Answer to our Thanksgiving Logic Puzzle!

Last week, we celebrated Thanksgiving with a social distance-themed logic puzzle in honor of this time of year and the peculiar circumstances of 2020.

So let’s take a look at how to untangle this puzzle and sort things out so everyone enjoys the holiday, shall we?


First, a quick reminder about the puzzle, so the clues are fresh in our minds (and you have one last chance to solve it before we walk you through the solution).

On a curious Thanksgiving in 2020, five housemates were social distancing, each engaged in different activities throughout the day. (One was streaming Hulu.)

Each housemate (including Brian) wore a different outfit — one was wearing a tank top and shorts — and was doing their activity at a different time that day (1 PM, 2 PM, 2:30 PM, 3 PM, or 3:30 PM).

From the information provided, can you determine what time each housemate did which activity, as well as what outfit they were wearing?

1. The person doing Zoom trivia did so earlier than Alex but later than the one who wore a t-shirt and jeans.

2. Luke’s activity was earlier in the day than Denise’s, but later than that of the person who wore a Christmas sweater and pants.

3. Alex (who was wearing a Pokemon onesie) had her activity earlier than the person texting Grandma but later than Denise.

4. The person playing Among Us did so later than the person Facetiming their Mom, but earlier than the one wearing pajamas (who did their activity earlier than Adam).


Okay, first things first, let’s organize the information we have.

  • There are five housemates: Adam, Alex, Brian, Denise, Luke.
  • There are five activities: Facetiming Mom, playing Among Us, streaming Hulu, texting Grandma, doing Zoom trivia.
  • There are five outfits: Christmas sweater/pants, Pajamas, Pokemon onesie, Tanktop/shorts, T-shirt/jeans.

Since many of the clues reference who or what happened earlier or later than other events, it makes sense to use the times as our anchor points, so our starting grid should look like this:

turkey logic 1

And we can immediately mark down who did the activity at 1 PM. In clue 1, the person doing Zoom trivia did their activity earlier than Alex, so Alex wasn’t the person at 1 PM. Clue 2 tells us that both Luke and Denise had someone doing activities before them, so it couldn’t be them at 1 PM. And Clue 4 tells us that the person in pajamas did their activity before Adam, so he couldn’t be the 1 PM person either. That leaves Brian as the 1 PM person.

That information tells us more as well. Alex can’t be the 2 PM person, because Clue 1 says both the Zoom trivia person and the person in t-shirt and jeans did activities before Alex. Denise can’t be the 2 PM person, because Clue 2 says both Luke and the person in the Christmas sweater did activities before Denise. And Adam can’t be the 2 PM person because Clue 4 says that both the person playing Among Us and the person wearing pajamas did activities before Adam. So Luke must be the 2 PM person.

Not only that, but since Luke did his activity after the person in a Christmas sweater and pants, that makes the sweater/pants Brian’s outfit.

We can fill in one person based on time as well. Clue 3 tells us that Alex’s activity was after Denise’s, so Alex can’t be the 2:30 PM person. And Clue 4 tells us that Adam’s activity happened after the person Facetiming Mom, the person playing Among Us, and the person in their pajamas, so Adam can’t be the 2:30 PM person. That leaves Denise as the 2:30 PM person.

So now our chart looks like this:

turkey logic 2

Let’s look at the outfits now. We know from Clue 3 that Alex is wearing the Pokemon onesie, but we’re not sure where to place Alex yet. But we can place the pajamas based on what we know.

In Clue 4, we’re told that the person wearing pajamas has their activity after the person Facetiming Mom and the person playing Among Us, and before Adam. So Adam is out. Alex and Brian are also out, because we know what they’re wearing. And Luke can’t be the person in pajamas, because his activity is second (2 PM) and at least two activities have to be done before the person wearing pajamas. That leaves Denise as the person in pajamas.

That leaves only two outfits unaccounted for: the tanktop/shorts and the t-shirt/jeans. But we can eliminate those as well. In Clue 1 we’re told that the person in t-shirt and jeans does their activity before both the person doing Zoom trivia and Alex. But Adam can’t be that person, because Adam’s activity happens after the person Facetiming Mom, the person playing Among Us, and the person wearing PJs. So Adam is wearing a tanktop and shorts, and Luke is wearing a t-shirt and jeans.

Let’s look at our chart now:

turkey logic 3

As you can see, I’ve added notes below for person/outfit combos we know that we can’t yet place.

But the information above does tell us something else.

Clue 4 tells us that the person playing Among Us did so later than the person Facetiming Mom, but earlier than the person wearing pajamas. And we know the person wearing pajamas is Denise. So that means Luke is playing Among Us and Brian is Facetiming Mom.

