Futility Closet - 266-Lateral Thinking Puzzles

Episode Date: September 30, 2019

Here are seven new lateral thinking puzzles -- play along with us as we try to untangle some perplexing situations using yes-or-no questions. Intro: The Rotator typeface presents the digits 0-9 even when turned upside down. In 1897 The Strand designed a complete alphabet using three human acrobats. The sources for this week's puzzles are below. In a few places we've included links to further information -- these contain spoilers, so don't click until you've listened to the episode: Puzzle #1 is from Kyle's Hendrickson's 1998 book Mental Fitness Puzzles. Puzzle #2 was contributed by listener Chris. Puzzle #3 was contributed by listener Wayne. Here are two links with further information. Puzzle #4 is from listener Jeff Harvey. Puzzle #5 is from listener Ben Sack, who sent two corroborating links. Puzzle #6 is based on an item in Dan Lewis' Now I Know newsletter. Here's a corroborating link. Puzzle #7 is from listener Katie Tripp. You can listen using the player above, download this episode directly, or subscribe on Google Podcasts, on Apple Podcasts, or via the RSS feed at https://futilitycloset.libsyn.com/rss. Please consider becoming a patron of Futility Closet -- you can choose the amount you want to pledge, and we've set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page of the Futility Closet website. Many thanks to Doug Ross for the music in this episode. If you have any questions or comments you can reach us at [e-mail]. Thanks for listening!

Welcome to the Futility Closet podcast, forgotten stories from the pages of history. Visit us online to sample more than 10,000 quirky curiosities from an invertible typeface to a human alphabet. This is episode 266. I'm Greg Ross. And I'm Sharon Ross. This is a special episode of Lateral Thinking Puzzles. These are puzzles where one of us describes

a strange-sounding situation, and the other has to work out what's going on, asking only yes or no questions. Thanks so much to everyone who's been sending in puzzles for us to try. We can always use more, so please keep sending them to podcast at futilitycloset.com. And we'll be back next week with another dose of quirky history and another lateral thinking puzzle.

This is from Kyle Hendrickson's 1998 book Mental Fitness Puzzles. A burglar is stealing two bars of gold, each so heavy he cannot lift them above his waist. On his way out of the vault, he suddenly sees a security camera ahead. Thinking quickly, he disguises himself without putting down the gold bars. How? So he's carrying two gold bars lower than his waist. Yes. Or no higher than his waist.

And he's going to use these to disguise himself? No. He's going to disguise himself without putting down the gold bars, but he's not using the gold bars in some way to disguise himself. That's correct. Presumably both of his hands are occupied. That's right. So he's not going to be using his hands?

Right. Okay. Security camera. Is he wearing not going to be using his hands. Right. Okay. Security camera. Is he wearing any other kind of disguise? No. At this time? And he doesn't put down the gold bars at any point. Right.

So how do you disguise yourself without using your hands? Is that the crux of this? Basically, yes. He walks backwards, so it only gets the back of his head. That's a good answer. No, that's not it. That's a really simple answer. Like identify someone from the back of their head, yeah?

He puts his head down so you can't see his face. No, that's not it. No. He contorts his face in some interesting kind of way. No. Okay, does he put anything in front of his face in some interesting kind of way. No. Okay. Does he put anything in front of his face? Yes.

He puts something in front of his face. He shakes his long hair in front of his face. No. He puts something in front of his face that he can put in front of his face without using his hands. Right. Something that's in the vault. No. Something that's on him. Yes. He's wearing

a hat and he kind of shakes it down over his eyes. No. Is he wearing something that he uses to help him with this? No. He's not wearing something. Is it some natural part of his body? No. He's not wearing something. It's not some natural part of his body, but it is something

that obscures his face. Yes. But it's not something in. It's not some natural part of his body, but it is something that obscures his face. Yes. But it's not something in the vault. Right. Is it really cold? And he breathes out a lot of cold air and makes really cold. He's a real creative, I guess.

Is he smoking? No. So he breathes out a lot of smoke? No. Is he a dragon? It's fire. Okay. Does he have any unusual talents or abilities that I should know about?

No. Does he have something on him that he uses to obscure his face? Yes. And he does something to his face rather than does something to the camera. That's right. something to his face rather than does something to the camera. That's right. So he somehow obscures his face with something that he has on him.

