The Diabolical Long Division Brain Teaser!

From time to time, I’ll receive an email with a brain teaser I’ve never seen before. Sometimes they come from friends, or fellow puzzlers. Other times, PuzzleNationers will ask for my assistance in solving a puzzle that has flummoxed them.

That was the case with today’s puzzle, and I’ll admit, this one was a bit of a doozy to unravel.

Yup, an entire long division problem with only a single digit set. No letters or encryption to let us know which digits were repeated, as there are in Word Math puzzles published by our friends at Penny Dell Puzzles.

Just a 7 and a bunch of asterisks. “Is this doable?” the sender asked.

Yes, this is entirely doable, friend. Let’s break it down step by step.

First, we need to know our terminology. The 8-digit number being divided is our dividend. The 3-digit number we’re dividing into it is the divisor. The 5-digit number on top is our quotient.

For the other lines, let’s label them A through G for ease of reference later.

There we go. Now, where do we go from here? We start with what we know.

We know that 7 is the second digit in our quotient.

So our divisor, times 7, equals the number on line C. That’s a 3-digit number, which means the first number in our divisor is 1. Why? Because if it was 2, 2 times 7 would give us 14, which would be a 4-digit number on that line.

That means the quotient is somewhere between 100 and 142. (Why 142? Easy. I divided 1000 by 7, and 142 is the last 3-digit number you can multiply 7 against and still end up with a 3-digit answer for line C. 143 times 7 is 1001, which is too high.)

What else do we know from the puzzle as it stands?

Well, look at lines E and F. We bring both of the last two digits in the dividend down for the final part of the equation. What does that mean?

Remember how long division works. You multiply the divisor by whatever number gets you closest to the given digits of the dividend, subtract the remainder, bring down the next digit from the dividend, and do it all over again until you get your answer.

You multiply the first digit of the quotient times the divisor to get the number on line A. You multiply 7 times the divisor to get the number on line C. You multiply the third digit of the quotient times the divisor to get the number on line E.

Following this route, you would multiply the fourth digit of the quotient against the divisor to get the number on line G. But bringing just one digit down didn’t give us a number high enough to be divided into. Instead of needing more lines (H and I, in this case), we bring the last digit of the dividend down and press onward.

That means the fourth digit of the quotient is 0, because the divisor went into the dividend zero times at that point.

And there’s more we can glean just from the asterisks and what we already know. We know that every one of those 4-digit numbers in the equation begin with the number 1.

How do we know that? Easy. That first number in the divisor. With a 1 there, even if the divisor is 199 and we multiply it times 9, the highest possible answer for any of those 4-digit numbers is 1791.

So let’s fill those numbers in as well:

Now look at lines D, E, and F. There’s nothing below the 1 on line D. The only way that can happen is if the second digit in line D is smaller than the first digit on line E. And on line F, you can see that those first two columns in lines D and E equal zero, since there’s nothing on line F until we hit that third column of digits.

That means the second digit on line D is either a 0 or a 1, and the first digit on line E is a 9. It’s the only way to end up with a blank space there on line F.

I realize there are a lot of asterisks left, but we’re actually very close to knowing our entire quotient by now.

Look at what we know. 7 times the divisor gives us a 3-digit answer on line C. We don’t yet know if that’s the same 3-digit answer on line E, but since it’s being divided into a 4-digit number on line E and only a 3-digit number on line C, that means the third digit in our quotient is either equal to or greater than 7. So, it’s 7 or 8.

Why not 9? Because of the 4-digit answers on lines A and G. Those would have to be higher than the multiplier for lines C and E because they result in 4-digit answers, not 3. So the digit in the first and fifth places in the quotient are higher than the digit in the third. So, if the third digit in the quotient is 7 or 8, the first and fifth are either 8 or 9.

So how do we know whether 7 or 8 is the third digit in the quotient?

Well, if it’s 7, then lines C and E would have the same 3-digit answer, both beginning with 9. But line C cannot have an answer beginning with 9, because line B is also 3 digits. The highest value the first digit in line B could have is 9, and 9 minus 9 is zero. But the number on line D begins with 1, ruling out the idea that the numbers on lines C and E are the same.

That makes the third digit in the quotient 8, and the first and fifth digits in the quotient 9.

