This is my favorite brain teaser/logic puzzle, by far. I learned it in my high school math class one morning and spent the rest of the day figuring it out. It comes in two parts.
1) The Heavier Coin
You have a balance and twelve coins, one of which is heavier than the rest, but you don’t know which one it is. Using just 3 weighings on the balance, can you identify which coin is the odd one out?
Okay, you’re probably wondering why that’s so hard, right? It’s a pretty simple puzzle. (I’ll not ruin it in case you haven’t figured it out, though.)
Let’s make it harder by making one very simple change — instead of me telling you that the odd coin is heavier than the other 11, I’m going to make it simply “different.” It could be lighter. It could be heavier. Who knows? Everything else stay the same. Here’s the new question:
2) The Different Coin
You have a balance and twelve coins, one of which weighs a different amount than the rest, but you don’t know which one it is — and you don’t know if the different coin is heavier or lighter than the rest. Using just 3 weighings on the balance, can you identify which coin is the odd one out — and whether it’s heavier and lighter than the others?
That’s a small change but it makes the puzzle much harder. Give it a try, you’ll see.
(If you want the solution, click here.)Originally published on December 30, 2014
One of the habits we try and encourage in my house is reading, and we believe it’s important to instill a love of books at a young age. We’ve been through a lot of books over the last almost-decade and we therefore have some built-in expertise on the subject. I now have three experts on children’s books at the ready to help anyone who wants to know what books make for good presents, so I decided to try a little experiment: Zagat-style reviews of books for young children. (I’m defining “young children” as ages 0-8.)
If you’ve never flipped though a Zagat, what the editors do is pretty simple and effective. They survey a bunch of diners, read through the responses, and then select quotes which summarize the overall take by the diners in aggregate. I’m doing the same thing, below, except that my survey has only three participants, all between the ages of three and ten. (The one over the age of 8 asked that I put this line here, objecting to the characterization that he is a “young child.” So noted.) also happen to live with me, making this rather convenient.
A disclaimer: The opinions stated below aren’t necessarily that of my employer or anyone else I’ve ever known. In fact, they’re not even my opinions, really; I’ve tried to stay as true as possible to the kids’ opinions, even in selecting the books.
All age ranges are via Amazon, if provided; all links are Amazon affiliate links.
Llama Llama Red Pajama (Ages 3-5):
“I have that book!” one reviewer excitedly exclaimed. “Yes!” “It tells kids that pajamas are good clothes” and “to go to bed.” And of course, “don’t scream when it gets dark at night but you’re still awake.” The children advise that this is a good book if your children need to be told to go to sleep when they wake up in the middle of the night.
Dinosaur Versus Bedtime (Ages 2-5):
The children think this book is very funny because “the dinosaur keeps on winning and winning and winning” but in the end, he loses. One kid thinks that the book has a good lesson — you don’t always win — but the other two think that this book doesn’t have a lesson at all. “I met the author in Kindergarten,” beamed one child, who recommends the entire “Dinosaur vs.” series.
“This is one of my favorites!” even though it starts off sad — the girl “loses her monkey balloon!” The girl keeps looking and looking for her monkey balloon “but could not find it” until the end. “Then they find it,” one kid notes, but asked the person typing to not ruin the ending, “because that’s not fun.”
The Day the Crayons Quit (Ages 3-7):
“Everybody should like this” says the oldest of the three but the youngest disagrees — “I don’t like that book!” The oldest warns “don’t read the peach page” because “it makes you want to do this” (he says while wiggling his midsection). The middle guy explains: “the peach page is funny — it’s really funny! — because it says ‘I’m naked’ and the crayons asks ‘would you like to go to school without underwear?'” The only adult in the room adds that the quotes from the book may not be entirely accurate, but they correctly capture the plight of the peach crayon.
Press Here (Ages 2 and up):
It’s a “good book” because “on the page it tells you do something” and when you turn the page, “things happen and it always makes sense.” The book is like an iPhone app but on on paper (except that you have to turn the page). “The end is the same as the beginning!” says one child with gusto. The youngest of the three asks that we stop reviewing books right now because “I want to read this book right now” but the oldest would rather get a snack. “A banana, please,” he asks.