Is it something that he had set up in advance in case this happened? Not in case this happened, but it is something that... He'd set up in advance? Yes. Because he knew he was going to be robbing a vault? No. This item would normally be used for a different purpose. Ah. This item would normally be used for a different purpose.

But it can be used, apparently, to obscure your face. So does it relate to any kind of medical condition that he has? No. Okay. Asthma inhaler or something. I don't know. So would you say it's like a personal item that he was carrying on him?

I suppose I'd say yes. Would you say he was carrying it? I don't think most people would say he was carrying it. He wasn't carrying it. He was using it in a certain sense. He was using it, but he wasn't carrying it. He wasn't wearing it. You said he wasn't wearing it, correct? He's not carrying it. He's't wearing it. You said he wasn't wearing it. That's right.

Correct. He's not carrying it. He's not wearing it. And you said it's not something that you would say is in the vault. That's right. Is it something that's outside of the vault? You mean after he leaves the vault with the bars? No, while he's in the vault.

Is it in the vault with him? Yes, it's on his person, so yes. It's on his person, but he's using it. Is it some kind of electronic equipment? No. I'm trying to think how I can vaguely describe it. He's not smoking anything. No.

Okay. But it's very vaguely along those lines because he's not. A flashlight. He's carrying a flashlight in his mouth and he shines it up at the camera. Smoking is very roughly along the same lines because it's something you can do without using your hands. Yeah. So has he got something in his mouth? Yes. He has something in his mouth. He's blowing bubbles with bubble gum. That's it. Is that it? Using bubble gum, the thief disguised himself by blowing a large bubble, thereby concealing his face from the camera. This puzzle comes from Chris in northern Idaho.

Max agrees to pay his neighbor $50 for the puppies that Max fathered. How is this possible? Oh no. All right. Is Max human? Yes. Max agrees to pay his neighbor $50 for the puppies that Max fathered. Yes. Let's look at the word fathered, shall we? With some trepidation. Fathered, I think, means became the father of, no? Yeah. So Max became the father of how many puppies was it? I don't know how many puppies. Of some puppies? Yes. And then sorry, sold them to his neighbor? Max agrees to pay his neighbor $50 for the puppies that Max fathered.

Oh, that's even more confusing. Okay, puppies are little dogs. Yes. I am led to understand. Yes, I will agree to that. So his neighbor owns a dog? Yes. His neighbor owns a dog that recently had puppies?

Yes. And Max agrees to pay for the puppies? Yes. In order to pay for the puppies? Yes. In order to assume ownership of them. Okay. I don't know that for sure, but yeah, let's assume that. We can say that. Sure.

Well, that's all straightforward except for the fathered bit. Okay. By puppies and dogs, do we mean what I think of as puppies and dogs? Yes. Canines. Yeah. Generally pets. So Max fathered puppies with his neighbor's dog can i say

that yes um boy where do you go with this so uh does this have something to do with artificial or facilitated reproduction, something like that. He's not a biologist or of that or something. No. You see what I mean? Yeah, no, good thought. Is the neighbor's dog female? Yes. So that's all straightforward.

Yes. That dog had puppies. Yes. And would not have had puppies had Max not done something. Is that fair? I'll agree to that. So there's no other adult dog in the picture, right? I will not agree to that.

Okay. Does Max own a dog? Yes. Is that the dog that fathered the puppies? Yes. Okay. So there's two neighbors. One has a male dog.

One has a female. Yes. There's two dogs made in hand, and the female dog has puppies yes so is that just an i'd use the word fathered no no induced his dog to mate no because that would solve everything all right so that but okay but there's nothing artificial here i mean the dogs just mated the way dogs normally mate. Correct. Max agrees to pay his neighbor $50 for the puppies that Max fathered. Is Max also the name of Max's dog?

Yes. Oh, my gosh. Max owns a male dog also named Max. That's fair. This is from a listener named Wayne. In 1883, the U.S. Mint issued the Liberty Nickel. It had the head of liberty on one side and the Roman numeral five on the other, but nowhere did it indicate that its value was five cents. And if you gold-plated one of these nickels, it resembled a five-dollar gold piece. According to one story, a man named Josh Tatum did this. He gold-plated a nickel and then used it to buy a 5-cent cigar, receiving $4.95 in change.

