

Thankfully, friend of the blog Jennifer Cunningham — puzzler, artist, musicologist, and former Tabletop Tournament Champion — has returned to the blog with the lowdown on the recent May Day event.

So, without further ado, let’s turn things over to Jen for her piece on Animal Crossing: New Horizons.


Possibly one of the most anticipated video game releases of the year, Animal Crossing: New Horizons arrived at just the right time, hitting Nintendo Switch consoles at the end of March.

The latest installment in the Animal Crossing series finds its players arriving at a beautiful island paradise. There are multiple goals in the game including expanding your home, gaining wealth, collecting insects and fish to donate to the local museum (or to sell for profit), and of course improving your island’s appeal so that popular singer/songwriter K.K. Slider will play a concert for you and the other residents.

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[Image courtesy of VG 24/7.]

Players across the world have gone wild for this game, making it their entertainment of choice while stuck at home at this uneasy time. The social aspect of the game, which allows players to virtually invite their friends to their islands, share gifts and resources, and even to chat, has helped many feel less isolated.

And the makers of Animal Crossing are doing their part to keep the game interesting and engaging for players who have likely been obsessively playing since the release date. As months change, so do your island’s insects and fish, and special events ensure players keep coming back. An Easter-themed event called Bunny Day saw players collecting eggs to build themed objects, and more recently an environmentally centered event called Nature Day encouraged activities related to planting trees and flowers.

May Day on May 1st was part of the Nature Day celebration. Starting on this day, everyone’s favorite raccoon/tanuki mogul Tom Nook gave players a special ticket for a May Day Tour on a special getaway island via Dodo Airlines. Unlike other island excursions that players may take, this particular tour package had an unusual surprise. Players were transported to an island with a puzzly secret: a maze!

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[Image courtesy of Jennifer Cunningham.]

Normally Animal Crossing doesn’t involve much in the way of problem solving — it’s a pretty straightforward collect-and-build-style game — so to challenge players with a puzzle was a surprise.

The entire May Day Tour island is composed of a hedge maze, blocked off in spots by boulders, trees, and shrubs. Using a simple shovel supplied at the maze entrance, players must collect resources such as fruit, wood, and iron ore to build more tools and make their way through the maze.

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[Image courtesy of Newsweek.]

In addition, players could collect “Bell vouchers” which can be traded in for Bells (the game’s currency). At the end of the maze awaited the main prize as supplied by a mysterious returning character popular to fans of the game’s previous generations. (I admit as a new fan, this wasn’t a big draw for me, but for die-hard fans, this was a very big deal.)

The maze was intuitive, and it didn’t take long for me to figure out how to navigate it, although it does involve a lot of backtracking to meet the necessary steps in the correct order.

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[Image courtesy of Super Parent.]

That said, the maze did offer some challenges. I completed my first attempt fairly quickly, but failed to maintain enough fruit in my stores to remove three boulders and access a group of bell vouchers. (For a bit of context, consuming fruit boosts players’ strength, allowing them to dig up whole trees or break boulders).

Thankfully the maze offered a reset option. It took me about three attempts to finally perform every necessary action in the correct order to collect all of the maze’s prizes.

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[Image courtesy of Animal Crossing World.]

Overall, while not the most challenging of puzzles, it was refreshing to do some problem solving in a game that can admittedly get a little repetitive. There was a hint within the game’s dialog that there may be more islands of this sort, and I do hope that is true. Likely these will be included in future events to keep players coming back for more.

If you haven’t jumped on the Animal Crossing bandwagon yet and want to try your luck at the maze before it’s too late, the May Day event runs through May 7.


Thank you Jen for that marvelous report!

Will you be participating in the May Day Animal Crossing event, fellow puzzlers and PuzzleNationers? Let us know in the comments section below. We’d love to hear from you!

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You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!