Those Sudoku Puzzles Can Be Criminally Tough!

Even when I’m not thinking about puzzles or intending to learn about puzzles, puzzles find me.

I was reading one of the most recent editions of Ripley’s Believe It or Not!, those delightful compendiums of all things amazing, weird, and unlikely. Everything from world records and peculiar habits to once-in-a-lifetime events and mind-bending coincidences are found between the covers of these collections.

And one particular fact caught my eye:

Eighty-six prisoners at Exeter Jail in Devon, England, signed a formal letter of complaint claiming that a Sudoku puzzle in the local newspaper — the Exeter Express and Echo — on May 21, 2015, was impossible to solve.

I was instantly intrigued.

[Image courtesy of The Telegraph.]

Here is the message the prisoners sent to the editor of The Exeter Express and Echo:

Dear Sir/Madam, I am sadly writing this letter in A LOT of disappointment.

As you will see, I’ve enclosed last week’s Sudoko [sic] page and we (along with 84 other prisoners) believe you printed a ‘hard’ Sudoku which is IMPOSSIBLE to complete.

As being prisoners we are only aloud [sic] access to Thursday’s issue, so we couldn’t verify the truth.


Michael Blatchford
Shane Smith

Yes, The Exeter Express and Echo is printed twice a week, and since the answers to Thursday’s puzzles appear on Monday, and the inmates don’t have access to Monday’s issues, they were unable to check their own work.

So, naturally, I had to see whether this Sudoku puzzle was as unsolvable as the inmates claimed.

Finding a copy of the puzzle wasn’t hard. Here, I’ll post it here, in case you want to try your hand at it yourself:

[Image courtesy of The Telegraph.]

So, is it impossible?

Well, no.

In all honesty, I’m not the strongest or the fastest Sudoku solver. But I did complete this puzzle, difficult as it was. I suspect, given time, you would complete it as well. I don’t mean to impugn the Sudoku skills of the Exeter Jail population. I’m just saying.

As it turns out, the inmates had made a few key mistakes, mostly in the middle section, and since they apparently solve in ink, it made things much harder.

But, in a lovely response, the staff at The Exeter Express and Echo promised to make Monday papers available to the inmates as well, so they can double-check their answers next time. That’s nice.

And here’s hoping their Sudoku solving has been smooth sailing ever since. Apparently, it has been, since Ripley’s has yet to mention them a second time.

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The UK Sudoku Championship! (Or should that be Sudo-UK?)

Hot on the heels of The Indie 500 crossword tournament last weekend, the UK is also gearing up for a major puzzle event: The UK Sudoku Championship!

The event spans June 10 through June 13, and chairman Alan O’Donnell of the UK Puzzle Association sent out the Instruction Booklet for this year’s event a few days ago, which kicks off a string of major puzzle events in Europe and across the world, including the UK Puzzle Championship in a few weeks.

Although the UK Sudoku Championship is only open to competitors from the UK — with the top two earning a place on the UK team for the 2016 World Sudoku Championship — international players are welcome to test their puzzly mettle as guest solvers.

But even if most PuzzleNationers aren’t eligible to compete, you can still enjoy the challenge of some topnotch Sudoku puzzles. Let’s take a look at some of the diabolical puzzles they’ve cooked up for this year’s event!

[An Extra Regions puzzle, a variation on Classic Sudoku.]

In addition to some Classic Sudoku, Extreme Sudoku, Sum-Doku (or Killer Sudoku), Jigsaw Sudoku (or Geometric Sudoku), and Thermo Sudoku — all of which I explored in detail in my Wide World of Sudoku post — there are some variants I’ve never seen before, like this Linked 6×6 Sudoku.

In this puzzle, you have two grids to complete, but with the additional wrinkle that no number placed in the left 6×6 grid will occupy the same square in the right 6×6 grid. So you have more solving information than expected, but it’s spread out across two grids.

This Deficit Sudoku puzzle also uses the 2×3 box format, but arrayed in a 7×7 grid. This means that any of the numbers 1 through 7 can be in each 2×3 grid, which makes it slightly harder than if you were only using the numbers 1 through 6.

(Plus you have no information on what number goes in that solo square in the center of the grid.)