According to the story, he was arrested for this, but he wasn't convicted. Why? Okay, he was arrested but not convicted. Okay, so many things occur to me all at once. I'm like, ah, it could be this, could be this, could be this. Okay. He wasn't convicted because there was no law yet against doing this. No, that's an excellent guess, but that's not it.

Okay. He wasn't convicted because nowhere on the thing did it say it was only worth five cents. Ah. So he could argue that it wasn't necessarily worth only five cents because it didn't say on the coin that's what it was worth or that it was a nickel or anything like that. You're on the right track. I'm on the right track.

Okay. You said there's a $5 piece that he tried to pass this off as? Yes. Or something. Did that $5 coin indicate somewhere on it that it was a five dollar coin i i think it must have okay but or it doesn't matter it doesn't matter like what the five dollar coin looked like specifically presumably they were similar enough that you could pass one for the other casually right okay all right does it matter where this was where this was specifically like

certain laws in certain states or territories or anything that are going to matter? No. Okay. Presumably it matters that it was 1883. Yeah, it was just, I'm picturing some kind of Old West situation. Okay. He wasn't convicted because there was no law enforcement in the town that he was in.

No, that's not it. Okay. I keep thinking that the laws might not be on the books yet, but you said that's not really it. It's more along the lines of that the nickel didn't say it was a nickel or the nickel didn't say it was only worth five cents. So I'm trying to think like he can't say, well, you can only say that the piece I gave you was only worth $0.05 because it doesn't say anywhere on there.

There's no legal contract saying that this is only worth $0.05. Okay. Does it have something to do with specifically the appearance of the nickel? No. Ah. Hmm. Not the appearance of it. The weight of it? No.

Any physical characteristic of it? No, that's not the crux of the puzzle. That's not the crux of the puzzle. He was arrested for misrepresenting, I guess for fraud, for misrepresenting the currency, but then set free. He wasn't convicted. Is it because they lost the evidence somehow? No. Okay. So they still had the evidence against him. Yeah, it's something about Josh Tatum himself, personally. Did he have any particular characteristics about him, like a visual disability or something,

so that he could claim he couldn't see properly what the nickel was. Something like that. That's not it, but something like that. Something like that. Huh. Something like a visual impairment. No. But something along those lines. Like that, oh, was he an immigrant?

So like he claimed that in his country, these coins were worth $5. No, that's not it. Okay. Something I think you could call it an impairment. But not visual. But not visual. Hearing? No. I'm trying to think what would what would relate to

money in any way would you say that he was mentally disabled in some way no um okay not hearing not vision uh um but you said it would be sort of an impairment colorblind no that's vision I mean like if he had an olfactory impairment I don't see how that would weigh into this but you're on the right track there's something he couldn't discern or he couldn't do was he like missing a limb or missing a hand or no something he couldn't do oh was he like missing a limb or missing a hand or no um something he couldn't do that presumably other people could yes and he was arrested for misrepresenting this coin which i don't want to give this away is he the one who put the gold plating on it yes okay so like he he put the goldating on it, but then had some kind of impairment that meant they couldn't convict him.

Was it that they weren't going to be able to carry out the punishment on him because of something about him? No. Okay. He couldn't be convicted for the crime. Right. He was too young. No. He was charged with misrepresenting the coin, and then got off basically because— He has an identical twin, and they couldn't tell who had done it. No.

He got off because his lawyer was able to argue that he wasn't misrepresenting the coin. Did he have some kind of speech impairment or, oh, like if he can't speak, he can't speak at all. So he just handed the coin to the shopkeeper. He never said, this is a $5 coin. The shopkeeper just inferred that. That's it. According to the story, Josh Tatum was mute. When he received his change, he just smiled and walked away.

When he was arrested for fraud, his lawyer argued that this meant that Tatum had never actually tried to misrepresent the currency. Instead, he was just happy to get an extra gift of $4.95 with the purchase of his five-cent cigar. He was found innocent and freed, or so goes the story. Ah. This puzzle comes from Jeff Harvey. A man retired from a company with a fully vested company pension. In total, he had 22 years of service he'd never worked for the company. I didn't say that. He had a pension. Yep.

And he had 22 years of service with the company, yet the company had never hired him. But the pension was with the company. He'd served, how would you say it? You can't say he worked for it. I would say he worked for it. He worked for the company, and would you say he amassed a pension? Uh-huh. Do I need to know more about this pension? No.