We know our quotient now, 97809. What about our divisor?

Well, remember before when we narrowed it down to somewhere between 100 and 142? That’s going to come in handy now.

On line F, we know those first two digits are going to be 141 or below, because whatever our divisor is, it was larger than those three digits. That’s how we ended up with a 0 in our quotient.

So, the number on line D minus the number on line E equals 14 or below. So we need a 900-something number that, when added to a number that’s 14 or below, equals 1000 or more. That gives us a field from 986 to 999.

And that number between 986 and 999 has to be divisible by 8 for our quotient to work. And the only number in that field that fits the bill is 992. 992 divided by 8 gives us 124, which is our divisor.

From that point on, we can fill out the rest of the equation, including our lengthy dividend, 12128316.

And there you have it. With some math skills, some deduction, and some crafty puzzling, we’ve slain yet another brain teaser. Nice work everyone!

[After solving the puzzle, I did a little research, and apparently this one has been making the rounds after being featured in FiveThirtyEight’s recurring Riddler feature, so here’s a link.]


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Puzzle Plagiarism: One Year Later

This weekend marked the one-year anniversary of one of the biggest stories in puzzles: the USA Today/Universal Uclick crossword plagiarism scandal, aka #gridgate.

If you’re unfamiliar with the story, you can click here for more detail, but here’s a quick rundown of what happened. Programmer Saul Pwanson and constructor Ben Tausig uncovered a pattern of unlikely repeated entries in the USA Today and Universal crosswords, both of which are edited by Timothy Parker.

Eventually, more than 65 puzzles were determined to feature “suspicious instances of repetition” with previously published puzzles in the New York Times and other outlets, with hundreds more showing some level of repetition.

The story originally broke on data analysis website FiveThirtyEight.com thanks to Oliver Roeder, but the real credit belongs to Tausig and Pwanson. The article sparked an investigation, and a day after the story first broke, Universal Uclick (which owns both the USA Today crossword and the Universal syndicated crossword) stated that Parker had agreed to temporarily step back from any editorial role for both USA Today and Universal Crosswords.

We were among the first to report that constructor Fred Piscop would serve as editor in the interim, but after that, the story went quiet for two months.

Then, in early May, Roeder reported that Universal Uclick had completed its investigation, and despite the fact that they’d confirmed some of the allegations of puzzle repetition, they were only giving Parker a three-month leave of absence.

The puzzle community was unhappy with the reaction, and USA Today and Universal Uclick soon felt the pressure from constructors and content creators alike.

Among the most vocal was Mike Selinker, puzzle constructor and president of Lone Shark Games, who stated that he and his team would boycott both USA Today and Universal Uclick until appropriate action was taken:

Up until now, we liked USA Today. We thought that a newspaper of its size would be violently opposed to plagiarism. But they do not appear to be. It’s way past time for USA Today and Universal Uclick to take a stand against plagiarism and for creators’ rights, and maybe it takes some creators to stand up for those. So we’re doing it.

Many other game companies and constructors joined in the boycott, and less than a week later, Gannett (who publishes USA Today) declared that “No puzzles that appear in Gannett/USA TODAY NETWORK publications are being edited by Timothy Parker nor will they be edited by Timothy Parker in the future.”

We’d never seen anything like this. Not only did it galvanize the puzzle community like nothing before, but it raised the very important issue of creator’s rights when it comes to puzzles. After all, plagiarism isn’t tolerated in publishing or college term papers, so why should the efforts of crossword constructors be considered any less sacrosanct?

And except for the occasional joke on Twitter (or scathingly clever puzzle) referencing the story, that was it. As far as anyone knew, Parker was still employed by Uclick, and they wouldn’t confirm or deny his involvement in any non-USA Today and Gannett-published puzzles in the future.

So naturally, as the one-year anniversary of the story loomed in the distance, I got curious. What had become of Parker? Was he still involved with Universal Uclick?

Sadly, I have no new answers for you. I reached out to Universal Uclick for comment, and they declined to reply. Parker was similarly difficult to reach.

But even without new threads to follow, this is an important story to revisit. It represents the solidarity, pride, and support of the puzzle community. It represents the rights of creators to be respected and to have their hard work respected. It represents the power of concerned citizens speaking up.