The curiously named Odd-Even-Big-Small Sudoku employs clues outside the grid to help you fill in some of the squares along the perimeter of the grid, telling you that two odd numbers, two even numbers, two small numbers, or two big numbers will occupy the nearest two spaces in that row or column.

This is a solving mechanic I’ve never encountered before in Sudoku, and I can see it posing an impressive challenge to the average Sudoku solver.

That unconventional style of cluing sets the tone for the rest of the unusual puzzles that competitors and solvers will encounter here. In the above grid, a Consecutive Pairs puzzle, those dots indicate that the neighboring numbers connected by those dots are consecutive numbers, like 5 and 6 or 2 and 1.

(You can also try Consecutive Pairs Sudoku in Will Shortz’s Sudoku and Sudoku Spectacular, both published by our friends at Penny Dell Puzzles.)

XV Sudoku works in similar fashion, with x’s and v’s instead of those little dots. The x’s mean the neighboring numbers add up to 10, and the v’s mean the neighboring numbers add up to 5.

This Eliminate Sudoku uses arrows to indicate that the number in the arrow box will not be repeated in any of the boxes that follow that arrow. So, for instance, if you place a 3 in that arrow box next to the 2 in the upper-right 3×3 grid, none of the boxes that arrow points at along that diagonal will contain a 3.

Like the dual grids in the Linked 6×6 Sudoku, this puzzle is interesting in offering more information on what’s NOT in a square than what IS.

The final new puzzle in the Instruction Booklet is my favorite, but that’s because I’m a sucker for palindromes in puzzles. This Palindrome Sudoku features gray lines that indicates spots where — you guessed it! — the chain of numbers reads the same backwards and forwards.

Similar to Thermo Sudoku in its solving style, Palindrome Sudoku takes advantage in the restrictive nature of Sudoku solving by adding a neat little twist.

You can check out the full Instruction Booklet here, and remember to keep your eyes peeled on June 10 when the actual puzzles go live!

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The end of Sudoku?

I recently read in Owen O’Shea’s book The Call of the Primes that there are 5,472,730,538 unique solutions for a 9×9 Sudoku grid.

Yes, five billion is a very big number, but these days, billions aren’t what they used to be. I mean, think about how many newspapers, magazines, and puzzle books feature Sudoku puzzles. It’s a huge amount of material every year.

So, the thought occurs to me…how long before those 5,472,730,538 unique solutions run out?

To be fair, it’s not like reaching Peak Oil or a point of no return. I’ve solved a lot of Sudoku puzzles, and never once have I felt like I was re-solving a grid I’ve seen before, even if I was. This is purely a matter of mathematical curiosity. How long would it take for us to use up every last possible 9×9 grid?

Man, where do I begin?

Well, if I’m going to talk Sudoku puzzles, it makes sense to start with our friends at Penny Dell Puzzles.

Across seventeen Sudoku titles, they publish approximately 23,236 Sudoku puzzles a year, and probably an additional 350 per year across their Crossword/Variety and Variety titles for a total of 23,586 puzzles in a calendar year.

Now, Penny Dell Puzzles is the top puzzle publisher in North America — #humblebrag — and let’s assume there are another half-dozen publishers worldwide matching their output. That gives us a ballpark of 165,100 Sudoku puzzles published worldwide.

But what about newspapers?

According to the Newspaper Association of America, there were 1,331 daily newspapers in 2014, and there were 1,450 daily newspapers in 2005, making an 8.2% decrease from a decade before. If we apply that percentage to the number of daily newspapers worldwide as of 2005, 6,580 titles, we get 6,040 daily newspapers worldwide. And although they may not ALL have a daily Sudoku, this will help cover some of the major magazines that also carry Sudoku that I’ve excluded from my ballpark calculations.

That gives us 6,040 newspapers x 365 puzzles a year for a total of 2,204,600 puzzles a year.

Now, for other publishing efforts regarding Sudoku, lists 20,718 results for Sudoku, and if we apply an average of 217 puzzles per title — which seems a fair approximation, based on the stats published by our friends at Penny Dell Puzzles, the fact that some books will have more puzzles, and some results will be ABOUT Sudoku and probably contain few to none actual puzzles — that’s 4,495,806 puzzles available right now in the world’s biggest bookstore. (Yes, obviously not all of them were published this year, but hey, this is meatball mathematics.)