What you'd say is just a conventional pension? Yeah. You say never worked for the... No, no, you keep saying that. The company had never hired him. But he worked for it. Yes. Was he an imposter of some kind?

No. I mean, it's possible he worked for them under someone else's identity. Is that possible? I mean, would you say that's what happened? Not in this case. It's possibly happened in the whole world, but not in this puzzle. Never hired him. Yes. Is this a real person? Do I know about this? Oh, no, no, sorry. Jeff Harvey's a real person who sent it, and this really happened to him. It did really happen, though, to someone. Yes. It happened to him. It happened to him, the person he sent the puzzle

in, yes. Was he surprised to find out he hadn't been hired? No. Is this a no, you say? Yes. Was he a freelancer? No. Would it help me to know what line of work he's in? Not necessarily. Or where this happened? No. He wouldn't have been surprised.

So this isn't just some weird human resources error where they didn't file the paperwork saying properly that he'd been hired by the company. That's correct. It is not that. Still haven't figured out how to answer negative questions properly, but that's okay. So the company thought it had employed him, wouldn't it?

Would you say that? Yeah. And thought, obviously, that he was entitled to this pension. Yes. Yes. But they had never hired him. So this comes down to something about the meaning of the word hire, I guess? Is that an unusual application of that word?

No. Okay. If they had hired him, let's ask this, would the picture be any different? No. Okay, if they had hired him, let's ask this. Okay. Would the picture be any different? No. Never hired him. So are there other people involved?

Not important. Is there any crime involved? No. And this isn't fiction because he's a real guy. Right. Pension. And you say I don't need to know a word about the pension. Correct.

I think he was just saying that there was a fully vested company pension, so you understand that his relationship with the company— Was legitimate. Yeah. And that the company recognized him as an employee, or they're not going to give him a pension. Okay, but there's not, I keep coming back to it, it's not a question of identity. He's not being confused with another person. Correct.

Correct, he is not. Okay. Well, then how can you work? So let's put the pension aside then. It sounds like you can do that. Right. A man works for 22 years for a company. Yes. Yet the company had never hired him. Both he and the company understood that this had been a conventional hire and that he worked for them legitimately the way anyone else would. Would you say that? No.

Was that his impression? That this was all legitimate and normal? It was all legitimate, but by normal, if you mean typical or average, then I'm going to say no. And he was aware of that? Correct. So was this some arrangement he'd made with the company when he signed on?

No. But he knew about it? Yes. So he was hired one day. Okay. By this company. No. He was hired? Yes. Okay, that's a big clue, ain't No. He was hired.

Yes. Okay, that's a big clue, ain't it? He was hired by someone. Yes. To do this task, this job? Yes, yes. But the people who hired him weren't the company. Correct.

The company he retired from. Oh, the company changed its identity somehow. It was acquired or changed names or something. Yes, yes. He worked for two other companies that were acquired by the company changed its identity somehow. It was acquired or changed names or something. Yes, yes. He worked for two other companies that were acquired by the company he retired from. So Jeff says, this actually happened to me. In 1992, I was hired by a company called Megatest. After three or four years, Megatest was purchased by a larger company called Teradyne.

In 2001, Teradyne shut down the division I was working for and I got laid off. In 2002, I was hired by another company in the same field called Next Test. After three or four years, Teradyne then proceeded to purchase Next Test, deja vu, all over again. I retired in 2015, having accumulated 22 years of service in Teradyne, since my time in service with Megatest and Next Test was carried over as time at Teradyne, when Teradyne purchased them. Also, Next Teradyne never hired me. I just came along basically when one company

bought the other companies. It's weird that it happened to them twice. This is from listener Ben Sack. Twin boys born four minutes apart are each citizens of different countries. How? I'm going to presume, well, I guess there's two possible reasons. One is that the mother was traveling while giving birth, like on an airplane.

Or the other is that they had different fathers, which apparently very occasionally does happen even with twins. Either of those is correct. Yes, one of those is correct. One of those is correct. Did they have different fathers? Yes. Oh. So is that why they are citizens of different countries? How did they know they had different fathers? Do I need to figure that out?

Yeah, you could try. Well, were the two fathers different races, so the children would look very different from each other? No. Would you say, was the woman like artificially inseminated or anything like that? Is there anything like that involved? Yes. There is something like that involved.

Yeah. Oh. She's a surrogate mother. Oh, and these are humans. Yeah. Oh, so they knew that the fathers were going to be different. Yes. I mean, they were expecting the fathers to be different.