The Very Hungry Caterpillar (Ages 1-6):
“The caterpillar book!” screams the youngest one when asked what book should come next. “I love that book! It’s one of my favorites in the whole world!” She likes that “the caterpillar eats a lot of food” and “gets a tummy ache” and “gets big big big big big.” She explains that he flies away at the end. The oldest one says “that’s called metamorphosis” but she objects — “no! it’s called a butterfly.” The middle child laughed at the misunderstanding.
Interrupting Chicken (Ages 4-8):
This book “teaches you not to interrupt” one child says as another, of course, interrupts over and over again. “Just like the chicken” the reviewer notes. It’s “really funny” and the defining theme of the book is that chicken “always interrupts” suggesting that the book lacks the depth of some other choices. Nevertheless, it involves chicken and is evocative of a massively-underrated joke, both of which are pluses.
Chicka Chicka Boom Boom (Ages 1-4):
The oldest didn’t want to discuss the book — “it’s not for kids my age.” The middle agrees: “I don’t want to talk about this.” The youngest likes that “all the letters drop on the floor” even if “some get boo boos.” The father reminds the other two that they really liked this book until they were, rightfully in their opinions, too old for it.
The Book with No Pictures (Ages 5-8):
A huge hit and all three agree for the main reason: it makes the grown-up say “Boo Boo Butt.” One objection, from the youngest: “I don’t like how it says eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee.” None of the three care that the book has no pictures, but all believe that the book wouldn’t be fun to read — you really need the grown-ups to do the reading so you can laugh at them.
The Monster at the End of This Book (Ages 3-7):
“Grover is really silly” laughed one child who then began giggling uncontrollably, unable to add further commentary. Another took over: “Grover really tries hard to stop you from turning the pages and even builds a wall” but “it’s easy to break the wall, you just turn the page!” The popular opinion: the book is more fun of the reader tries to read in Grover’s voice, but that is, graciously, not required for enjoyment.
One Fish Two Fish Red Fish Blue Fish (Ages 3-7):
The book for everyone: varied enough where you’re bound to have a favorite part, but never quite disinteresting. Selected highlights include “when the girl brushes the pet’s hair,” “the guy with eleven fingers,” “the animals that need haircuts every day,” and “the mouse that cut the phone wire” (he’s “pretty funny,” one smiled). No one likes the man with the old hat and gold teeth though — he was “weird” and kind of “scary.”
Green Eggs and Ham (Ages 3-7):
A “silly” way to teach kids “to try new foods,” says one child, charitably. It’s a “rhyming book” like “most Dr. Seuss books,” some select examples — from memory — are “ham and Sam,” “house and mouse,” “with a fox’ and ‘in a box’,” and “train and rain.” To underscore how memorable the book is, when asked where Sam will not try green eggs and ham, all three, in chorus, acclaim (correctly), “anywhere!”
Pete the Cat and his Four Groovy Buttons (Ages 4-8):
Pete keeps losing his buttons but he always says “that’s OK.” He still doesn’t cry when he is out of buttons because he “lifts up his shirt” and “still has a belly button!” One child wondered why Pete can’t grab the first button as it flew off his coat, but then remembered that “it’s because he can’t grip it” because cat’s don’t have opposable thumbs. (He needed reminding about the word “opposable.”)Originally published on December 13, 2014
This is mostly for my future use. A note to my future self, if you will.
— Now I Know (@NowIKnow) September 3, 2014
Dr. Awkward is a palindrome.
— Now I Know (@NowIKnow) September 5, 2014
There are exactly 11 characters which are common to the Russian, Latin, and Greek alphabets. pic.twitter.com/8BawWbTwzR
— Now I Know (@NowIKnow) September 3, 2014
Originally published on September 6, 2014
This is what happens if you cut a grape almost in half, put a glass over it, and microwave it. http://t.co/uoCe9Cj9KG
— Now I Know (@NowIKnow) September 3, 2014
Now I Know takes me dozens of hours each month to write and put together. If you appreciate the content, please consider making a recurring or one-time gift in support of the project. And thanks to all of you who already have!
Here are some questions I’ve gotten about this so far.
