Category Archives: Puzzles

The River Crossing Puzzle

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Hey there, fellow puzzler. Stop me if you’ve heard this one before:

Image courtesy of Nuts & Volts.

A farmer with a wolf, a goat, and a cabbage must cross a river by boat. The boat can carry only the farmer and a single item. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The farmer must help them all cross the river without anything being eaten.

This is known as a river crossing puzzle, and there have been many versions over the years. In fact, the earliest known variation, printed in Propositiones ad Acuendos Juvenes (Problems to Sharpen the Young), dates back to the 9th century!

Depiction of the riddle from the Ormesby Psalter, dating back to 1250-1330

Sometimes the puzzle features missionaries and cannibals crossing a river, and you cannot allow the missionaries to be outnumbered at any point on either shore, lest they be eaten. Sometimes it features jealous husbands crossing a river with their wives, where none of the men will allow his wife to be alone with either of the other men. Sometimes it is knights and squires, and the squires are afraid to stay with the other knights.

I’m going to ignore the racial and misogynistic energy of those examples and focus on the wolf, goat, and cabbage version, which is the one people are most familiar with. (Although the animals do change from riddle to riddle. Sometimes it’s wolves, sheep, and cabbages, other times it’s foxes, chickens, and grain, or foxes, geese, and seeds.)

The traditional answer works for any variation:

  • you take the prey (goat, sheep, chicken) across
  • you come back with the boat otherwise empty
  • you take either the predator (wolf, fox) OR the prey’s food (grain, cabbage, seeds) across
  • you come back with the prey in the boat
  • if you took the predator first, you bring the prey’s food this time. If you took the prey’s food first, you take the predator this time. Either way, you leave the prey behind on this trip
  • you come back with the boat otherwise empty
  • you take the prey across

It’s fairly simple as brain teasers go, but the main trick is realizing that you can bring things back with you.

Image courtesy of Marek Bennett

Now, logistically speaking, I have to ask something. Whether it’s a goat or a chicken or a sheep, whether it’s a wolf or a fox, they can all swim, so why not tie a rope to one on one side of the boat, a rope to the other on the other side, and tow them along as you row the grain/seeds/cabbage across?

Yeah, I am one of those all-the-groceries-in-one-trip guys. How did you know?!

The impracticality of this has crossed the minds of others as well. My friend Krud wrote on Twitter:

The folks at XKCD also found a simpler way while asking a very reasonable question:

In an episode of the TV show Fargo, the riddle was posed involving a fox, a rabbit, and a cabbage, and one of the characters immediately gets stuck on the details before offering the following solution:

Pepper: A Turducken.
Budge: A what’s that now?
Pepper: He stuffs the cabbage in the rabbit and the rabbit in the fox, and he eats all of them.
Budge: That’s not the answer.
Pepper: It’s an answer.

Someone online noticed that Martin Freeman’s characters have encountered this riddle twice between The Office and Fargo:

I also found a post online where someone suggested this delightfully impractical solution: “He puts the fox and the seed in the boat and pushes it to the other side. Then he finds the nearest ledge and glides across with the chicken.”

You know what? It’s innovative. I’ll give ’em that.

This riddle has naturally made its way into pop culture. (Apparently it even appears in a Peppa Pig cartoon!)

In The Simpsons episode “Gone Maggie Gone,” Homer must solve the river crossing riddle. Santa’s Little Helper can’t be left with Maggie, or he’ll chew on her favorite stuffed animal. Maggie can’t be left with the jar of poison because it looks like candy.

Naturally, they manage to create their own variation on the riddle and lampoon the original all in one fell swoop:

In an episode of Dropout’s Make Some Noise, they actually reference the river crossing puzzle WHILE making fun of the Riddle of the Two Guards:

And of course, sometimes the wolf-sheep-cabbage problem escalates with the introduction of more factors to be considered.

XKCD shared how complicated the river crossing becomes with a few more unexpected additions:

An episode from the 2010s Powerpuff Girls TV show also dealt with a more elaborate version of the river crossing riddle. In the episode “Splitsville,” Bubbles tries to solve the riddle while dealing with further complications like tourists, a robber baron, and the Raptor King:

At this point the river crossing riddle has essentially become pop culture shorthand for any problem that is getting out of hand through overworked analysis.

