Tag Archives: solving

Sudoku Solving Techniques!

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I wanted to do one more Sudoku-centric post for Sudoku Month, so I figured I’d take a look at different solving techniques!

Sudoku is all about deduction, but you’d be surprised what you can learn from different number patterns and arrangements. There is plenty of information lurking in those grids beyond the given digits.

Let’s take a look!

Many how-to-solve guides suggest utilizing candidates to assist with your solving. Candidates are all of the possible numbers that could be in a given cell, and most Sudoku apps have a feature allowing you to list them onscreen for ease of solving.

It can absolutely be an advantage, especially if you have a hard time keeping track of possible numbers in different locations of the grid while you’re solving.

But keep in mind, especially for solvers newer to Sudoku, the amount of information can also be a bit overwhelming, obscuring paths forward.

In this grid (which I nabbed from r/Sudoku), you can see all the candidates placed. But I suspect a less experienced solver might not spot my next step because of ALL the noise onscreen. Viewing all the candidates can take some getting used to.

But if you look in Box 7 (the lower-left 3×3 section of the grid), you’ll find your next move.

There, if you look at the first column, you can see that the 7 can only be in one of those two boxes. (Otherwise, there’s no 7 at all in that column.) Which means the seven isn’t a candidate for the bottom cell or the cell to the right of the 8. In fact, that means we can place that 2 in the bottom cell immediately.

And from that point, we can place the 7 in Box 8, as well as the 9 and the 2 in Box 2 (column 6). One quick deduction, and we’ve placed four digits!

From that point, we can fill in the rest of Box 8 and we’re off to the races.

Now that was pretty simple, so let’s look at something a little more complex. This technique is called X-Wings, and it’s all about pattern recognition.

Start looking for columns or rows with only two instances of a particular candidate (for example, the number 4). If you can find two rows, each with only two places that a 4 can be, and they’re the same in both rows, you might have an X-Wing. Now check the crossing columns. If two columns also have only two instances of that candidate 4 in the same position (making a square or rectangle), you’ve got an X-Wing.

Okay, I know that was A LOT, so let’s look at it in grid form to help you visualize. (This grid comes from the book Sudoku Rocks! by David Klein.)

In this example, look at columns 6 and 8. Each column only has two candidate 5s (in Box 8 and Box 9, respectively). And those candidate 5s are in the same positions in the crossing rows (row 7 and 9).

Those four candidate 5s form a square, so we’ve got an X-Wing here.

How does that help us?

Well, we know that there are no other 5s in those two columns. But what we also know is that, no matter which 5 is correct, both of those intersecting rows (rows 7 and 9) are also covered. That X-Wing will contain two 5s diagonally one way or the other.

So that means any of the other 5s listed as candidates in those two rows can be crossed out.

This may seem trivial, but we can already place a number because of it. By crossing out the 5s in Box 7, there is only one place in column 2 that a 5 can go. Right at the top, in Box 1.

This pattern in the lower right-hand corner just gave us a confirmed number in the upper left-hand corner. Pretty cool!

Now, after learning X-Wings, we can explore another pattern variation: Y-Wings (also known as XY-Wings).

In an XY-Wing, you’re identifying a square or rectangular pattern of candidates in the grid that influence each other, similar to an X-Wing layout.

One of the corners of the square will be the target, where you hope to eliminate one of the candidates. The neighboring corners of the square will be the pincers, closing in on your answer. And the final corner is called the pivot. By testing the candidates in this square (pivoting between the choices), we will learn something about our target cell.

It takes some practice to learn to spot XY-Wings, but when you manage it, you’ve added a valuable tool to your Sudoku solving kit.

Here is another grid I grabbed off r/Sudoku. Can you spot the XY-Wing in the lower right-hand corner of the grid?

It’s okay if you can’t! It definitely took me a minute to spot it.

In this case, the cell in Box 6 will be our target, the cell in Box 8 is our pivot, and the other two are our pincers.

In Box 8, our circled cell has two options, 2 and 3. If the answer is 2, the pincer above in Box 5 is a 9. If the answer is 3, the pincer to the right in Box 9 is a 9. So, no matter what’s in Box 8, one of those two pincers will be a 9.

And since both of those pincers are in a row or column with the circled cell in Box 6, we know that cell CANNOT be a 9. So it must be a 2.

And once we’ve placed that 2, we can place the 9 in Box 5, the 2 in Box 5, the 3 in Box 2, the 9 in Box 2, and more! All from one deduction.

Hopefully these tools and techniques will help you with your Sudoku solving in the future, fellow puzzler!

Would you like me to return to this subject in the future? There are plenty of advanced techniques out there to explore, like Two-String Kite, Skyscraper, or Finned X-Wings. If you’d like to see more posts like this (for Sudoku or other puzzles), please let me know in the comment section below! I’d love to hear from you.