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There are two ways:
(1) Become a Supporting Member: You can make a monthly ($5/mo) or annual ($60/yr) gift. Click either link and you’ll be taken to Tugboat Yards’ website — they’re powering the program. Then hit the “Pay Now” button on that page. These auto-renew unless you cancel them, and if you chose this option, you’ll also receive a bonus weekly email called the “member letter,” as a token of my gratitude. That will happen automatically, but make sure you enter your email address on that page so Tugboat Yards can subscribe you to the “member letter” list.
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* Wait, what’s this bonus email thing again?
Every week, on Wednesdays at 3 PM-ish, I send out an email like this one to all Supporting Members. It’s a collection of interesting things I’ve come across lately but doesn’t really make sense for Now I Know itself.
Any other questions, email me and I’ll answer them, or check back here to see if the answer pops up. Thanks!
Originally published on January 29, 2014
So this is a pretty big deal:
For the next week or two, you can download the ebook for three bucks. Even if you don’t own a Kindle, you can still get it — there are Kindle apps for just about every device. Oh, and if you’re interested in sending a temporarily $3 copy to someone as a gift, here’s how.Originally published on December 9, 2013
What would happen if you gave a homeless person a pre-paid debit card? That’s what a writer for the Toronto Star explored in 2010. Related: NPR has a story about a charity which gives money to impoverished people in developing countries, with no strings attached. The results are similar.
* * *
If you’re not following CGP Grey’s videos on YouTube, you should be. He creates great, incredibly informative videos on topics you’d not think to explore. I asked him which one was his favorite, and he said it was this one, below, explaining the difference between Holland and the Netherlands. If you’re a long-time Now I Know reader, you may have seen this before, as I mention it in the bonus fact of this issue of the newsletter.
While we’re on the topic of CGP Grey, you should probably follow him on Twitter, as he makes other interesting observations such as this one. And if you’re a redditor, he has a subreddit which he’s active on, here.
* * *
Two long-ish quotes about the education system: I found both of the mind-boggling, and am passing them along without further comment:
Anne Ruggles Gere, a professor at the University of Michigan, serves as director of the Sweetland Center for Writing, which oversees first-year writing at the university. She speaks with SAT essay-graders often. “What they tell me is that they go through a very regimented scoring process, and the goal of that process is to produce so many units of work in a very short period of time,” she says. “So if they take more than about three minutes to read and score these essays, they are eliminated from the job of scoring.” According to Perelman, especially speedy graders are rewarded for their efforts. “They expect readers to read a minimum of 20 essays an hour,” he says. “But readers get a bonus if they read 30 essays an hour, which is two minutes per essay.”
Back in California, when I raised the issue of too much homework on that e?mail chain, about half the parents were pleased that someone had brought this up, and many had already spoken to the math teacher about it. Others were eager to approach school officials. But at least one parent didn’t agree, and forwarded the whole exchange to the teacher in question.
As the person who instigated the conversation, I was called in to the vice principal’s office and accused of cyberbullying. I suggested that parents’ meeting to discuss their children’s education was generally a positive thing; we merely chose to have our meeting in cyberspace instead of the school cafeteria.
He disagreed, saying the teacher felt threatened. And he added that students weren’t allowed to cyberbully, so parents should be held to the same standard.
I explained that we never intended for the teacher to read those notes. This was a forum where we were airing our concerns.
What was frustrating me was that the underlying issue of ridiculous amounts of busywork was getting buried beneath the supposed method we had used to discuss the issue.
* * *
- I’ve wasted way too much time playing this game. Now, you will too.
- LEGO Riddles.
- An incredible gallery of photos from around the world, showing what a weeks’ worth of groceries look like. It’s really interesting to compare some, like Italy versus Egypt.
- I wrote for free about writing for free on Medium. That took a while, which is probably why I didn’t write all that much above.
- The Spanish equivalent of “eye candy” is “tacos de ojo,” or “eye tacos.” But if you followed me on Twitter, you’d know that already.
- What happens when you pour liquid nitrogen on a giant knock-off Koosh ball? This. (Confession: When I first saw this link, I got really excited because I have a giant knock-off Koosh ball… and then I realized that wait, the liquid nitrogen is the hard-to-get part of the recipe.)
