Getting Started with Crosswords

We spend a lot of time talking about crosswords here on PuzzleNation Blog, and rightfully so.

For more than a century now, crosswords have been the standard-bearer for paper-and-pencil puzzles. From your local paper to The New York Times crossword, from online solving to puzzle apps like our very own Penny Dell Crosswords App, crosswords sit comfortably at the apex of the proverbial puzzle mountain, atop worthy also-rans like word searches, cryptograms, and Sudoku.

[Apparently Puzzle Mountain is actually a place. Who knew?]

But in talking about crosswords, it’s easy to forget that not everyone solves them. In fact, plenty of people find them intimidating, given the mix of trivia, wordplay, and tricky cluing that typify many crosswords these days, particularly in outlets like The New York Times, The LA Times, The Guardian, and more.

So today, I thought I’d offer some helpful resources to solvers just getting started with crosswords.

First off, if you need help filling in troublesome letter patterns, Onelook is an excellent resource. Not only can you search for words that fit various patterns, but you can narrow your searches according to cluing, look up definitions and synonyms, and even hunt down phrases and partial phrases.

Along the same lines, there are websites like Crossword Tracker that offer informal cluing help culled from online databases. For something more formal, there’s XWordInfo, an online database of entries and cluing that also serves as an archive of NYT puzzles you can search for a small fee.

The NYT Wordplay Blog chronicles each day’s puzzle, including insights into the theme, key entries, and more, plus they’ve begun amassing helpful articles about crossword solving. Not only are there sample puzzles to download and solve to get you started, but there are lists of opera terms, rivers, and sports names to know to make you a stronger solver.

And if British-style or cryptic crosswords are your puzzle of choice, look no further than The Guardian‘s Crossword Blog, which frequently posts about various cluing tricks employed by crafting cryptic puzzle setters. Their “Cryptic Crosswords for Beginners” series of posts has discussed all sorts of linguistic trickery, covering everything from the NATO alphabet to elementary chemistry.

For other variety puzzles, our friends at Penny Dell Puzzles offer sample puzzles and helpful solving tips for many of the puzzles in their magazines. For example, you can find a sample Kakuro or Cross Sums puzzle on the page for their Dell Collector’s Series Cross Sums puzzle book, as well as a How to Solve PDF.

Is there a particular puzzle that troubles you, or one you find too intimidating to tackle, fellow puzzlers? If so, let us know! We can either point you toward a solving resource or tackle the puzzle ourselves in a future post to provide helpful solving tips!


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5 Questions for Constructor Doug Peterson

Welcome to 5 Questions, our recurring interview series where we reach out to puzzle constructors, game designers, writers, filmmakers, musicians, artists, and puzzle enthusiasts from all walks of life!

It’s all about exploring the vast and intriguing puzzle community by talking to those who make puzzles and those who enjoy them! (Click here to check out previous editions of 5 Questions!)

And I’m excited to welcome Doug Peterson as our latest 5 Questions interviewee!

Crossword gentleman and constructor Doug Peterson is a regular in the Los Angeles Times and many other outlets, offering topnotch grids and brilliantly fun, pop-culture-savvy cluing. Doug was also one of the constructors in this year’s Lollapuzzoola crossword tournament and a winner at this year’s American Crossword Puzzle Tournament. Anytime you encounter one of his puzzles, you’re guaranteed a great solve.

Doug was gracious enough to take some time out to talk to us, so without further ado, let’s get to the interview!


5 Questions for Doug Peterson

1. How did you get started with puzzles?

Like many others, I caught the puzzle bug from older family members, specifically my dad and maternal grandmother. I’d spend summers at my grandparents’ house, and my grandma always had a stack of Dell puzzle books on hand. My favorite thing was to tackle one of the huge 21×21 crosswords, which would literally take me days to finish. And that was great, because I had a lot of long, boring days to get through.

2. What, in your estimation, makes for a great puzzle? What do you most enjoy — or most commonly avoid — when constructing your own? What do you think is the most common pitfall of constructors just starting out?