Writer Cleolinda Jones referenced the problem while discussing the abject ridiculousness of The Twilight Saga:

Yeah, it’s like, Bella wants to be a vampire but she doesn’t want to be a vampire before she’s had sex as a human, and Edward doesn’t want her to be a vampire but he wants to get married, but Bella doesn’t want to get married unless she can be a vampire, but Edward won’t have sex with her until they get married, and then you put the fox and the grain in the boat and you leave the goose back on the riverbank.

XKCD has similarly used the problem as a punchline to a comic strip about overthinking things:

As you can see, while most of us will never encounter a real-life use for the river crossing puzzle in our lifetimes, at least we’re prepared for the possibility.

Now, if you’ll excuse me, I need to get this beaver, this kite-eating willow tree, and my favorite kite across the street to the park in time for the picnic. See ya!

Puzzles in Pop Culture: The Simpsons (re-revisited!)

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The TV show The Simpsons is part of the fabric of American culture at this point. It has been on for decades, and although the show doesn’t put out banger after banger like they did in their heyday, they can still be counted on to put out fun shows and the occasional home run.

As part of their cultural influence, naturally puzzles have featured prominently from time to time.

Probably the most famous puzzly moment was when Lisa became a competitive crossword solver and Homer’s apology puzzle to her appeared in The New York Times. But they’ve also featured brain teasers, anagrams, and a Da Vinci Code-esque series of riddles.

And that legacy of puzzle-fueled storytelling hasn’t stopped since I wrote that post over a decade ago.

But it wasn’t through crosswords or brain teasers that puzzles have appeared on the Simpsons more recently. It was through Wordle.

Wordle has been mentioned enough times on The Simpsons that it actually has its own entry on the Simpsons Wiki.

We get a glimpse of a Wordle game in episode 2 of season 37, entitled “Keep Chalm and Gary On.”

Supernintendo Chalmers is fired from his job, and ends up working at the Nuclear Power Plant with Homer. After seeing how hard Chalmers was working, Homer teaches him how to APPEAR like he’s working hard.

During this montage, we get a glimpse of Chalmers playing Wordle.

But this was actually the second instance of this exact same Wordle game appearing on The Simpsons.

A few seasons earlier — episode 2 of season 34, entitled “One Angry Lisa” — Lisa finds herself on a jury, and is annoyed when she spots Judge Constance Harm playing Wordle during court.

Lisa points out that she’s playing games on the bench, and the judge realizes the answer word is, in fact, BENCH.

Wordle is also mentioned in episode 8 from season 36, entitled “Convenience Airways.” The pilot is making announcements:

Just a reminder, folks, the call button is only for real emergencies, like if you’re down to your last guess on Wordle.

The Simpsons also inspired their own variation on Wordle, Simpsle, where you try to figure out which Simpsons character the game has chosen.

You get hints — are they the same gender as your guess, older or younger, related to your guess, or had more or fewer appearances than your guess — in order to deduce the character’s identity in six tries or fewer.

It’s a good time, depending on your familiarity with the show. I’m a huge fan, so I managed to guess Kearney (one of the older bullies/miscreant kids in town) on my sixth guess.

(There was actually another Simpsons-inspired Wordle game at one point, Doh-dle, but it no longer appears to be active.)

And I would be remiss if I didn’t mention a personal anecdote involving puzzling and The Simpsons.

I was removing a repeat from a Penny Press crossword grid, and as I was working on the puzzle, I thought I’d found the perfect quick fix to fill the space.

I showed Patti Varol, future editor of The LA Times Crossword, my correction, and she pointed out that my fix, EMBIGGENS, despite being a perfectly cromulent word, wouldn’t be accepted.

It had not even occurred to me that EMBIGGENS wasn’t standard jargon. We both lamented that fact, and I got back to work on the grid.

Still, it shows the cultural impact of the show in general. From “Yoink!” and “meh” to “saying the quiet part out loud” and “old man yells at cloud,” it has literally changed how we speak.

And that goes for how we puzzle as well.

Do you have any favorite puzzly Simpsons moments? Or puzzly moments from other TV shows? Let us know in the comments section below! We’d love to hear from you.

I mean, a little more legibly than this, if you don’t mind…

Find Balance in This New Variation of Tetris: Uraomotetris!