I’m trying something new here. It’s going to be a running list of stuff that I’ve thinking about but am not otherwise writing about (which is to say, isn’t likely going to be a Now I Know). I’m loosely following a format I used a decade (wow!) ago when I got my start as an erstwhile sportswriter, but I’m not sure how it’s going to totally play out yet. Suffice it to say that this is actually a long time coming — I’ve been thinking about this for a long, long time but haven’t been able to figure out the details, so I’m just going to figure it out as I go along. If you’d like to reply to anything below, or about this idea generally, please let me know. I’d prefer if you sent me a tweet (it’s easiest for me) but email is a good-enough second choice.
Anyway, let’s get on with the show.
* * *
Shel Silverstein was an author and cartoonist some of the world’s greatest children’s books — Where the Sidewalk Ends, A Light in the Attic, and a bunch of other stuff. But he also wrote a lot of non-children’s work, including cartoons for Playboy. He’s an interesting person, but he’ll never write an autobiography — he can’t, because he died in 1999.
But Joseph Thomas, a professor at San Diego State University, wants to write the definitive Shel Silverstein biography. He’s been studying the poet/cartoonists work for years and when you read this article on Slate, you’ll likely find Silverstein as fascinating as Thomas does. Unfortunately, you’ll also learn that Thomas won’t likely be able to publish the biography — because of a really strange unintended consequence of how American copyright law plays out.
Thomas wants to quote Silverstein’s works in his book, which is a mix between “obvious” and “necessary,” given what the former is writing. And legally, he should be able to. I was once a lawyer — that’s my I-can’t-still-give-legal-opinions legal opinion on the matter. It’s most likely fair use, which is described here.
The problem? First, fair use gets argued in front of a judge, and therefore, is an expensive thing to assert — you have to hire lawyers and all that stuff. Second, the fair use analysis is a fickle beast, and there’s always a non-zero chance you’re going to lose — so it can be VERY expensive. And while the universe would probably be better off if Mr. Thomas gets to publish his biography of Mr. Silverstein, well, let’s face it, there’s not a lot of money in it for anyone. The publisher can’t afford to take the risk of having to pay off a bunch of legal bills (if not worse).
Typically, an author and/or publisher will get permission from the rights holder — in this case, Silverstein’s estate — and avoid the legal ambiguities above. But Silverstein’s estate refused to grant these rights. I don’t think there’s anything nefarious going on here, by the way; Silverstein apparently was a big believer in the medium being a large part of the message, and taking his poems and cartoons out of the mediums in which they were published would, in his mind (assuming he were still alive), change them dramatically. So his estate is simply carrying out that wish. Regardless, Thomas therefore can’t find a publisher who will take his work and turn it into a book. Self-publishing isn’t an option for the same reason.
This is a ridiculous outcome, and a serious flaw in American copyright jurisprudence. Fundamentally, the fair use doctrine exists to make sure that copyright doesn’t trump the First Amendment, and to protect discourse and the marketplace of ideas generally. Being able to survive a lawsuit, financially speaking, shouldn’t be a prerequisite.
* * *
In the U.S., we tend to rate non-profits based on how much of their annual budget goes toward the problem they’re aimed at solving. The video above is 19 minutes long and will have you thinking for at least five times that. Dan Pallotta, the speaker (here’s his Wikipedia entry) makes a few really interesting points arguing that (a) that’s the wrong way to measure what we’re after and (b) other factors limit our ability to solve the large scale problems out there. Worth watching the whole thing.
* * *
Quick hits: This is a ship-shipping ship, shipping shipping ships. … One of the early Now I Know articles I wrote was about how the Earth has a finite amount of helium, and how it’s incredibly underpriced given the scarcity. According to a recent Washington Post article, that’s actually being addressed. … Mental Floss interviews the generally reclusive, incredibly interesting Bill Watterson. If the name isn’t immediately recognizable, he’s the cartoonist who brought Calvin and Hobbes to the world. The interview is a HUGE win for Mental Floss, who has no idea why Watterson picked them. … If you’re a baseball fan, this guy’s attempt to go 9 innings with Mariano Rivera in MLB 13 The Show is a great story. If you don’t know what that means, oh well. … The Dutch have created an “eco-friendly bicycle bus” to transport school children.Originally published on October 22, 2013
Tomorrow, officially, my book comes out. If you haven’t ordered it already, you can online at Amazon, Barnes and Noble, or Powell’s, and it should be on shelves at B&N as well as a bunch of independent bookstores, too.