I think the most important element in a puzzle is craftsmanship, meaning that significant effort has gone into making that puzzle as enjoyable as possible. I realize that’s a little vague, but it’s like the old line about pornography: “I know it when I see it.” Basically, the theme, fill, and clues should all demonstrate care and a personal touch.

I’m not the best at coming up with themes, so I strive to make my fill and clues pick up the slack, so to speak. There’s plenty I avoid in my grids, and I’m getting pickier all time. For the record, I’ve never used ÉTÉ in a grid. I don’t trust three-letter words with two accent marks. Also on my “banned list” are IDI, AMIN, and ULEE. I’m not going there. I hate brutal dictators, and bees kinda scare me.

The most common pitfall I’ve found among newbies is trying to do too much right out of the gate. My advice is to get a few 15×15’s under your belt before trying to construct that 21×21 triple rebus with five meta-answers and a tribute to your favorite band hidden diagonally. My first published puzzles are embarrassing to look at now. I used PATLY in my debut puzzle. PATLY? That barely resembles a word that a human would use. But I got better, and by the time I was ready to tackle something truly challenging, I had some constructing chops.

Teaser: I’ll give my best advice to newbies (and all constructors) in my answer to Question 5.

[Two of Doug’s books currently available on Amazon: Sit & Solve© Brain-Straining Crosswords and Sit & Solve© Lickety-Split Crosswords.]

3. Do you have any favorite crossword themes or clues, either your own or those crafted by others?

We’re living in a golden age of crosswords, and there are so many superb themes and clues out there, and of course I can’t think of anything specific off the top of my head right now… I solve a crapload of puzzles, more than 20 per week, so honestly it’s hard to single out themes or clues that made me say “Oooh!”

Constructors whose themes I admire include Brendan Emmett Quigley, Andrew Ries, and Erik Agard. They’re at the top of my “why the hell didn’t I think of that?” list. BEQ publishes two free high-quality puzzles a week, which boggles my mind. And he used to do three a week! Just recently, he posted puzzle #900. I would have burned out years ago. BEQ’s puzzles are a blast to solve, and they’re hip without being eye-rolly.

Andrew Ries publishes a weekly crossword (www.ariesxword.com) that’ll run you $12 bucks a year (a steal!) and consistently features fresh themes and clues. It’s often my favorite puzzle of the week. And then there’s Erik Agard over at gluttonforpun. Mind-bending, multi-level themes and clues that make me laugh out loud. This dude is the next wave of crossword puzzles.

The best venue for stand-out themes by a variety of constructors is Fireball Crosswords, edited and sometimes constructed by Peter Gordon. Shameless plug: I constructed the first Fireball puzzle of 2017, which will hit solvers’ in-boxes in January. It’s a theme that’d been bouncing around in my brain for over two years, and I finally got off my lazy butt and made the puzzle.

Cool entries do tend to stick in my head, and a couple recent entries I loved (and wish I’d thought to use myself) were BEER O’CLOCK and DC UNIVERSE. Both were in puzzles by another of my favorite constructors, C.C. Burnikel. She turns out quality puzzles on a regular basis. In fact, on a more-than-regular basis. C.C. is remarkably prolific. Nary a week goes by that I don’t solve a well-crafted Burnikel puzzle in one of the major outlets.

4. What’s next for Doug Peterson?

On the constructing front, I’d like to branch out a little and create more non-American style crossword puzzles. I love constructing cryptic crosswords. I had a couple published in the New York Times ages ago, and then I drifted away from them. I got my start writing cryptic clues back in the Dark Ages in the rec.puzzles.crosswords Usenet group. (Psst, constructors. No one remembers USENET anymore, so stop putting it in your grids. SYSOP, too.) And maybe I’ll try my hand at constructing a Rows Garden or a Marching Bands puzzle. Something outside my comfort zone.

[A. A familiar Sudoku grid; B. A Kakuro (or Cross Sums) grid; C. A Nurikabe
grid, a variation on Minesweeper-style solving; D. A Hashiwokakero grid,
which readers might remember from this year’s UK Puzzle Championship.]

