Mar 132013

All right, math people, help me out.

I just completed a section on probability with my daughter, and by and large she’s got it down. We both understand that if you flip a coin and roll a die, the probability of getting tails and a five is 1/12. (You multiply the odds of getting tails (1/2) by the odds of getting a five (1/6).) We made a little pie chart to show why this works and… well, I’m not going to drone on about this, but in short: Lea not only understands how to do the calculation, but she understands why. And so do I.

Similarly, we understand that the probability of rolling a two or a three on a 6-sided die is 1/3. This is even easier to grasp: The odds of rolling a two are 1/6; the odds of rolling a three are 1/6. Add ‘em up, and you get 2/6, or 1/3. No problemo — the reasons for this are pretty easy to visualize.

You add up the probabilities when the “or” events are, as the math textbook tells us in boldfaced words, mutually exclusive. You can’t roll a five and a six on a single roll of the die. (Although God knows when I ask Lea if this is possible — just so I can see that she’s with me — she’ll say something about the die rolling into a crack on the table, or bring up the idea of a time machine, or…)

It’s when two events aren’t mutually exclusive that my mind goes kabloo. The example in the book is:

The Yankees have a .4 chance of winning today’s baseball game. The Red Sox have a .6 chance of winning their baseball game. (This was obviously written by a Red Sox fan.) What is the probability that one team or the other will win, assuming they are not playing each other?

The formula for this is straightforward enough: First you add up the probabilities (.4 + .6 = 1) and from this you subtract the product of the probabilities (.4 * .6 = .24). So the odds of one team or the other winning is .76, or 76%. Easy enough — I can memorize a formula, and so can my daughter. I just don’t get why this works. We were able to visualize and fully grasp the other principles in this section, but this one is eluding us.

Is there a way of looking at this that will make me say, “Oh! Sure!”

Mar 102013

(Contains spoilers for the final puzzle of the tournament.)

Hundreds of people compete each year at the American Crossword Puzzle Tournament, and the vast majority of these people have no expectation of winning anything. A couple dozen people will win trophies, and precisely nine people will get to compete onstage in the finals — three each from the A, B, and C divisions. Everyone else will watch from the audience.

But everyone’s gotta have a goal, heading into the tournament, even if it’s as general as “improve a little” or “not fall back too much” or “try not to make any errors.” My goal tends to take the form of certain solvers around me, people I have nominated as my personal pace cars: They can be found near me in the standings (by which I mean, ahead of me). These are the people I compete with, a mini-tournament within the larger tournament, except that my rivals don’t know that I am gunning for them.

It’s a random group of friends and strangers. My friend Kevin Wald is one of them; so is the former New York Times ombudsman Dan Okrent, with whom I have exchanged maybe ten words over the years. There’s a particular woman from Connecticut on my list — I always look for her name when I’m checking the scores, like some kind of crossword stalker. Punch line: I don’t even know what this woman looks like.

But if there’s one person I’m really trying to catch, it’s my friend Amy Goldstein. To me, she represents a skill level I might realistically attain someday, but only if I perform at my very best.

Each year, it seems possible: For the first few puzzles of the tournament, I am able to keep pace with her, or at least not drag too far behind.

But then comes puzzle 5.

Puzzle 5 is traditionally the killer of the ACPT. There have been years where the timer runs down to zero and most of the solvers are still sitting there, baffled and shaken. There have been years where I cannot so much as figure out the puzzle’s theme — I’ll poke around at the grid, filling in words here and there, knowing with certainty that my place in the standings will once again plummet.

Generally you can find my name somewhere around 100th place, give or take. Last year, Amy said it plain: “If you can just beat puzzle 5,” she told me, “you’ll be thirty or forty places higher!” In other words, where she is.

Well, this year I beat puzzle 5. I KO’ed it like I never have before.

Solvers were given half an hour to solve it. Many years, I need every second and still have blank squares when I hand in my paper. (To say nothing of the squares that are filled in with wild guesses.) This year, I completed the puzzle in about fifteen minutes — perfectly. I found myself leaving the tournament room side-by-side with some really great solvers. I couldn’t believe it. This was the puzzle 5 I’d been waiting for. And I beat Amy by a solid ten minutes. Ten minutes! That is an eternity in a crossword tournament. I couldn’t wait to see the scores! I couldn’t wait to see the rankings!

When the scores for the first day were posted, it turned out I was right: I had thoroughly torn apart puzzle 5…

…and I had mistakes on not one but TWO earlier puzzles, puzzles I had thought I’d solved clean.

End result: A ranking of 97, pretty much where I am every year.

There’s one last tournament puzzle on Sunday morning, and I solved it without errors, boosting myself up to a still-unofficial 92, a dozen spots lower than last year’s 80. It’s hard to believe that I solved puzzle 5 perfectly — and, for me, blazing fast — and still managed to do worse overall than last year. One of these years I have got to get my act 100% together. I think that’s going to be next year’s goal.