It reminded people that crosswords represent much more than a way to pass an idle Sunday morning.


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Puzzle Plagiarism, Part 3: Parker Out

After months of nothing, things are suddenly moving forward with the Universal Uclick/USA Today puzzle plagiarism scandal.

A quick recap: Programmer Saul Pwanson and constructor Ben Tausig uncovered a pattern of unlikely repeated entries in the USA Today and Universal crosswords, both of which are edited by Timothy Parker.

Eventually, more than 65 puzzles were determined to feature “suspicious instances of repetition” with previously published puzzles in the New York Times and other outlets, with hundreds more showing some level of repetition.

Parker “agreed to temporarily step back from any editorial role for both USA Today and Universal Crosswords” in March.

Last week, there was finally a new development, as Universal Uclick stated that they’d confirmed “some” of the allegations against Parker, and he’d be taking a three-month leave of absence.

That underwhelming semi-admission of Parker’s guilt led Lone Shark Games and Mike Selinker to call for a boycott of USA Today and Universal Uclick, and many other game companies and puzzle constructors have followed suit.

So where are we now?

Well, as reported by Oliver Roeder of FiveThirtyEight, Christopher Mele of the New York Times, and Deb Amlen of Wordplay, Timothy Parker is out as editor of the USA Today crossword.

According to Gannett, who publishes USA Today:

No puzzles that appear in Gannett/USA TODAY NETWORK publications are being edited by Timothy Parker nor will they be edited by Timothy Parker in the future.

This still leaves some important details up in the air. For one thing, Parker is still employed by Universal Uclick, even if USA Today and Gannett won’t be using any puzzles he’s touched.

We also don’t know who will be taking his place providing puzzles for USA Today and other Gannett publications.

According to Oliver Roeder:

Fred Piscop, who has been interim editor, told me that his position was temporary unless he was officially informed otherwise, and that there was nothing else he could tell me at this point. A call to Universal Uclick was not returned.

Clearly things are far from settled for Parker, Universal Uclick, and USA Today.

Regarding the #gridgate boycott, Mike Selinker and the team at Lone Shark Games had this to say:

As far as we can tell, USA Today and its parent company Gannett just vowed not to use puzzles edited by Timothy Parker ever again. That bold statement — sure, months late, but welcome nonetheless — was all we were looking for. If they stick to their word, we’ll stop our boycott. We can’t claim credit for the result, but we can say that our friends shining a flashlight on the wrongdoing did help get USA Today to speak out publicly and settle the score.

We’re maintaining the boycott of Universal Uclick, though. They’re continuing to employ someone they’ve admitted is a plagiarist—someone who apparently plagiarized our friends’ work. And just because USA Today isn’t buying Parker’s puzzles doesn’t mean no one else will. We can’t even be sure if the person editing the puzzles isn’t Parker, because he’s made a habit of hiding behind pseudonyms. So we’ll keep this boycott going until we’re sure they’ve got a plan for puzzles that aren’t edited by someone they think is a plagiarist.

Uclick, the ball’s in your court.


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Puzzle Plagiarism, Part 2: Uclick Responds

It’s Follow-Up Friday, but it doesn’t feel right to open this post with our usual exuberant intro.

Today, I’m returning to the subject of Timothy Parker and the USA Today/Universal Uclick plagiarism scandal.

You know, when I first wrote about this topic, I suspected I’d be returning to it in Follow-Up Friday fashion, and sadly, that’s proven true.

If you don’t recall, or you hadn’t heard, here’s a quick rundown of what happened. Programmer Saul Pwanson and constructor Ben Tausig uncovered a pattern of unlikely repeated entries in the USA Today and Universal crosswords, both of which are edited by Timothy Parker.

Eventually, more than 65 puzzles were determined to feature “suspicious instances of repetition” with previously published puzzles in the New York Times and other outlets, with hundreds more showing some level of repetition.

Back in March when I first blogged about this, Parker “agreed to temporarily step back from any editorial role for both USA Today and Universal Crosswords.”

Well, Oliver Roeder from FiveThirtyEight has reported that Universal Uclick has completed its investigation, and despite the fact that they’ve CONFIRMED some of the allegations of puzzle repetition — they don’t explain which allegations they’ve confirmed — they’re only giving Parker a three-month leave of absence.