A lot of you have been asking questions about the book, how you can help, etc. So, here are some answers!
1) Want to help spread the word? Please consider posting about the book on your social media accounts, particularly Facebook and Twitter, and anywhere else you think is appropriate. If you’ve bought the book, please also leave a review on Amazon, here. (If you haven’t, please don’t do that, because Amazon doesn’t take kindly to false reviews, apparently.)
2) If you’d like to make a bulk order — 10 or more books, for gifts, events, corporate giveaways, or whatever — please email me, and I’ll connect you up with the publisher.
3) Not convinced yet? My friends at Smithsonian Magazine have run an excerpt, here. It’s one of the fifty stories which aren’t from the email newsletter you’re already subscribed to, and you’ll see the format and voice are very similar to the email.
Thanks for reading and for your continued support. I’ll be in your inboxes again tomorrow with Friday’s edition of Now I Know.Originally published on October 17, 2013
I was on the 5:46 train from Manhattan to Westchester yesterday. The first stop was White Plains and almost everyone gone off. A lot of people were standing, including me. Two of the other guys standing were 20-somethings who, given my eavesdropping, seemed to have entry-level-ish sales jobs. Somehow or another, they started talking about population density, wondering aloud which state had the lowest. We were underground, so it was going to be a few minutes before one of the could fire up an iPhone web browser and Google their way to a Wikipedia entry. Instead of just accessing the answer within a minute or two, they swapped speculation.
* * *
Earlier in the day, I read this article about the incredibly large amount of homework that middle schoolers get. It’s a great read, so click the link and take a moment to peruse it at least, or bookmark it for later or something. For now, though, focus on this part:
Another exercise required Esmee [the author’s daughter, then in sixth grade] to find the distance from Sacramento—we were living in California—to every other state capital in America, in miles and kilometers. This last one caused me to question the value of the homework.
What possible purpose could this serve?, I asked her teacher in a meeting.
She explained that this sort of cross-disciplinary learning—state capitals in a math class—was now popular. She added that by now, Esmee should know all her state capitals. She went on to say that in class, when the students had been asked to name the capital of Texas, Esmee answered Texas City.
But this is a math class, I said. I don’t even know the state capitals.
I don’t agree with the author here, generally. I don’t see an issue with cross-disciplinary learning and actually see it as a net positive good idea, although that’s definitely a lay opinion. (In fact, everything here is a lay opinion — I’m just a guy with a good head on my shoulders, and not an expert on education at any level.) If you’re going to learn how to measure distance in math class, which makes sense to me, it further makes sense that you’d be better off doing so with some sort of practical application attached. Now, state capitals is an odd choice, because there’s little practical application in knowing how far Sacramento is to Jefferson City, Missouri. The odds of that having any relevance in your life, especially as a 12-year-old, is roughly zero, so it probably doesn’t aid you in learning about the math. And it also doesn’t tell you anything important about the world at large.
In short, why does Esmee have to know her state capitals?
* * *
That was the first state that popped into my head. Very small population — the smallest among the states — and relatively large in land area. That’s a great recipe if you want a low population density. And then I remembered Alaska.
The maps screw with our sense of things, I think. Alaska isn’t to scale in most any map you’ll see, for a variety of reasons. But it’s huge. It’s bigger than Texas. It’s bigger than California. It’s bigger than Montana. Sure. But did you know that it’s bigger than all three of those states — combined? Alaska is huge.
If you know that, even if it’s just a glib memory of that fact, Alaska is clearly the right answer — once you remember that Alaska is a state, which make take a moment. But that’s not what happened on the train. The two sales guys were talking, and one said “Alaska” and the other said “one of the Dakotas.” That’s not a terrible guess — the Dakotas rank 46th (South) and 47th (North) in population density. But they have an average population density of about 10 people per square mile, compared to about 1.25 people per square mile in Alaska. That’s an 8:1 ratio. West Virginia has a population density of approximately 77 people per square mile, which is (very roughly) a 7:1 ratio compared to the Dakotas. West Virginia is the 29th most populous state in the Union. The ordinal gap between the Dakotas and Alaska is incredibly misleading. Alaska is the least dense state in the U.S., and it isn’t close. At all.