Unfortunately, statistics on Sudoku are sketchy at best for the mobile app market, online puzzling, and downloadable puzzles through Playstation Network, Wii, and other gaming platforms, so I can’t factor those puzzles into my calculations.

But just with the numbers I’ve got here, we’re talking about 6,865,506 Sudoku puzzles worldwide. So, if each of those Sudoku puzzles is unique — which is possible, if unlikely — that barely makes a dent in our total of possible Sudoku grid layouts, which you recall is 5,472,730,538.

So, if we’re producing 6,865,506 unique Sudoku puzzles a year, it’ll take nearly 800 years to use every possible 9×9 grid! (For the folks at Penny Dell Puzzles, it would take nearly 232,033 years! So they’re in the clear. *laughs*)

I guess we won’t be running out anytime soon.

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It’s Follow-Up Friday: International Puzzle Day edition!

Welcome to Follow-Up Friday!

By this time, you know the drill. Follow-Up Friday is a chance for us to revisit the subjects of previous posts and bring the PuzzleNation audience up to speed on all things puzzly.

And today, I’d like to return to the subject of puzzly holidays!

[Let’s celebrate with some crossword cake!]

Today is International Puzzle Day (or National Puzzle Day, depending on who you ask), and we here at PuzzleNation couldn’t resist getting involved in the puzzly celebrations!

In fact, we went all out this year, building a puzzle fort from various puzzle magazines! Check it out!

puzzle fort

And that’s just for starters. We’ve also assembled a new rundown of all the terrific puzzle apps and games PuzzleNation has to offer!

From the iOS and Android versions of the Penny Dell Crossword App (including new puzzle collections for both!) to our Classic Sudoku, Classic Word Search, and Bible Word Search apps, you can get all the details on our library of apps right here!

And to cap off the day’s festivities, we’ve collaborated with our pal Darcy over at Penny Dell Puzzles to concoct a little puzzly quiz for you!

Click here to find out What Kind of Puzzle Am I?, complete with links to share your results across social media!

So how are you celebrating International Puzzle Day? Are you kicking back with your favorite app or puzzle book? Meeting with friends to do a bit of tabletop gaming? Or maybe tackling an Escape the Room event and testing your puzzle mettle! Let us know in the comments!

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The Wide World of Sudoku


[A classic Sudoku grid with a colorful twist, where the 3×3 blue squares also have all 9 numbers inside them. One of many MANY Sudoku variants. Grid from]

For more than a century now, crosswords have been the premier pencil-and-paper (or pen-and-paper, if you’re confident) puzzle, but a close second would have to be Sudoku, which has exploded in popularity over the last decade or so.

The simple concept behind Sudoku — a 9×9 grid arranged so that the numbers 1 through 9 only appear once in each row, column, and 3×3 square — is easily modified for any difficulty level, from beginners to topnotch solvers.

The classic form of Sudoku, originally known as Number Place or To the Nines, is instantly recognizable.


[A Sudoku grid from PuzzleNation’s own free Classic Sudoku app for iPad.]

But virtually any set of nine different symbols, characters, numbers, or letters can be used as clues for a Sudoku-style solve. That gives us variations like Picture Sudoku or Color Sudoku, where the same deduction is involved, but the solution is a bit more vibrant.


[A color Sudoku from]

Word Sudoku follows the same concept, replacing the numbers 1 through 9 with letters, allowing for the added bonus of a 9-letter word reading out along one of the rows. I’ve seen Word Sudoku variations in all sorts of languages, which is neat, because you can still solve the puzzle even if you don’t know the language; you’re simply choosing different symbols.


[A Word Sudoku from Magic Word Square on Blogspot.]

Using letters instead of numbers often factors into larger Sudoku puzzles. While Penny/Dell’s Mega Sudoku is a 16×16 grid using the numbers 1 through 16, other large-scale Sudoku puzzles use letters instead of numbers above 10, while others go so far as to remove the numbers altogether, giving you the option of puzzles that span nearly the entire alphabet!