According to the Universal Uclick press release:

During his leave, Mr. Parker will confirm that his process for constructing puzzles uses the best available technology to ensure that everything he edits is original. We will work with Mr. Parker on this effort and redouble our editorial process so that there is a stronger second level of review.

Roeder points out that Universal also doesn’t say if the last two months count toward Parker’s three-month leave of absence, since Fred Piscop has been serving as interim editor since the scandal broke.

As you might expect, some in the puzzle-game community are underwhelmed, to say the least, with Universal Uclick’s decision.

For instance, Mike Selinker, puzzle constructor and head honcho of Lone Shark Games, sent out a release last night regarding Parker’s situation, stating that he and his team will boycott both USA Today and Universal Uclick.

From their Tumblr post:

But USA Today and Universal Uclick, two important providers of puzzles to the world, have abandoned all pretense that originality and credit for content is important to them. So we’re abandoning them. As of today, we’re boycotting both companies.

Up until now, we liked USA Today. We thought that a newspaper of its size would be violently opposed to plagiarism. But they do not appear to be. It’s way past time for USA Today and Universal Uclick to take a stand against plagiarism and for creators’ rights, and maybe it takes some creators to stand up for those. So we’re doing it.

I suspect Mike and the wonderful crew at Lone Shark Games won’t be the only ones giving USA Today and Universal Uclick the cold shoulder. Kudos to them for taking a stand against plagiarism and standing with friends and colleagues in the puzzle community.

You’d think a major publication like USA Today would be against plagiarism instead of downplaying it like this. I doubt they’d tolerate plagiarism anywhere else in their paper.

It will certainly be interesting to see where the story goes from here. Here’s hoping Universal Uclick does the right thing and stands with content creators, not against them.

I’ll conclude this post the same way the team at Lone Shark Games concluded their release:

If you share this on Twitter or Facebook, please tag @usatoday and @UniversalUclick to tell them that you stand with the puzzlemakers, and add the hashtag #gridgate. Or, if you want to talk to USA Today directly, send them a note addressed to Reader Feedback/Letters saying that you find plagiarism in any department unacceptable. Now would be awesome.


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Puzzle Plagiarism?

[Image courtesy of PlagiarismToday.com.]

Today’s post isn’t the usual Follow-Up Friday fare. Instead of returning to a previous subject, I’d like to discuss a topic that I expect I’ll be returning to in Follow-Up Friday form in the near future.

There is a certain pride and sense of accomplishment you experience as a puzzler when you come up with an exciting, innovative, unexpected theme idea for a puzzle, or when you pen a terrific clue for a word. Whether the wordplay is spot on or you’ve simply found a way to reinvigorate a tired bit of crosswordese, you feel like you’re adding something to the ever-expanding crossword lexicon, leaving a mark on the world of puzzles.

Unfortunately, there’s also the flip side of that coin, and those who would pilfer the hard work of others for their own gain. And in a story broken by the team at FiveThirtyEight, there may be something equally unsavory going on behind the scenes of the USA Today crossword and the Universal syndicated crossword.

You can check out the full story, but in short, an enterprising programmer named Saul Pwanson created a searchable database of crossword puzzles that identified similarities in published crosswords, and it uncovered an irregularly high number of repeated entries, grids, and clues in the USA Today and Universal crosswords, both of which are edited by Timothy Parker.

More than 60 puzzles feature suspicious instances of repetition — the word “plagiarism” comes to mind, certainly — and it has sparked an investigation. In fact, only a day after the story first broke, Universal Uclick (which owns both the USA Today crossword and the Universal syndicated crossword) stated that the subject of the investigation, Parker himself, “has agreed to temporarily step back from any editorial role for both USA Today and Universal Crosswords.”

I’ve heard that oversight of the USA Today crossword has already passed to another editor of note in the crossword world, constructor Fred Piscop (author of last Wednesday’s New York Times crossword), but I wonder if more examples of crossword duplication are lurking out there.

With resources like XWord Info and the Pre-Shortzian Puzzle Project out there, the history of crosswords is becoming more and more accessible and searchable. I can’t help but wonder if more scandals are lurking down the pike.


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