Speaking of comfort zones, on the solving front, I want to get much better at solving logic puzzles. And by “get much better at,” I mean “actually be able to solve.” I’m talking about Sudoku, Kakuro, Nurikabe, Hashiwokakero (yes, that’s an actual puzzle type I just found on Google), all the puzzles with Japanese names and little lines and boxes and circles. I’ve solved maybe ten Sudoku puzzles in my life, and it would be cool to stretch my brain in another direction or many other directions.

And hey, it will open up a whole new world of puzzles that I can print out and never quite get around to solving!

5. If you could give the readers, writers, aspiring constructors, and puzzle fans in the audience one piece of advice, what would it be?

To aspiring constructors, my best advice is: Solve puzzles! I cringe when I hear a constructor say that they don’t solve puzzles or “can’t” solve puzzles. Just looking at answer grids or reading reviews of puzzles isn’t enough. To me, solving is the only way to figure out what sorts of things make a puzzle enjoyable. There’s a reason I don’t use ULEE in my grids, aside from my slight apiphobia. It’s because it bugs me when I see it in a puzzle I’m solving.

Create the kinds of puzzles that you enjoy solving, and you can’t go wrong. (Unless you like solving really crappy puzzles for some reason.) And if you’re interested in being published and getting paid a few bucks for your hard work, it’s essential to solve puzzles from the venue you’re submitting to.

OK, I’ve rambled on long enough. Look for my été-free puzzles in all the usual places. Thanks for reading. Peterson out.


A huge thank you to Doug for his time. Be sure to follow him on Twitter for the latest updates on all his puzzly creations!

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It’s Follow-Up Friday: More UK Puzzles 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’m returning to the subject of big international puzzle events!

A few weeks ago, the UK Puzzle Association hosted the 2016 UK Sudoku Championship. And this weekend, they’ve got another major puzzle event in store for puzzlers worldwide: The 2016 UK Puzzle Championship!

The event spans June 24 through June 27, and chairman Alan O’Donnell of the UK Puzzle Association sent out the Instruction Booklet for this year’s event a few days ago, continuing a string of major puzzle events in Europe and across the world.

Although the UK Puzzle Championship is only open to competitors from the UK — with the top two earning a place on the UK team for the 2016 World Puzzle 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 puzzles. Let’s take a look at some of the diabolical puzzles they’ve cooked up for this year’s event!

This Banknotes puzzle sets the tone for much of the Instruction Booklet to come, offering a number-placement puzzle with clues outside the grid. In this case, you have different valued 3×1 “banknotes” to place in the grid, and their total values add up to the numbers outside a given row or column.

So this is a bit like the game Battleship, except with different valued ships instead of different sized ones.

Here we have a more traditional Fill-In puzzle, but with an nontraditional grid shape. This one is all about efficient word placement.

Instead of placing words into this grid, the Cloud puzzle asks you to fill in which squares are covered by “clouds,” based on the total number of cloud-covered cells given on the outside of the grid. This is essentially a small Logic Art puzzle.

This Hidoku turns the usual Sudoku-solving on its ear by requiring you to place the numbers 1 through 25 into the following grid so that they form an unbroken chain. Consecutive numbers must touch, either horizontally, vertically, or diagonally.

For fans of Penny Dell Puzzles, this is like Sudoku and Word Maze had a diabolical little baby.

[I left the solution in with this one to help illustrate the solving style.]

Hashi is an intriguing deduction puzzle that follows the same cluing mentality as Blackout! or Minesweeper. Each circle contains a number indicating how many “bridges” connect that “island” to the other islands either vertical or horizontal to that island.

You’re essentially building your own Word Trails puzzle with Hashi, except you’re using numbers instead of the letters in a famous saying.

This is probably my favorite of the puzzles I’ve encountered in this Instruction Booklet, and I’m definitely looking forward to solving it this weekend.


These puzzles are just a sampling of the numerous puzzles you’ll tackle if you accept the UK Puzzle Championship challenge.