* * *
The train was more crowded than usual but it wasn’t a big deal. The trip was about 45 minutes and while standing isn’t fun, it’s doable, even if you have to do it every day. (I typically get a seat, though.) By my count, there were about 125 people on my train car. There were eight cars. Less than ten minutes behind us, there was another train — the 5:51 — which I almost had to take because I barely made the one I was on. It was likely packed as well. That’s sixteen cars, each of about 125 people, all going to the same place at the same time and not really thinking much about it. Commuting is just part of the daily routine.
* * *
The population of Alaska isn’t evenly distributed. Of the 730,000 or so who live there, nearly 300,000 live in Anchorage. Fairbanks is second with about 31,500 and Juneau is third with 31,200 or so. Juneau is the capital. It is 2,464 miles (3,965 km) from Sacramento.
Juneau is tiny. My home state of Connecticut has 30 different municipalities with a large population. Juneau is roughly the size of Newington, Connecticut, which has about 30,500 residents. Newington is roughly 3,000 miles (4,828 km) from Sacramento. The number of people who care about that is roughly zero, because it’s wholly unimportant. The distance from Sacramento to Juneau is only marginally more important.
That’s because the mere fact that Juneau is Alaska’s capital tells you nothing about Alaska’s culture, demographics, or anything else. There’s a certain arbitrariness here — Anchorage has 40% of the state’s population and is ten times the size of Juneau. Would making Newington the capital of Connecticut make it important? Hardly.
The distance from Sacramento to Juneau is roughly (very roughly) the same as the distance from Sacramento the similarly town of Newington. That tells us nothing. We’re teaching the unimportant stuff and making it seem important.
* * *
After figuring out that Alaska was the least densely populated state, the two guys started wondering what the most densely populated state was. One said (with conviction) New Jersey, which is the correct answer, at 1, 205 people per square mile. The other guessed Rhode Island, which at 1,016 people per square mile, is second. It’s a solid guess, especially when you see that the drop-off to #3 (Massachusetts, 852 people per square mile) is rather large.
Rhode Island is slightly over a million people, which puts it 43rd in population among the states. It’s the smallest state by area, at about 1,200 square miles, which is why its population density ranks so high. No surprises there.
* * *
So let’s do some math. Just like Esmee had to. But instead of learning distances, let’s do some division and multiplication and fractions and that stuff.
- The population density of Alaska is 1.25 people per square mile.
- There are about 125 people on my train car.
- There are eight cars on my train, and I had my choice of two equally-crowded trains. So that’s 16 train cars.
Those last two bullets are my (basically) everyday life. It’s part of my culture and the culture of the entire Westchester area — even those who don’t commute. And if those of us on the train — not our families, neighbors, or friends, but just those of us commuting — had to spread out to match the population density of Alaska, we’d need 1,600 square miles. (Really, the math is easy.)
Rhode Island is only 1,200 square miles. We’d need one and one-third Rhode Islands, just for those of us who commute home from New York City to the White Plains area between 5:46 and 5:51 each afternoon. It’s pretty clear, from this, that Alaska is very, very different than the New York City suburbs I now live in. And to get there, I had to learn math. And when I did it, the math had meaning.
Shouldn’t this be how we teach?Originally published on September 27, 2013
I sent the below to my Now I Know subscribers today.
As promised, I have big news to share today. The subject line of this email probably gave it away. Available for pre-order, today, is Now I Know: The Book. Here’s the cover:
It’s about 250 pages long and contains 100 stories, just like the ones you’d expect in the newsletter — bonus facts and all. Fifty of the entries are brand new, and there are about 53 or so never-before-seen bonus facts — I kind of lost count along the way. Regardless, it’s more of what you’re used to, bound together on paper with a side order of ink.
Thanks for reading and for your continued support. I’ll be in your inboxes again tomorrow with another Now I Know.
DanOriginally published on August 1, 2013