[A 25×25 monster Sudoku grid using letters, courtesy of]

And since we’re already discussing bigger Sudoku puzzles, it’s worth mentioning smaller Sudoku puzzles. Often called Mini-Sudoku or Sub-Doku, these puzzles start at 4×4 grids (using only the numbers 1 through 4) and increase in size all the way up to the standard 9×9 grid.

Those are just the puzzles that use standard Sudoku rules. There are numerous types of Sudoku that add new rules or curious wrinkles to the standard solve.

Perhaps the most famous variant is known as Extreme Sudoku, Diagonal Sudoku, or X-Sudoku, and there’s one crucial difference: the numbers 1 through 9 also appear only once along each diagonal. This additional rule helps with solving, but Extreme Sudoku puzzles often have fewer set numbers in order to keep the difficulty level interesting.


Another popular variation is known as Jigsaw Sudoku or Geometric Sudoku. These puzzles abandon the standard 3×3 boxes, instead using various Tetris-like shapes within the 9×9 grid. Each of these pieces contains each number 1 through 9, and the standard rule of no repeats within a row or a column remains.

These puzzles can either have random shapes or shapes with the same diagonal symmetry that rules both crossword grids and the placement of set numbers in classic Sudoku grids.


[A Jigsaw Sudoku grid from]

Some variations involve more deduction as well, like Neighbor Order Sudoku or Greater Than Sudoku. These puzzles feature small arrows that indicate whether the number in a given square is larger or smaller than its neighbor.

That’s just the start of math-based Sudoku variants that exist. Sum-Doku or Killer Sudoku uses the standard one-per-row, column, and 3×3 box Sudoku rule, but also adds numerous smaller Tetris shapes and boxes, each with a total. The numbers within that smaller box add up to that total.

Those totals are a crucial aid for solving, since Sum-doku puzzles often feature many fewer starting numbers. (The shapes of the smaller boxes often follow the diagonal symmetry of the set numbers.)


[A Sum-Doku grid from]

Another popular variant involves overlapping Sudoku grids. You could have two 9×9 grids that share one 3×3 box, or two 9×9 grids sharing four 3×3 boxes, or you could have more grids overlapping in all sorts of ways.


[A quadruple overlapping Sudoku grid, courtesy of the forums of]

The best known overlapping Sudoku puzzle is probably Samurai Sudoku, which features five 9×9 grids, one at the center and one at each corner, so the 4 corner 3×3 boxes of the center grid link the puzzle together.

Check out this masterpiece I discovered on


Not only is it a Samurai Sudoku with diagonal symmetry for all the set numbers, but each of the four corner grids operates under a different set of variant rules.

The upper left grid uses Extreme Sudoku (or Diagonal Sudoku) rules, the upper right grid is an asymmetric Jigsaw Sudoku (or Geometric Sudoku), the lower left grid has shaded the location of every even-numbered number to aid your solving, and the bottom right has two shaded ribbons weaving throughout the grid, each of which also includes each number from 1 through 9 once.

As you might expect, there are plenty of variations of Samurai Sudoku. My personal favorite is known as Shogun Sudoku; it’s two linked Samurai Sudoku grids — meaning there are ELEVEN linked 9×9 grids — and there are even larger variations out there for the solver who simply can’t get enough of overlapping Sudoku puzzles.


[Upper left: Tight Fit Sudoku, Upper Right: Thermo Sudoku,
Lower Left: Arrow Sudoku, Lower Right: Consecutive Sudoku.]

Our friends at Penny/Dell Puzzles have several titles that offer a variety of different Sudoku puzzles. The four grids above all appear in various issues of Will Shortz’s WordPlay, all courtesy of Sudoku constructor Thomas Snyder.

You should also check out the Sudoku Spectacular title (featured in our Holiday Puzzly Gift Guide!) as well as their upcoming Will Shortz’s Sudoku title.

I would also be remiss if I didn’t mention the mathier cousins of Sudoku.


Kakuro, also known as Cross Sums, follows the same no-repeats rule of classic Sudoku, but the grids are much closer to Crosswords. The numbers along the top and left-side are the total for each row or column, and they are the primary clues for solving the puzzle. Kakuro rarely features set numbers the way Sudoku does, instead opting for a single filled-in row or column to get the solver started.