For a while, it seemed as if this year’s Division A finals would be a replay of last year, and the year before that. The same three people stood at the top of the rankings. Dan Feyer was first, to no one’s surprise. Before the start of the tournament, Dan had demurred a little about his chances — David Plotkin had been outsolving him of late, he said, and Joon Pahk, too, was reporting impressive speed-solving times. That might well have been true, but something about the tournament brings out the very best in Dan. When the scores were tallied up, no one was even close to him.

In second place was five-time champ Tyler Hinman. Shortly after puzzle 7 ended on Sunday morning, I found him slouched in a chair in the lobby, looking very much like someone resigned to his fate. This would be Tyler’s third time facing Dan in the finals. Dan had trounced him every time. It was certainly possible to imagine Tyler coming out on top — anything can happen up there, as we have learned over the years, and Tyler is an extraordinary solver — but if so, the finals would surely be a heart-stopping squeaker. Dan is not one to be left in the dust. More likely, he’s the one doing the leaving.

And in third place — for the third fourth year in a row — was Anne Erdmann, a sweet, good-natured woman who, in past years, had seemed somewhat at a loss during the finals, which is played on large whiteboards at the front of a crowded, boisterous room. Solving up there is a radically different experience from solving in your seat, surrounded by people but essentially alone. Anne is astonishing at regular speed-solving, but she struggled during her previous appearances in the finals. Still, she now had plenty of experience at this, and nobody was dismissing her.

Dan, Tyler, Anne. Deja vu.

Except that it wasn’t deja vu, because when the final puzzle started, it was Tyler, and not Dan, who exploded out of the gate. Tyler had the upper right corner of the puzzle done with lightning speed, while Dan sputtered and jumped around, trying to find a place that would give him some traction. As for Anne, she had one word written in the grid, and it was wrong.

The puzzle itself was a grade-A killer. Constructor Kevin Der had laced his crossword with dangerous, easy-to-misread clues. “Challenge for one who’s lost” doesn’t refer to somebody lost in the woods, but rather somebody who has lost money — the answer is RECOUPING. “Activity involving three steps” might not lead you immediately to CHACHA.

The final crossword of the ACPT is always themeless, and themeless puzzles sometimes have a nasty little trait — you can walk your way through one corner of it practically with your eyes closed, and just as you think, “Man, I am acing this!”, that’s when you discover the rest of the puzzle isn’t nearly as easy.

With a quarter of the puzzle locked away, Tyler jumped into the rest of the grid and discovered it was made out of bricks. He had a few letters in place thanks to his earlier work, but they didn’t seem to be helping. Jittering in place, radiating comic-book lines of energy, he jumped around the grid, trying to find a new place to break in. There wasn’t any.

Meanwhile, Dan had performed a magic trick. Dan is very calm and still when he’s at the big board (certainly in comparison to Tyler), and it’s easy to let yourself be fooled: Because he is not moving fast, he must not be solving fast. But then you suddenly become aware of just how much progress he’s made. I glanced away for a moment — I swear it was just a moment — and when my eyes went back to the board, it was a whole lot closer to solved. Great swaths of white had been filled in with letters, all correct. “When did THAT happen?” asked the person next to me, also caught off guard.

That was it — Tyler’s advantage was lost, and he would not get it back. But Anne was not out of the picture: She had corrected her every mistake, and had picked up speed as she went along. And what’s this? Dan has an error in his grid?! Indeed, yes. Needing a president’s initials, Dan had gone with DDE instead of FDR. Was it possible that this might trip him up, allowing Anne to pass him? Dan stood back, trying to figure out what had gone wrong. Anne kept writing away. She had a whole corner left to fill, and then some, but she was clearly rolling. The audience began to murmur, and everyone sat forward in their seats.

But Dan spotted his minor mistake, corrected it, and broke into the final section of his grid. That was the end: Within seconds, he had claimed the championship for a stellar fourth year running.

And Anne came in second, which was a delight to see. She seemed so nervous her first year in the finals — she wasn’t able to complete the puzzle at all. The next year she was back on stage, and while this time she completed the crossword (I think), it was well after her competitors were done. This third time, she inked in her last letters while a frustrated Tyler still faced a half-blank grid. Her look of surprised delight when she took off her headphones and saw Tyler still at work is the great moment of this year’s tournament. (And on her birthday, too — the audience would serenade her as she picked up her second-place trophy.)

Of course, I felt bad for my friend Tyler — I can’t imagine it’s much fun standing in front of 500 people without the slightest idea what you’re doing. “Well, this is awkward,” he shouted as he danced his adrenaline-pumped dance and tried to figure out the rest of his puzzle. He wrote random words in the blanks: BLAST, DAMN, UGH. Finally he had a breakthrough, but too late — the clock got away from him, and at the end he had several squares blank: His first tournament errors in years.