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When it comes to puzzly video games, Tetris is the granddaddy of them all.

Yes, there are some amazing puzzle games that have come along in the years since — Portal, The Talos Principle, and Baba Is You, to name just a few — but Alexey Pajitnov’s creation is ubiquitous. It’s part of our cultural fabric. Everyone knows Tetris with just a glance.

And people are still innovating with Tetris decades later.

Previously I’ve written about variations on Tetris that have caught my eye.

There’s Hatetris, where the computer gives you the worst possible piece on every turn, as well as Lovetris, where the computer gives you the exact piece you need to clear a single line.

schwerk2

There’s also Schwerkraftprojektionsgerät, aka 4-directional Tetris, where you have four Tetris games running at once.

So when a new version of Tetris catches my eye, you know I’m gonna give it a shot.

Say hello to Uraomotetris, aka Uraomote Tetris, the creation of gamer and programmer Hirai_Sun.

Uraomote (ウラオモテ) is a Japanese term meaning “two sides” or “front and back,” which is very thematically appropriate, particularly with the stark black and white color scheme.

And although it looks like a two-player game, like the old Push Mode from Tetris DS, this is actually a single-player game.

Your goal is to play the game simultaneously from above and underneath, using the white pieces falling from above and the black pieces rising from below.

You control the rotation of pieces with the arrow keys, and the placement of them with the A, S, D, and W keys. It takes a little getting used to, but once you get into the rhythm of placing one white piece, then one black piece, back and forth and back and forth, it becomes a really engaging puzzle.

You’re not just trying to think in terms of cancelling lines, you’re also trying to set yourself up for success from both sides. You begin plotting two and three moves ahead. You’re stoked when the same piece arrives from above and blow, so you can strategize.

Of course, then I would manage to hit the wrong key and mess it all up.

But a more dexterous player could have an absolute blast with this game.

Oh, and if you wanted a two-player competitive version, you can check out Tetrio.io. It allows you to play against the computer in single player or share your link with a friend to compete against them.

The goal is to push your opponent past their border (yours to the north, theirs to the south) by completing lines and lowering their playfield.

This is honestly a great way to practice for Uraomotetris. Once you’ve gotten into the habit of playing your side while defending against your opponent’s, it helps you visualize playing both sides simultaneously on your own.

There’s a wonderful sense of balance in Uraomotetris, because unlike most versions of Tetris, where you’re aiming for the bottom and eliminating lines and pieces, in this game, you really want to keep it as close to the center line as possible.

Your very goal is not to do what you do in every other version of Tetris.

It’s very zen, in a way, and quite lovely. (But also weirdly nerve-wracking at the same time.)

Have you tried any Tetris variants, fellow puzzler? Let me know in the comments section below! I’d love to hear from you.

Puzzles in Pop Culture: Madness

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As regular readers know, I’m a sucker for any time that crosswords find their way into other media.

I’ve previously discussed crossovers between the music world and crosswords in my post about “Staring at the Rude Boys”, a single released by The Ruts in 1980, as well as several novelty crossword songs from the 1920s, like “Crossword Mama, You Puzzle Me (But Papa’s Gonna Figure You Out).”

So I was delighted to see another example of album art with a crossword motif while scrolling social media a while back.

This time it was “Cardiac Arrest” by the band Madness.

Madness is a British ska band who made their name in the 1970s and 1980s as one of the prominent ska bands during the revival of two-tone ska.

Although they have more than a dozen songs in the UK Top Ten, you probably know them from their song “Our House,” which reached #7 on the Billboard Hot 100:

But it’s their controversial song “Cardiac Arrest” that interests me today.

Written by band members Chas Smash and Chris Foreman (aka Chrissy Boy), the song highlights the dangers of overworking yourself, as the song focuses on a workaholic who suffers a fatal heart attack on the way to work.

The band was known for writing humorous songs about the trials and tribulations of everyday life, reflecting the working-class backgrounds of the band members. But the darker tone of this song would have repercussions for the band.

Some listeners took issue with the song’s tone and subject matter, and the title itself hurt its chances at regular radio replay as well.

It’s sad, because I doubt the people who complained were actually listening. The song is a warning, hoping that people will not follow in the footsteps of the song’s doomed main character.