[A 6×6 KenKen grid, courtesy of The Math Magazine on Blogspot]

KenKen takes the addition from Sum-Doku and adds subtraction, multiplication, and division to the mix. Each box has a number and a mathematical symbol. The number is the total, and the symbol is how the missing numbers interact to reach that total. For instance, in the upper right corner of the grid, there’s 24X. That means the two missing numbers from that box, when multiplied, equal 24.

And since this is a 6×6 grid, following the same one-per-row and column rules of Sudoku, you know that 4 and 6 are the missing numbers in that box, but you don’t necessarily know where to place them yet.

When it comes to Sudoku, the variations on shapes and layouts are seemingly endless. I’ve seen diamonds and snowflakes, cubes and five-pointed stars, in all sorts of sizes. You can get Samurai Sudoku with 6×6 grids, Jigsaw Sudoku in miniature, and Word Sudoku with Egyptian hieroglyphics.

While researching this post, I encountered this marvelous Sudoku variant, which the constructor calls Star Sudoku.


The numbers 1 through 9 appear once in each triangle, and there are no repeats along any row or slanted column. This puzzle is not only clever, it’s flat-out neat.

So, fellow puzzlers, what’s your favorite variation of Sudoku? Or do you prefer to stick with the classic version? Let me know! I’d love to hear from you!

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Prep for College the Puzzly Way!

It’s summer here in the United States, which means many high-school graduates are already looking forward to starting college. But for those soon-to-be freshmen, as well as high schoolers looking for an edge before university, have you considered puzzles and board games?

Now, it comes as no shock to me, but this article from the U.S. News and World Report website might surprise some, since it lists puzzles and board games as two of its five tools to develop critical thinking skills before college!

Naturally, I’ve been an advocate of puzzles as a learning tool for a long time, so it’s gratifying to see a major publication sharing the same views and ideas.

From the article:

Collections of crossword puzzles, logic problems, riddles, sudoku, word problems and word searches can be found at your local bookstore or library. The puzzles in these books are a wonderful strategy to activate different parts of your brain for a round or two of mental gymnastics, and many collections even discuss what each puzzle is meant to target within the mind.

Allow me to expand on this for a bit. Different puzzles can target different skills, so which puzzles you solve can make a big difference when it comes to critical thinking.

Crosswords encourage deduction (figuring out words from a few common letters) and a facility with wordplay (dealing with crafty clues and alternate definitions), while word searches offer great practice in pattern recognition and quick reaction times.

And the demand that Sudoku puzzles place on active attentiveness and concentration exercises parts of the brain associated with forming new memories, encouraging better memory retention.

[All three of the above pics come from our line of puzzle apps! Perfect for puzzly pre-college practice! Shameless plug now concluded!]

But the article also mentioned that certain board games can be excellent tools for honing valuable mental skills for college.

Choose board games that require more than luck – namely, strategy – for players to win. Any game where players must carefully consider their next move, recognize patterns and remember details will aid in honing critical thinking skills.

The article goes on to suggest some classics, like Chess, Checkers, and Mastermind for learning chain-thinking (planning several steps ahead) as well as Scrabble and Boggle (speedy information analysis, as well as word formation) and Clue and Risk (anticipating and reacting to the gameplay of others).

But I think they’re excluding some prime examples of board games that could benefit younger minds.

  • You could pick a cooperative game like Pandemic or Forbidden Island, which not only encourage strategic thinking, but teamwork and the free exchange of ideas (something that forced group exercises in school never really managed).
  • You could choose a rapid-change game like Fluxx (either the board game or the card game), which forces the players to adapt quickly to constantly changing rules and gameplay (a perfect microcosm of problem-solving in the real world, where things rarely remain static for long).
  • You could select a mixed-play game like The Stars Are Right, which incorporates several forms of gameplay (in this case, pattern-forming, tile-shifting, and a strategic card game akin to Magic: The Gathering or Munchkin) and forces players to exercise different forms of strategy and puzzle-solving all at once.

Just think about it. You could turn Family Game Night or Family Puzzle Time into College Prep Time in a snap. It’s win-win, or perhaps even win-win-win. What could be simpler, or more fun, than that?

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