Not only are Kakuro and Sum-Doku (or Killer Sudoku) included, but also other twists on classic solving styles like Fill-Ins, Deduction puzzles, and Logic Problems.

You can check out the full Instruction Booklet here, and remember, you’ll have two and a half hours to solve as many of the 29 puzzles in the packet as possible, so good luck on June 24!


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Other puzzles you might not know! (Volume 3)

In previous editions of this series, we’ve presented some new puzzles for crossword devotees and Fill-In fans to try out. Today, let’s turn our attention to Sudoku enthusiasts.

Now, before we talk about other types of puzzles, there are numerous Sudoku variants to choose from, if you’d like just a little twist on the familiar Sudoku formula. In fact, I did an entire blog post about them, as well as posts about new variants like Will Sudoku and Pentdoku Puzzles!

There are a few lesser-known number-placement puzzles out there that might scratch your puzzly itch if you’re a Sudoku fan: Futoshiki and Beehive Hidato.

[Futoshiki image courtesy of PuzzleMagazine.com.]

Futoshiki will seem fairly familiar, since the row and column rules of Sudoku are in effect. But you have an additional placement rule to consider: the less than/greater than signs in the grid, which indicate where to place lower or higher numbers in the grid. (Futoshiki translates to “not equal” in Japanese.)

[Hidato image courtesy of TheGuardian.com.]

Beehive Hidato eschews the traditional Sudoku row/column system of the deduction in favor of chain-placement of numbers in its hexagonal grid. Your goal is to fill every cell in the grid by filling in the missing numbers between 1 and the highest number. So, instead of placing the same numbers in every row and column, you’re placing a different number in each cell, forming a single chain from 1 to the last number.

The cell containing the number 1 must neighbor the cell containing the number 2, and the cell containing the number 2 must neighbor the cell containing the number 3, and so on, all the way around the grid.

If you’re looking to go a little farther afield and leave numbers behind, I’ve got you covered.

After all, some people tend to think of Sudoku as a math puzzle, but it’s really not; it’s more of a deduction and placement puzzle. You could check out not only Fill-Ins, but also all the puzzles I’ve previously recommended for Fill-In fans. That’s a great place to start.

You could also try your hand at Brick by Brick.

[Click here or on the grid for a larger version.]

Brick by Brick puzzles are a terrific bridge between placement puzzles and crosswords, using aspects of both. You’re given the complete first row of a crossword, and all of your clues, both across and down.

But, instead of the black squares you’d normally rely on to help guide you through answering those clues and placing your words, you’ve got 3×2 bricks filled with letters and black squares, a scrambled jigsaw puzzle to reassemble.

Here you can use your deductive Sudoku skills to place black squares and entire bricks into the grid as you apply crossword-solving skills toward answering the across and down clues, working back and forth between the two to complete your grid, assembling chunks of answer words as bricks fit neatly together.

And if you prefer quote puzzles to crossword puzzles, there’s always Quotefalls.

[Click here or on the grid for a full page of Quotefalls.]

Quotefalls gives you all of the letters in a given quote, plus the black squares that separate each word from the next. But it’s up to you to figure out where in each column to place the letters above so that the quotation reads out correctly.

Sometimes that’s easy, like in the fourth column of puzzle 2 above. Since there’s three black squares and only one open square, you know exactly where that E will go. Seedling letters like that can go a long way toward helping you fill each word, and eventually, the entire quote.

It’s a different form of deduction, but one not too terribly far from the number-placement solving of Sudoku.

Any one of these puzzles could add some welcome variety to your puzzle solving, while still honoring the style and play inherent in your favorite puzzle. Give them a shot, and let us know how you like them.


Next time, we’ll be tackling recommendations for Cryptogram fans, but if you’ve got puzzle recs for your fellow puzzlers in the meantime, please let us know in the comments!

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It’s Follow-Up Friday: Wordplay-action pass 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’m posting the results of our #PennyDellFootballPuzzles hashtag game!