Hearty and amazed congratulations to Dan Feyer for his fourth tournament win, to Anne for her exciting second place finish, and, yes, to Tyler as well — third place in this group is nothing to shrug at, and he handled his finals predicament with good humor. Congrats as well to my friend Jeff Schwartz, 2nd place finisher in the B division. He used to be one of my pace-car solvers, but he’s gotten too damn good. Luckily, there are lots of other solvers I can shoot for — and will, next year.

Mar 082013

The Maze of Games is a Kickstarter project from puzzlemaker Mike Selinker — he is promising a puzzle-filled update on a “Choose Your Adventure” story, and so appealing is this notion that he’s raised well over $100,000. (His target had been $16K.)

People who buy the book will also get a complementary “Conundrucopia,” a whole bunch of puzzles from a wide variety of constructors. The more money raised by the project, the more puzzles in the Conundrucopia. I’m the next puzzle constructor on the list: I’ll be added to the project when it hits $140K. I am not yet “unlocked,” and so for now I remain in the Puzzle Cage (which I am sharing with game designer Richard Garfield, which is pretty impressive). So if you want a really cool-looking puzzle adventure book, AND you want a puzzle from me in the Conundrucopia, AND you somehow haven’t already heard about this, go take a look and maybe back the project.

Mar 062013

When you’re having doubts and apprehensions about the path that you’re on, there’s nothing like an inspirational TEDx talk from an eloquent, homeschooled, 13-year-old kid to turn those doubts into outright panic.

It doesn’t feel to me like homeschool is going particularly well these days. It’s just… school, moved into our living room. Lea reads historical fiction with her mom; she does vocabulary and science lessons via software; I go home at lunchtime and we work on math. We used to work on the computer programming language Scratch as well, but that has faded away — I don’t really know what projects to suggest to her and she is not terribly interested in continuing it on her own. I give her writing assignments — book reports, short stories, etc.

There’s little about this that Lea actually enjoys. She does what she needs to do largely because if she does it without complaint, she’ll get to play videogames for a while as a reward. Then it’s back to work.

Too often, our math lessons end in tears. That’s not really how it’s supposed to be.

Logan LaPlante, the kid in the above video, seems to have an idealized homeschool life. He and his parents clearly have a ton of resources to draw upon, both financial and social. My guess is that he didn’t just build a giant Newton’s Cradle in his garage — that this project took place within a homeschool co-op or a similar group environment. We belong to a homeschool co-op, too. It’s a disorganized mess. It’s small, tends toward younger kids, and has a low level of participation by the adults, in terms of organizing classes or even hanging around for a few extra minutes to clean up at the end of the day. We stick with it mainly for social reasons… but with so few kids in the group close to Lea’s age, it’s not even performing this function very well. There are other, better homeschool co-ops in Connecticut, but they are much further away.

My big takeaway from Logan’s talk is that he is not only learning, he is inspired to learn, which is the far greater success. He enjoys it, and thus he is willing to put in the work. (He doesn’t seem to think of it as work at all.) Lea has learned a lot, but she tolerates homeschool the way I remember tolerating school. It’s something she does because she has to.

There are elements she finds inspirational — not many, but they are there. She has taken to 3D design like a duck to water, creating dozens of objects and inventions in TinkerCAD. Similarly, I was content to let her spend hours designing her own game levels using the Portal 2 editor. She has stuff she does away from the home — rock climbing, and pottery, and tennis.

When we discuss the path of homeschooling with her, she says she wants to spend more time on science. Combined with her occasional assertion that she would like to stop homeschooling altogether, we went to look at a nearby magnet school that focuses on science and engineering. It seemed like a slam dunk, if we could get in (there’s a lottery and a long waiting list). She came away from the school’s open house in tears. She thought it would be too hard and doesn’t want to go.

Therefore, it must be up to us to push forward on science. I confess that I don’t know how to do this. It’s easy to teach Lea math: Just open up the book to the next chapter and start reading the examples. I fear that this is the real reason why I teach her math — not because kids should know math (though of course they should) but because it’s a subject where I know what I’m doing.

We’ve edged into science now and again over the past couple of years, but our approach has been hesitant and toe-in-the-water. Science is hands-on, science is all over the place. Science requires a base of knowledge from the teacher, a base that neither my wife nor I have. Furthermore, I am not sure about my daughter’s sincerity when she mentions “science.” I’m afraid that “science” to her begins and ends with reading fun facts about animals. When I ask her to write a few paragraphs about what she’s learned, she sags as if I just dropped a fifty-pound weight on her shoulders.