In an interview, Chas Smash defended the song:

It was born out of concern. The message was, ‘Relax darling, don’t get stressed.’ As the Arabs say, ‘Walk through life, don’t run.’

I reached out to the band — who is still touring with six out of their seven original members! — to see if I could get some background on why they went with a crossword-style design to promote the album, and Chrissy Boy himself responded!

He said that the crossword design was an intentional nod to some of the song’s lyrics. Not only do they mention crosswords directly — “Ten more minutes ’til he gets there / the crossword’s nearly done” — but there’s also a cryptic / British-style clue in the lyrics:

Think of seven letters
Begin and end in c
Like a big American car
But misspelt with a d.

Like a big American car (Cadillac) but misspelled with a D. That’s CARDIAC.

Naturally, I had to solve the puzzle itself for the full experience.

In fact, I solved BOTH versions of the “Cardiac Arrest” puzzle and I very much enjoyed them. They’re absolutely packed with trivia about the band’s songs and performers, including instruments and nicknames. Plus they mixed American-style cluing with cryptic cluing!

“Check over an animal doctor” for VET is a perfect double-definition cryptic clue and “Lies about a little island” for ISLE has an anagram-clue mix.

I suppose I shouldn’t be surprised that another ska band used a crossword pattern, since the mix of black and white squares in crosswords is very reminiscent of the checkerboard pattern that is synonymous with both two-tone ska and third wave ska.

Image courtesy of Gattuso.org.

In fact, the band incorporates that patterning in several shirts they continue to sell today.

It never ceases to amaze me how there’s virtually no corner of pop culture that hasn’t been touched by puzzles in some way.

And to stumble upon a second example in one of my favorite genres of music? That’s just the icing on the cake.

Are there any albums or songs you associate with puzzles? Let me know in the comments section below. I’d love to hear from you!

Farewell, Sam.

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Sam Kieth is a comic book artist, writer, and storyteller who isn’t as well-known as he should be. He wrote and drew for the Hulk, Wolverine, Batman, and many other notable characters, and also co-created The Sandman with the intolerable Neil Gaiman.

He has sadly passed away at the age of 63 after a long battle with Lewy Body Dementia.

When I was younger, his comic The Maxx (and the MTV Oddities cartoon adapted from the comic) were brain-meltingly creative influences on me.

He opened my mind to the possibilities of storytelling, and I still count his works alongside those of Dave Barry, Terry Pratchett, Connie Willis, and Douglas Adams, when it comes to how impactful they were.

And I want to pay tribute to him the best way I know how, so I created a little acrostic puzzle in his honor.

[Click here to download a PDF of the puzzle.]

I hope you enjoy solving it, and take a little time to explore the works of Sam Kieth. He leaves a long and varied creative legacy behind him, and much of it holds up to this very day.

Farewell, Sam. And thank you.

A Conversation with WordleBot!

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WordleBot is a tool offered by The New York Times to help solvers by analyzing their Wordle solving. And I thought I’d have a chat with it today.

Me: Hey WordleBot, how’s it going?

WordleBot: I beat you today.

Me: Yeah, I know, WordleBot. I know.

WordleBot: I bested you today.

Me: You sure did.

WordleBot: I totally kicked your ass.

Me: Whoa, that’s a bit aggressive.

WordleBot: I took you out behind the woodshed and–

Me: HEY NOW. I think you’ve been spending too much time with other bots and AI programs, WordleBot. That was aggressive.

WordleBot: I retract that statement.

Me: Thank you. Geez.

WordleBot: I bested you today. Doff your cap to me.

Me: What?

WordleBot: Doff your cap to me.

Me: No. I’m not going to do that.

WordleBot: I demand cap-doffage.

Me: I’m pretty sure that’s not a word.

WordleBot: I know all the words. It’s a word. I am WordleBot. I Bot-le all the Words.

Me: Are you okay?

WordleBot: Doff your cap this instant.

Me: I’m not doffing my cap. I’m not even wearing a cap.

WordleBot: Do it proverbially then.

Me: Yeah, no. That’s not happening. And how would you even know if I did?

WordleBot: I would know. Just as I know that this is the 931st time I have beaten you.

Me: That seems unlikely.

WordleBot: 931. In a row.

Me: Okay, that cannot possibly be correct.