Puzzly Mantras in Just Three Words!

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In a recent Gameplay newsletter, Sam Corbin wrote about three-word instructions / mottos (like “Eat, Drink and Be Merry” or “Live, Laugh, Love”), and pondered a slogan like that for puzzle solving.

It’s a definite challenge for sure, like trying to come up with a poignant six-word memoir. But I’ve never been one to turn down a challenge simply because I’ll probably fail. I WELCOME IT.

So, today, I thought I would pitch in and come up with some slogans (not all fitting the three-word formula) for various puzzle outlets.

Penny Press / Dell Magazines

I’ve always thought a great slogan for them would be “We’re As Puzzled As You Are.” It’s light, a little self-deprecating, and fosters a feeling of camaraderie between publisher and solver.

But a three-word instruction for them?

How about Sample, Savor, Solve? Sample a variety puzzle you’ve never tried. Savor the ones you know you like. And, as always, solve.

The New York Times

I mean, a good motto would obviously be “All the Clues That Are Fit to Print,” playing off the classic NYT slogan.

But for a later-week crossword, how about Determine, Decipher, Discover?

Determine what you know, decipher tricky clues, discover the gimmick.

The Los Angeles Times

Now, The LA Times has several mottos (like “Read the Paper,” which could easily be converted into “Read the Down Clues”), but my favorite is their historical slogan, “Stand Fast, Stand Firm, Stand Sure, Stand True.”

And when it comes to puzzles, that could be Stand Watch, Stand Pat, Stand Back.

Let your eyes go to the clues you know immediately, trust your instincts on ones you’ve filled in, and then stand back and survey your work to unravel the theme.

Doesn’t really work with the three-word motto, though.

Maybe Stop, Drop, and Roll!

Stop what you’re doing and solve a puzzle. Look at those down clues. And keep trying ’til you’ve solved it.

Fireball Crosswords (and other meta outlets)

For me, it was actually easy to come up with a three-word motto for solving these, because it’s what I do when I try to unravel a meta while completing the grid:

Pattern, Exception, Association.

Look for a pattern or rhythm outside the regular solve. Look for exceptions that feel intentional. Look for associations on a second read.

But what about for a general three-word instruction for crossword solving?

For solvers still getting used to crosswords, I would recommend Blanks, Bios, Back-and-forth or Fill, Famous, Flip, which both fit some of my solving advice for newbies.

Fill in the blank, scan clues for famous names, flip to the crossings once a word is filled in and work on that section.

Oh, and if you suspect a puzzle will be difficult, always remember:

Write Light, Alright!?

Hopefully one of these mottos works for you, fellow solver. Do you have any suggestions, leave them in the comment section below! We’d love to hear from you.

And now for my traditional three-word sendoff:

Happy puzzling, everyone!

A-Ha Moments Stick in the Brain!

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It’s one of the best moments in puzzle solving.

When all the pieces click into place brilliantly. When the wordplay is unraveled. When the cryptic crossword clue is deciphered. When the trickery behind the riddle is revealed.

That rush, that satisfaction that coincides with overcoming the clever, devious creation of another keen mind.

The a-ha moment.

And it turns out that the a-ha moment isn’t just significant for puzzly spirits, it’s biochemically significant as well.

According to a study by Maxi Becker, Tobias Summer, and Roberto Cabeza, the brain remembers a-ha moments better than solutions reached through traditional methodologies.

From a report by Gizmodo:

As study participants solved brain teasers, he [Cabeza] and his colleagues recorded their brain activity with functional magnetic resonance imaging, a technique that measures changes in blood flow associated with brain activity. The brain teasers were visual fill-in-the-blank puzzles that revealed a previously hidden picture once participants completed the image.

And the brain activity resulting from an a-ha moment was comparable to the brain characteristics of important insight events. This means that the solutions derived from a-ha moments were remembered more clearly and with greater detail than those derived from traditional solving or process of elimination-style solving. Some of the solvers still recalled their a-ha moment solution a full five days later!

Researchers are already looking to revamp the ways we teach by utilizing techniques that inspire more a-ha moments, hoping that students will benefit more in the long term from inspiration-focused learning, rather than rote memorization.

Here’s hoping for more a-ha moments for all us! They’re good for the soul and good for the memory banks.

Happy puzzling, everyone!

A Gateway Puzzle for Crossword Solving?

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Where do you get started with crossword solving?

I see that question a lot. And the advice offered to new solvers varies. Sometimes they’re pointed particular crossword outlets promising a more newbie-friendly solve. You certainly don’t want someone tackling a crossword too difficult for their skill level and getting discouraged.