You may be familiar with the board game Schmovie, hashtag games on Twitter, or @midnight’s Hashtag Wars segment on Comedy Central.

For the last few months, we’ve been collaborating on puzzle-themed hashtag games with our pals at Penny Dell Puzzles, and this month’s hook was Penny Dell Football Puzzles, mashing up Penny Dell puzzles and the world of American football. Players, teams, plays, terminology, anything and everything!

Examples include: The San Francisco Three-From-Niners, Coin Tossing & Turning, or Joe Namathboxes!

So, without further ado, check out what the puzzlers at PuzzleNation and Penny Dell Puzzles came up with!


Tim Tebowl Game

Bricks and Marshawn Lynch

Up the Middle of the Road

Triple Play-action pass

Crozzle Dazzle

Pine Cone defense

Offensive Line ‘Em Up

Around the Bend Roethlisberger

Move the Chain Words

Punt reTurnabout

Running Throwbacks

End of the Line judge

Four Square pass

First and Last down

Places, Please kicker

St. Louis CryptogRams

Detroit Draw-the-Lions

Carolina’s Cam Scrambles Across Success

Tom Bull’s Eye Brady’s Perfect Spiral

Dallas’s Unlucky Star Quarterback

Beat the Clock: 2 Minute Warning Edition!

New York J-E-T-S Alphabet Style Soup

Tom Double Trouble Brady

Jim Brownders

Cris-crossword Carter

Mike Ditkakuro

Los Right Angles Rams

Fill-In-adelphia Eagles

Green Bay Crackers

Howie Many Triangles Long?

John Madd-One

San Francisco 49 of Diamonds

Emmitt’s Your Move Smith

Bart Starrspell

Michael Strahanagrams

Fearsome Foursomes

Complete-a-Word Pass

John El-Right-of-Way

Around the Blocker

Face to Faceguard

Halftime Show

Offensive Line ’em Up

QuarterPiggybacks

Endzone of the Line

St. Louis Anag-Rams

Walturnabout Payton

Gale Say-That-Again-ers

Joe Montanacrostic

Arizona Place Card-inals

Miami Dolphinish the Fours

Top to Bottom Brady


Our fellow puzzlers on Twitter also offered up some terrific entries themselves! @_screenhog contributed two great ones: Joe Montanagrams and Cryptograndstands

And @Francespuzzles blitzed us with many choice entries, including Extra Point the Way, Fourth & Aft, A Perfect Ten Yards, Gale You-Don’t-Sayers, Face to Facemask, Incomplete-A-Word, Across & First Down, Placekick Your Number, Solve & Sack, and my personal favorite, Fran Tar-KenKen-ton.

Have you come up with any Penny Dell Football Puzzles of your own? Let us know! We’d love to see them!

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You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!

A ten-digit brain teaser to melt your mind!

I’ve started to develop a reputation as something of a brain-teaser pro, given some of the beastly brain teasers we’ve featured on the blog over the last few months.

And, as such, I’ve started to receive brain teasers from friends and fellow puzzlers, challenging me to unravel them AND explain my methods to the PuzzleNation audience.

I’ve never been one to shirk a challenge, so here we go! This puzzle is entitled Mystery Number, and a little googling after solving it reveals it most likely came from this Business Insider link. (Although their solution is slightly flawed.)

Enjoy!


There is a ten-digit mystery number (not starting with zero) represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

1. A + B + C + D + E = a multiple of 6.
2. F + G + H + I + J = a multiple of 5.
3. A + C + E + G + I = a multiple of 9.
4. B + D + F + H + J = a multiple of 2.
5. AB = a multiple of 3.
6. CD = a multiple of 4.
7. EF = a multiple of 7.
8. GH = a multiple of 8.
9. IJ = a multiple of 10.
10. FE, HC, and JA are all prime numbers.

(And to clarify here for clues 5 through 9, AB is a two-digit number reading out, NOT A times B.)


[Image courtesy of Wikipedia.]