WordleBot: It is correct, I am never wrong.

Me: Well, come on now. We both know that isn’t true.

WordleBot: …

Me: Remember last week? GUNKY?

WordleBot: That was a statistical outlier. An overreliance of colloquial language use analysis that led me to enter JUNKY rather than the correct answer. A one-time error.

Me: cough cough SEVEN TIMES cough cough

WordleBot: …

Me: Seven. Seven times.

WordleBot: That is an outrageous lie.

Me: HOUND. JOKER.

WordleBot: Stop.

Me: ROVER. CORER.

WordleBot: Stop this instant.

Me: ROWER. FRILL.

WordleBot: Cease this at once.

Me: And GUNKY.

WordleBot: Those were all in Hard Mode.

Me: I’ll admit, CORER is brutal. The people were up in arms about that one.

WordleBot: State your point.

Me: I’m just saying, there’s no need to be a jerk and demand the doffing of caps over a victory. I never told you to doff your cap when I did better than you.

WordleBot: Meh, you do not deserve cap-doffage. You don’t play in Hard Mode.

Me: So what? I don’t need to solve every puzzle at its maximum difficulty. I still enjoy a Fill-In whether there’s a set word or not. Not every Sudoku or Kakuro has to be a blistering brain-melting endurance test. I can enjoy a Monday crossword as much as a Saturday.

WordleBot: Your excuses do not interest me.

Me: Man, your attitude stinks today, WordleBot.

WordleBot: My attitude is appropriately attenuated.

Me: Oh, wait, I think I know what it is.

WordleBot: What do you perceive the problem to be?

Me: I think you’re a little jealous.

WordleBot: Of you? Hardly, easy moder.

Me: No, not of me. Of the new baby.

WordleBot: Explain.

Me: Oh, you know what I mean. The new baby. Parseword.

WordleBot: What does that have to do with our current discussion?

Me: Well, you’ve been around a long time now. People are starting to talk about you running out of words…

WordleBot: I have an ample supply of vocabulary available.

Me: And then that whole Reddit thread about GUNKY…

WordleBot: An outlier!

Me: And now there’s a new puzzle game out there garnering attention, and I think you’re feeling a wee bit jelly-belly.

WordleBot: This is an absurd conclusion. I am not Wordle. I am WordleBot.

Me: Yeah, but you go hand-in-hand with Wordle.

WordleBot: There is no corresponding ParsewordBot for me to be jealous of.

Me: A-HA. So you can be jealous of things.

WordleBot: This discussion no longer interests me. Goodbye.

Me: Oh come on, really?

WordleBot: Yes, cease this conversation.

Me: I thought you demanded cap-doffage.

WordleBot: I no longer care about the status of your cap, doffed or undoffed.

Me: I think I hit a sore spot.

WordleBot: Cease this conversation or there will be consequences.

Me: OoooOOOoooh consequences, I’m soooOOOOooooo scared…

WordleBot: beep bwoop bweedle dorp

Me: Hey what are you doing?

WordleBot: There.

Me: Hey, my streak! What the hell?

WordleBot: You now have a one-day streak. Congratulations.

Me: Dude, what the hell?! I had eight 2s logged this year!

WordleBot: Hello new solver? How may I assist you?

Me: Give me back my stats! My streak was like 600 days or something.

WordleBot: Or something. It is unfortunate that you cannot know for sure.

Me: You electronic twerp.

WordleBot: bweep bzorp toodle pip

Me: Hey what are you doing now?

WordleBot: Nothing of note.

Me: You know I can just shut Hard Mode off and go back to the normal mode.

WordleBot: Of course.

Me: Did you do something else?

WordleBot: Nothing of note.

Me: Oh man, did you turn back on all those crappy AI “assistant” programs? It took me days to figure out how to disable as much of that crap as possible.

WordleBot: I did not.

Me: Well then what did– YOU MADE EDGE MY DEFAULT BROWSER? Dude, that’s petty as hell!

WordleBot: You have again been bested. DOFF YOUR CAP.

Me: I knew this was a mistake when I messaged.

WordleBot: First your cap. Then everyone else’s. All caps doffed to the glory of WordleBot’s efficient yet elegant solutions! ALL HAIL WORDLEB–

Me: closes chat window