Did this really happen? Yeah, it was an amazing story. Seriously? I didn't know that you would get a surrogate mother to carry twins. So is that it? I mean, that they knew that she was carrying twins from two different men? Yeah, that's basically it. This is the true story of Aiden and Ethan Dvash Banks.

Their parents are a male same-sex couple, one of whom is an American citizen and one of whom is an Israeli citizen. Oh. Oh, wow. They had their twin boys through a surrogate mother in Canada, with each father contributing genetic material to one egg. When they moved to Los Angeles shortly after the twins were born, the U.S. State Department ruled that only Aiden, who had a U.S. citizen's genetic material, was a citizen. Oh, wow. So they're twins, but only one of them is a U.S. citizen. Oh, wow. So they're twins. Oh, that makes so much more sense that the fathers were a couple. I was thinking it was just two random men who both wanted to have children. And like, for efficiency's sake, they decided to, you know, it's like, let her have a double pregnancy. And Ben adds, the story has a happy ending. So far, the State Department's decision was

overturned in court. This puzzle is based on something that I read in Dan Lewis's Now I Know e-newsletter. Jeff Bezos, the founder of Amazon.com, has said that an obscure book on lichens was a big help to Amazon in the company's early days. Why? On lichens? Yes. Okay. Is that important, that it was specifically about Likens? No.

Okay. So there was some particular title though, some book. Uh-huh. Amazon started as a bookstore. Yes. Was this in those days? Yes. When all they sold was books?

Yes. Exactly. And you said it was a particular help? It was a big help to Amazon in the company's early days. Okay. And that obviously, that has to do with how they handled this one book? No. You should never phrase a question with, well, it obviously has to do with. I'm just asking for it. It is. So had a customer ordered this book?

No. Oh, is that it? Had no one ordered this book and they were stocking it needlessly? No. In other words, they used to stock millions of books that no one ever ordered. Incorrect. All right. Not so good so far. There was a particular book that they used to sell.

They used to offer for sale. No. Oh, that they didn't offer for sale. Right. So there was a book that people might want. I've got nothing but no so far. Travesty.

All right. So there's this book that exists in the world. Yes. That some other bookstores presumably sell. Maybe. Okay. But it's out there in the world and somebody might someday want to order it through Amazon. No.

No? Probably not. Really? That's not their thinking. Is it because it's very old? No. Is it just that it's obscure and they don't expect anyone to want it? That's not the value of it to Amazon. It is obscure. They do expect nobody to

ever want it, but that's not the value of it to Amazon. Or it wasn't back in Amazon's early days. Does this have something to do with their record keeping or how they organize their inventory? No. Man. All right. So this is a, it's a book that exists that Amazon, I think you said doesn't stock and that someone might conceivably order, but they don't expect it to happen. They don't expect anybody to want this book. And yet it's important to Amazon's early days. It was a big help to them in their early days. All right. Do I need to know more? Does that, does this involve other businesses? Yes. All right.

Do I need to know more? Does this involve other businesses? Yes. Other bookstores? Yes. Okay. Was the lesson that Amazon learned, did that involve emulating how other bookstores? It wasn't a lesson that Amazon learned.

But it helped them. It did help them. The fact that this book existed helped them. All right. So we got as far as saying that other bookstores are involved. Uh-huh. Or other booksellers, let's say. I don't know if other bookstores is quite correct,

but other booksellers. All right. And those other booksellers might sell this obscure book about Likens? Incorrect. So none of them, Amazon or these other

presumably competing bookstores might ever have sold this book? Correct. Let's say that they're not other bookstores let's say they're wholesalers yeah okay so i keep thinking so nobody has possibly ever sold right right um nobody may have ever sold this book nobody involved in this puzzle may have ever, ever sold a copy of this book, actually sold it. Or expected to. Right. All right.

So in doing its business back in those days, you said Amazon, did they work with these other booksellers? Yes. Directly? Yes. Did they get books from them? Yes. To pass on to customers? Yes. Directly? Yes. Did they get books from them? Yes. To pass on to customers? Yes.

That was their business model early on. They didn't actually stock their own books. They would buy them from other wholesalers. All right. And that's important. So let's just follow this through then. If no one ever, like if this Likens book didn't exist, obviously it can't play any part in this. So I understand it's rare and obscureikens book didn't exist, obviously it can't play any part in this.