Now, anyone who has solved Kakuro or Cross Sums puzzles will have a leg up on other solvers, because they’re accustomed to dealing with multiple digits adding up to certain sums without repeating numbers. If they see three boxes (which would essentially be A + B + C) and a total of 24, they know that A, B, and C will be 7, 8, and 9 in some order.

[For those unfamiliar with Cross Sums or Kakuro solving, feel free to refer to this solving aid from our friends at Penny/Dell Puzzles, which includes a terrific listing of possible number-combinations that will definitely prove useful with this brain teaser.]

And since the digits 0 through 9 add up to 45, that provides a valuable starting hint for clues 1 and 2 (in which all 10 digits appear exactly once). A multiple of 6 (6, 12, 18, 24, 30, 36, 42) plus a multiple of 5 (5, 10, 15, 20, 25, 30, 35, 40, 45) will equal 45. And there’s only one combination that works.

So A + B + C + D + E must equal 30, and F + G + H + I + J must equal 15.

The same logic applies to clues 3 and 4 (in which all 10 digits appear exactly once). A multiple of 9 (9, 18, 27, 36, 45) plus a multiple of 2 (2, 4, 6, 8, 10, etc.) will equal 45. And there’s only one combination that works.

So A + C + E + G + I must equal 27, and B + D + F + H + J must equal 18.

And now, we jump to clue 9. Since IJ is a multiple of 10, and all multiples of 10 end in 0, we know J = 0.

This tells us something about JA in clue 10. J is 0, which means A can only be 2, 3, 5, or 7.

There may a quicker, more deductive manner of solving this puzzle, but I couldn’t come up with it. I went for a brute force, attrition-style solve.

So I wrote out all of the possibilities for clues 5 through 9, and began crossing them off according to what I already knew. Here’s what we start with:

AB = 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99
CD = 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96
EF = 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98
GH = 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
IJ = 10, 20, 30, 40, 50, 60, 70, 80, 90

Now, we can remove any double numbers like 33 because we know each letter represents a different number.

AB = 12, 15, 18, 21, 24, 27, 30, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96
CD = 12, 16, 20, 24, 28, 32, 36, 40, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 92, 96
EF = 14, 21, 28, 35, 42, 49, 56, 63, 70, 84, 91, 98
GH = 16, 24, 32, 40, 48, 56, 64, 72, 80, 96
IJ = 10, 20, 30, 40, 50, 60, 70, 80, 90

[Sorry guys, you’re out.]

And we know that J = 0, so we can remove any numbers that end in zero for AB, CD, EF, and GH.

AB = 12, 15, 18, 21, 24, 27, 36, 39, 42, 45, 48, 51, 54, 57, 63, 69, 72, 75, 78, 81, 84, 87, 93, 96
CD = 12, 16, 24, 28, 32, 36, 48, 52, 56, 64, 68, 72, 76, 84, 92, 96
EF = 14, 21, 28, 35, 42, 49, 56, 63, 84, 91, 98
GH = 16, 24, 32, 48, 56, 64, 72, 96
IJ = 10, 20, 30, 40, 50, 60, 70, 80, 90

And for AB, we know that A can only be 2, 3, 5, or 7, so we can delete any numbers that don’t start with one of those four digits.

AB = 21, 24, 27, 36, 39, 51, 54, 57, 72, 75, 78
CD = 12, 16, 24, 28, 32, 36, 48, 52, 56, 64, 68, 72, 76, 84, 92, 96
EF = 14, 21, 28, 35, 42, 49, 56, 63, 84, 91, 98
GH = 16, 24, 32, 48, 56, 64, 72, 96
IJ = 10, 20, 30, 40, 50, 60, 70, 80, 90

Hmmm, that’s still a LOT of options. What else do we know?

Well, we know from clue 10 that FE and HC are prime numbers. So they can’t be even numbers OR end in a 5. So we can eliminate any options from CD and EF that begin with an even number or a 5.