Logan’s video prompts a lot of questions. We see him at a Starbucks, typing merrily away a laptop with a book open next to him, working on a report or something. Is he doing that entirely on his own? Did no one steer him in that direction? Who will read his output, and will that person correct any run-on sentences and misunderstandings of grammar? Do they make him do a rewrite? Have they finagled things so that Logan wants to do a rewrite, and if so, how the hell did they manage that?

Just how “hacked” is his education?

We are tempted to give Lea the keys to the bus for a couple of months, just to see what happens. She’s years ahead in math, she has an advanced vocabulary, and she writes reasonably well — it would be no tragedy to stop what we’re doing and see what Lea does with her time. If she wants to read about animals, she can read about animals. If she wants to do science experiments, we can help her get the stuff she needs to do them. If she wants to play video games and read Calvin & Hobbes… well, I have to take it on faith that she is a smart, engaged kid, and won’t want to do that forever. But will that approach swing things around so that she is happier to explore and learn, and happier in general? I have absolutely no idea.

Sometimes it seems like we have less idea what we are doing now than we did when we first started homeschooling. That is not usually the way things work.

And that is the state of our homeschooling. Are we not an inspiration to you all? No? Then go watch that kid’s TEDx talk again. I plan to.

Jan 282013

Each answer refers to a form of divination, consisting of a prefix and the letters “-omancy.” (See the first three words of the flavortext for a little clue regarding this.) Each prefix can be found hidden in one of the Magic 8-Ball fortunes. Matching the fortunes to the answers and then indexing by puzzle number reveals the letters YOU CAN DO IT.

I’ve filled in the remaining answers; the original given answers are shown in bold.




Jan 252013

Every single practice meta I’ve created, for three years now, has been a “pure” meta — a list of words and nothing more. I really wanted to come up with a decent “shell” meta, which requires the solver to use other information as well as the list of words.

This time, I’ve decided not to give you all of the answer words. Let’s pretend you’re a little more than halfway through the puzzles, and you’ve decided to see if you can nonetheless crack the metapuzzle. Can you do it? Send your answer to

Magic 8-Ball

Oh, man! See, I got the idea of asking the Magic 8-Ball if we’re going to find the coin this year. The answers I got back were very strange. You can see them on this page. Maybe these puzzles will help me figure out what the 8-Ball is trying to say…


Solved by: Jeffrey Harris, Todd McClary, Mark Halpin, Michael Sylvia.

Jan 252013

The answers can be divided into two groups such that a word in Group 1 clues a word in Group 2… but only after two letters are removed from the second word. These bigrams can be reorganized to spell the phrase TWO ASPIRIN.


A couple of people asked if there was a logical, puzzly way to order the words so that the answer spelled itself out. No. I figured once you had the initial aha, you wouldn’t be thwarted by the need to rearrange five pairs of letters.

Jan 242013

Here’s another of the practice metas I presented to my MIT Hunt team in the weeks leading up to the hunt. As before, please do not reveal the answer in the comments — you can e-mail me ( and I’ll post the names of the people who get it right.


You and your team are rushing to cure a virus that is sweeping the world. And now a new disaster has struck: The data from your two control groups has gotten all mixed up! One group was given a miracle drug, the other a placebo. Can you figure out who belongs to each group, and then determine the cure for this terrible virus?

Subject 1: ATTEMPTS
Subject 2: BARBECUE
Subject 3: CONFRONT
Subject 4: FAVORING
Subject 5: FIANCE
Subject 6: GORILLA
Subject 7: LUNA
Subject 8: MOTOWN
Subject 9: PRIOR
Subject 10: STRIPES

Solved by: Jeffrey Harris, Todd McClary, Robert Hutchinson, Guy Jacobson, Todd Etter, Dan Katz, Trip Payne, Mark Halpin, Mike Sylvia.

Jan 242013

Many solvers picked up on the phrase “just your type” in the flavortext and took a look at their keyboards. Sure enough, the letters of each answer are contiguous on a standard keyboard… with the exception of a single outlier in each answer. These letters spell the word ISOLATION.


Jan 232013

In advance of this year’s Mystery Hunt, several of us on Palindrome created “practice metas” for our teammates to solve. I created three of them, and I’ll be posting these here over the next few days. is the only dating service exclusively for people who like puzzles! Examine the words below to see what this particular applicant appreciates more than anything. Maybe this person is just your type!


…hmm, maybe not.

No spoilers in the comments, please. If you know the answer, e-mail me (my full name, all one word @ I’ll add names to the solver list as they come in, and I’ll post the answer tomorrow.

Solved by: Jeffrey Harris, Mark Halpin, Todd McClary, Andy Arizpe, Scott Purdy, Trip Payne, Dorian Hart, Guy Jacobson, Doug Orleans, Chris Shabsin, Jaci Conrad and Albert Lin, Noah Snyder and Malia Jackson, Josh Mandel, Mike Greenberg.