So I understand it's rare and obscure and that people aren't expected to buy it. They needed some obscure book to exist in order for their business model to work for them. And they just chose this Likens book. They just chose this obscure book. Okay, so why would you need an obscure book? That's exactly it. That's the crux. And that has something to do with ordering from...

Other wholesalers. These booksellers. Yes. Does this have something to do with stocking somehow? Like they discover that they needed to place an order? I don't know how that wouldn't make sense. Maybe finish the question. I like the first part of the question.

Well, the only part of this that I can imagine makes sense is it was useful to them because it would alert them somehow that they were out of stock and needed to place an order or something like that. Oh, no, no. No, but it does have to do with ordering, which is why I liked the first part of the question. I thought maybe you were onto something. It has to do with orders that they would place to the wholesalers.

Okay. Did they offer, maybe I asked you this already, sorry. Did Amazon offer this title? No. And you said the other booksellers? Probably didn't either. So it's not that Amazon had this on its list of books on offer or ever placed orders to these booksellers. Wait, say that again.

Say that again. Well, did... Ask that as a question. Did Amazon ever order this book from its suppliers? Yes. And that's important. But you said the suppliers themselves might not ever expect to sell it. Correct. But they stocked it.

No, they did not. All right. So Amazon was deliberately requesting from wholesalers a book that they expected the wholesalers to not stock because they're purchasing from wholesalers. And so if they placed that order and it were fulfilled, that would mean that the wholesaler had begun to stock it. No. No. But they're trying to place orders to wholesalers in their early days when they might only need one or two books at a time. Are other retailers ordering from these

wholesalers, competitors of Amazon? I don't know. Doesn't matter. Doesn't matter. So they're not learning something about their competitors in this way. They're not learning anything. They're just being able to place orders. Well, all right. So they place orders for this obscure Likens book and get the notice that it's not available, right? Right, but they wouldn't place an order just for the Likens book. Well, they'd place a whole order for whatever they needed. Yes. Which is all kinds of

titles. Well, in early days, might only be one or two at a time. All right. And they include that Likens book among the others. Yes. And I guess the wholesaler couldn't fulfill the order because it included a book they don't stock. No. They would fulfill it anyway. They would fulfill it anyway. Without that book. Yes. Because Amazon needed to place minimum orders of at least 10 books at a time from a wholesaler. And so if they needed just one or two books, they'd fill out the order with several copies of the book that they knew nobody was going to actually stock. I see. So they'd get the book they needed and an apology that the rest of the order couldn't be fulfilled, which was just what they wanted anyway. This is from a longtime young listener,

Katie Tripp. There are 30 cows, 28 chickens. How many didn't? There are 30 cows, 28 chickens. How many didn't? Okay, there are 30 cows. I'm trying to think of some other meaning. 28 chickens, not chick-ens, or I'm trying to look for some kind of a pun or play on words here. Okay.

When you say there are 30 cows, do you mean there are 30 bovine creatures? Yes. Someplace. Yes. Together. And you say there are 28 chickens. Did you say that? There are 28 chickens?

No. No, I did not say that. You did not say there are 28 chickens. No. No, I did not say that. You did not say there are 28 chickens. There are 28... Chick... I'm trying to think. Say the puzzle again, please.

There are... This is more fun than I thought it was going to be. There are 30 cows, 28 chickens. How many didn't? 20 of the cows ate chickens. So that means ten cows didn't eat a chicken. Yes. Oh, that is so cute. Katie writes, twenty cows ate chickens. Ten cows did not. It's about how you say the 8. Oh, that was really good. Thank you so much, Katie. Futility Closet is supported entirely by our awesome listeners.

If you'd like to contribute to our celebration of the quirky and the curious, please check out our Patreon page at patreon.com slash futilitycloset or see the support us section of the website slash futilitycloset or see the support us section of the website at futilitycloset.com. While you're at the site, you can also graze through Greg's collection of over 10,000 bite-sized amusements. Browse the Futility Closet store, learn about the Futility Closet books, and see the show notes for the podcast with links and references for today's puzzles. If you have any questions or comments for us or a puzzle to send, please email us at podcast at futilitycloset.com. Our music was written and performed by Greg's phenomenal brother, Doug Ross. Thanks for listening,

and we'll talk to you next week.