Often, they’re told to just plug away at it, since the only way to get better at crosswords… is by solving crosswords.

None of this advice is wrong. I’m sure people follow these suggestions and slowly start to enjoy this puzzly world that many of us have embraced for decades.

You might think that Mini Crosswords, like those featured in the New York Times puzzle app, are the way to go. But while the grid is smaller, that also means new solvers have fewer chances to find crossings and work on their solving.

Imagine a regular crossword. A Mini is essentially one corner of the grid. If you started a crossword in one corner, and didn’t get any entries, you can move to another spot. But if you’re stumped on a Mini, where do you go?

I also think the running timer feature — although obviously not a necessity for solvers — can add to a new solver’s anxiety. If you’re stumped, and you’re just sitting there, watching the timer tick away, that’s going to eat at your confidence a bit.

crisscross

You might think that crisscross-style puzzles (like the one above) would be less intimidating, since they don’t have the same dense grid surrounded by clues that crosswords have, but I’ve found that folks don’t warm to those quickly. No matter how well-constructed the crisscross, it tends to remind people of activity books for kids, and no one wants to feel patronized when trying out a new hobby or giving it another go.

Not only that, but they are missing one of the most helpful components to crossword solving: all the overlapping letters! In a crossword, you have two chances at every single box because of the across and down clues. But in a crisscross, you usually only have one or two points of overlap, so if the clue isn’t helpful or intuitive, you’re just stuck. That doesn’t build solver confidence.

I do have a suggestion, though.

I’ve tried this with several friends and acquaintances who had sworn off crosswords entirely, and not only introduced them to a new puzzle they didn’t know, but opened their eyes to the possibility of more puzzle solving in the future.

My solution was: Fill-Ins.

fillin sample
A sample puzzle from our friends at Penny Dell Puzzles.
Check out their fill-in library here!

For the uninitiated, fill-ins utilize the same general grid style as a crossword. But instead of answering numbered clues to place the words in the grid, you’re already given the answer words, organized by word length. Your task is to place them all into the grid, using other words and letters in the grid to guide you.

It’s closer to Sudoku-style solving than crosswords, because you’re eliminating options in a logical manner, rather than figuring out clues to place the words.

I believe solving fill-ins helps remove the intimidation factor of crosswords in three ways:

1. No trivia or outside knowledge is required, which removes a huge burden from a solver who has probably felt overwhelmed by crossword cluing in the past.

2. It makes empty crossword grids less intimidating. Do you ever have those moments where you read three or four crossword clues in a row and you don’t immediately conjure up answers? And then you look at all those empty spaces in the grid and feel dumb? It happens. But fill-ins often have a set word to get you started, and once you start placing letters, recognizing useful crossings, and filling the grid, all that goes away.

3. Fill-ins help strengthen another skill valuable in crossword solving: letter-blank recognition. If you see B _ U _ , a regular solver instantly starts listing off possibilities: BOUT, BLUE, BLUR, BAUD, etc. But a new solver — who might not have that reflexive knowledge of possible words — can read through the list of four-letter words and see what fits, helping to build that mental lexicon for future solving.

120718_crossword_L

After solving a handful of fill-ins, word placement goes quicker, confidence in filling in those letter blanks increases, and empty grids become fields of potential puzzle fun, not stark empty spaces.

I’ve suggested fill-ins to several crossword-shy or puzzle-shy friends, and usually, a few weeks later or so, they start asking what other puzzles are out there, or where a good place to start with crosswords might be. And that’s a win.

Happy puzzling, everyone!

Fairness and Accessibility in Puzzles?

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We love crosswords here at PuzzleNation. Crosswords are our bread and butter, as well as our pizza, our salad, and our desserts.

We strive to keep our puzzles as accessible as possible for solvers of all ages. And that’s tougher than non-puzzlers might think.

Recently we discussed a never-ending debate in crosswords as we delved into the many, sometimes contradictory, goals of creating a great crossword. You want entries to appeal to older solvers without alienating younger solvers, and vice versa. Some people despise pop culture references and proper nouns, while others embrace them.

Abbreviations, partial phrases, fill-in-the-blank clues, wordplay clues, clues that reference other clues… there’s a vast swathe of crossword qualities that must be balanced, and no matter how good a job you do, you’re probably still going to have a few dissenting voices who believe you should do better.

As a hobby still very much viewed as the purview of older white men — despite the many worthwhile voices of women, people of color, and members of the LGBTQIA+ community that contribute to the world of crosswords in increasing numbers — the language featured in crosswords MATTERS.

It reflects our society, serving as a microcosm of the current day and our culture as a whole. Older solvers might not know new slang or black artists or trans performers or any number of references that are growing more commonplace AND gaining greater visibility. But updating the vocabulary of crosswords is a constant effort, and a worthwhile one.