AB = 21, 24, 27, 36, 39, 51, 54, 57, 72, 75, 78
CD = 12, 16, 32, 36, 72, 76, 92, 96
EF = 14, 35, 91, 98
GH = 16, 24, 32, 48, 56, 64, 72, 96
IJ = 10, 20, 30, 40, 50, 60, 70, 80, 90

Alright, now we need to look at those big addition formulas again. Specifically, we need to look at B + D + F + H + J = 18.

We know J = 0, so the formula becomes B + D + F + H = 18. Now, take a look at our lists of multiples for AB, CD, EF, and GH. Look at the second digit for each. There’s a little nugget of information hiding inside there.

Every D and H digit is an even number. Which means that B and F must either both also be even, or both be odd in order to make an even number and add up to 18.

But, wait, if they were both even, then they would use all of our even numbers, and some combination of B, D, F and H would be 2 + 4 + 6 + 8, which equals 20. That can’t be right!

So let’s delete any even numbered options from AB and EF.

AB = 21, 27, 39, 51, 57, 75
CD = 12, 16, 32, 36, 72, 76, 92, 96
EF = 35, 91
GH = 16, 24, 32, 48, 56, 64, 72, 96
IJ = 10, 20, 30, 40, 50, 60, 70, 80, 90

Okay, we’ve whittled down EF to 2 possibilities: 35 and 91. [Here is where the Business Insider solution goes awry, because they never eliminate one of these two options.]

Clue 10 tells us that FE is a prime number, but that doesn’t help, because both 53 and 19 are prime. So now what?

Let’s return to those starting formulas.

We know that A + B + C + D + E = 30, and our handy-dandy number-combination listing tells us there are six possible ways that five digits can add up to 30: 1-5-7-8-9; 2-4-7-8-9; 2-5-6-8-9; 3-4-6-8-9; 3-5-6-7-9; and 4-5-6-7-8.

Look at the possibilities for A, B, C, D, and E according to our work thus far:

AB = 21, 27, 39, 51, 57, 75
CD = 12, 16, 32, 36, 72, 76, 92, 96
EF = 35, 91

There’s not a single 8 in any of those pairings! And five of our six possible answers for A + B + C + D + E = 30 include an 8 as one of the five digits.

Therefore, 3-5-6-7-9 and A-B-C-D-E match up in some order.

EF is either 35 or 91, but with both 3 and 5 counted among the letters in A-B-C-D-E, EF cannot be 35, so EF is 91. Let’s eliminate any option for AB, CD, GH, or IJ that include 9 or 1.

AB = 27, 57, 75
CD = 32, 36, 72, 76
EF = 91
GH = 24, 32, 48, 56, 64, 72
IJ = 20, 30, 40, 50, 60, 70, 80

Because E = 9, that leaves 3, 5, 6, and 7 as the only possible digits available for A, B, C, and D. So let’s eliminate any combinations that use numbers other than those four.

AB = 57, 75
CD = 36, 76
EF = 91
GH = 24, 32, 48, 56, 64, 72
IJ = 20, 30, 40, 50, 60, 70, 80

We can also eliminate any combinations for GH and IJ that include those four numbers.

AB = 57, 75
CD = 36, 76
EF = 91
GH = 24, 48
IJ = 20, 40, 80

Since our only possibilities for AB use 5 and 7 in some order, CD cannot be 76, so it must be 36.

AB = 57, 75
CD = 36
EF = 91
GH = 24, 48
IJ = 20, 40, 80

So, here are our options at this point:

AB = 57, 75
CD = 36
EF = 91
GH = 24, 48
IJ = 20, 40, 80

All possible solutions for GH include the number 4, so we can delete 40 as a possibility for IJ.

AB = 57, 75
CD = 36
EF = 91
GH = 24, 48
IJ = 20, 80

Let’s look at those formulas one more time. We know A + C + E + G + I = 27.

We also know C = 3 and E = 9, so A + G + I = 15. And the only combination of available digits that allows for that is 5, 2, and 8, meaning AB = 57, GH = 24, and IJ = 80.

So ABCDEFGHIJ = 5736912480.


I don’t think I’ve tackled a puzzle this tough since the seesaw brain teaser!

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