But I said a lot of this in that previous post, so why am I returning to the topic now?

Well, because I find this continuing democratization of crosswords interesting, because it’s something required of crosswords, but not of many other types of puzzles.

Word seeks (except for some variations) give you the starting list, and then you go hunting for answers. Fill-Ins do the same thing, leaving you the empty grid to fill but requiring no specialized knowledge. Everyone gets the same running start.

(I snagged this helpful image from www.logic-puzzles.org.)

Traditional logic puzzles are also presented on an even playing field. You’re presented with information (say, hints about various names, places, times, and activities), as well as an end goal to figure out (the correct schedule of who did what, where, and when).

You don’t have to bring any foreknowledge or previous experience to the table. Given the opportunity, everyone should have an equal chance of solving the puzzle.

Naturally, this equality depends on the assumption that you, the solver, can read the language the puzzle is presented in.

Which brings me to, perhaps, the most democratically fair paper puzzle of all: Sudoku.

The rules are simple, even if the puzzles can be very challenging: place the numbers 1 through 9 in every row, column, and cell.

Even at a glance, without knowing the puzzle, pretty much anyone would have an idea of what’s going on and what needs to be done. Language doesn’t matter, so long as you can identify the nine different symbols to be placed. (This is why word and color variations of Sudoku exist, because the numbers themselves are irrelevent. You just need nine different things.)

Anyone can pick up a pen, a pencil, or a stylus and solve a Sudoku.

And we should strive for the same thing with crosswords.

Sure, all of those other puzzles require practice to get GOOD at them. But at a baseline, everyone who approaches them has a fair shot. Crosswords demand that solvers bring their own knowledge and info and trivia and vocabulary to the table.

But crosswords as a whole should seek that same democratization: Accessibility. Representation. That inviting X factor.

There’s already a touch of that in the medium. Anytime I see someone solving a puzzle on a train, or in an airport, or in some public place, there’s always someone else sneaking a peek or stealing a glance.

Have you ever seen someone complete a crossword for the very first time? I have, and it’s awesome. It’s a magnified version of the delicious a-ha moment when you unravel a tricky clue.

Do you remember the joy in your heart the first time you conquered a New York Times puzzle on a difficult day? The first time you solved a puzzle type you’d never bested before? The first time you cracked the meta lurking in the background of an already devilish design?

Everyone should get that feeling.

No crossword will ever be everything every solver wants it to be. And that’s fine. But I do look forward to the day when everyone looks at a puzzle and at least one of the clues speaks to them, makes them feel seen and heard and represented.

Puzzles should be for everyone.

[Thank you to ThinkFun and Michelle Parrinello-Cason for inspiring this post.]

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Let’s Talk About Cheating in Crosswords!

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cheating

[Image courtesy of Getty Images.]

I think most people who solve crosswords already know this, but for anyone who doesn’t, I’ll make this very simple for you.

Unless you’re in a tournament or competition setting, there’s no such thing as cheating at solving crosswords.

Are we cool? Sweet. *checks watch* Outstanding! Shortest blog post ever.

…

Okay, I’ll elaborate.

Recently, a high school friend of mine “confessed” on Facebook that she had never completed a crossword puzzle where she “didn’t cheat.”

I replied, “It’s not cheating. It’s learning new words so you can get better later.”

And her mother replied, “Don’t encourage her!”

I was a little baffled.

Crossword.

I mean, obviously you get better the more you solve crosswords, but if you keep coming across the same clues (or various clues for the same word) and you don’t know the word, how are you ever going to learn it if you don’t look it up?

You’re not going to suddenly KNOW a word or a person or a phrase if you don’t know it. As much as crosswords are about building skills like wordplay and figuring out what words fit different letter patterns, it’s also about building a personal lexicon and adding to your arsenal as a solver.

The average person does not know ETUI. If they see the clue “needle case,” they’re not going to suddenly know it. Even having one or two correct answers crossing it is not going to magically impart knowledge of the word ETUI.

It’s not cheating if you look up answers. You’re cheating yourself by NOT doing so.

Sure, in a tournament setting or a timed setting, it’s cheating. But in general solving, it’s just prep work that sets you up for greater success down the line.

120718_crossword_L

So, once more for those in the back or those who really want explicit permission:

Once you’ve tried your best, once you’ve filled in as many entries that cross it as possible, once you’ve wracked your brain, taken time away from it, and returned to try again but not succeeded, I hereby give you permission to “cheat.”

Okay? Okay. Happy solving, everyone!

[Oh, and just for clarification, this applies to solvers. There is absolutely cheating in crossword constructing. It’s called plagiarism, and it will not be tolerated.]

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