This information also tells us what Alex is doing. Clue 1 tells us Alex is not doing Zoom trivia, and Clue 3 tells us that Alex is not texting Grandma. And since she can’t be playing Among Us or Facetiming Mom, the only remaining option is streaming Hulu.

This same process of elimination can tell us who did the last two activities. We know Denise isn’t playing Among Us, Facetiming Mom, or streaming Hulu. But Clue 3 tells us she wasn’t texting Grandma either, so she must have been doing Zoom trivia.

Which means Adam was the one texting Grandma.

And since Clue 3 tells us that Alex’s activity happened before the person texting Grandma, we can complete our grid:

turkey logic 4

How did you do? Did you manage to unravel this holiday puzzler? Let us know in the comments section below! We’d love to hear from you!


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A Puzzle for Thanksgiving!

Happy Thanksgiving, PuzzleNationers!

Today is a day for celebrating with family and friends (although that’s harder this year), and giving thanks for all the good things in our lives.

We here at PuzzleNation want to thank you, our fellow puzzlers and PuzzleNationers, because you help make PuzzleNation one of the greatest puzzle communities in the world.

And when it comes to saying thanks, a Thanksgiving puzzle seems like the perfect offering. So we’ve cooked up a little Thanksgiving logic puzzle for you to enjoy!

Can you unravel this holiday puzzler?


On a curious Thanksgiving in 2020, five housemates were social distancing, each engaged in different activities throughout the day. (One was streaming Hulu.)

Each housemate (including Brian) wore a different outfit — one was wearing a tank top and shorts — and was doing their activity at a different time that day (1 PM, 2 PM, 2:30 PM, 3 PM, or 3:30 PM).

From the information provided, can you determine what time each housemate did which activity, as well as what outfit they were wearing?

1. The person doing Zoom trivia did so earlier than Alex but later than the one who wore a t-shirt and jeans.

2. Luke’s activity was earlier in the day than Denise’s, but later than that of the person who wore a Christmas sweater and pants.

3. Alex (who was wearing a Pokemon onesie) had her activity earlier than the person texting Grandma but later than Denise.

4. The person playing Among Us did so later than the person Facetiming their Mom, but earlier than the one wearing pajamas (who did their activity earlier than Adam).


Did you unravel this holiday puzzler? Let us know in the comments section below! We’d love to hear from you!

Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

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PuzzleNation Product Review: Escape the Room: The Cursed Dollhouse

[Note: I received a free copy of this game in exchange for a fair, unbiased review. Due diligence, full disclosure, and all that.]

All this week, we’ve been discussing different ways to enjoy escape room-style solving from home. We’ve measured each style against the various elements present in most escape rooms — searching the space, finding clues, interacting with the environment, solving puzzles, and experiencing the narrative — to see which ones help scratch this particular puzzly itch from the comfort of your own house.

Today, we continue that journey as we look at ThinkFun’s most elaborate and engaging escape room puzzle game yet. Join us as we accept the challenge of Escape the Room: The Cursed Dollhouse.

Now, unlike our typical reviews which are absolutely loaded with pictures showing you the art, the puzzle layout, different solving styles, and so on, this review may feel a little sparse on the details. But unfortunately, when you’re talking about an escape room puzzle game that’s this involved, this elaborate, and this labor-intensive to bring it to fruition, I wouldn’t want to ruin a single moment of puzzle-solving fun for one of our readers.

So instead, let’s get into the spirit with a nice, spooky little intro.


Every neighborhood has that one house, the one kids whisper about. The one that inspires spooky stories and dares to see how far you can progress into the yard before you panic and run back to your friends.

Your neighborhood is no different. Mr. Garrity’s house has become that mysterious house, ever since his young daughter went missing. Now there are strange lights coming from the shed in his backyard, and other children have been reported missing.

What is going on in that mysterious shed? You decide to find out.

You sneak in, and you’re baffled to find nothing suspicious at all. Just a dollhouse sitting on the work table.

Except it’s glowing…

Drawing you closer…

Until you take one step too many…

Suddenly, the real game begins. And your puzzly skills are the only thing standing between you and a monstrous curse!


A three-dimensional interactive puzzle-solving experience, Escape the Room: The Cursed Dollhouse is one of the most impressive puzzle games I’ve ever seen from ThinkFun. (And when you consider their previous efforts involving magnets, lasers, and other fantastic elements, that’s really saying something.)

Designed for solvers 13 and older, The Cursed Dollhouse is expected to take upwards of two hours to solve, and between the setup, exploring the various rooms, and tackling the numerous different puzzles inside, that feels like a very fair assessment.

After sliding the box from its protective (spoiler-preventing) sleeve, both the top and bottom of the box itself open up to form the frame of the dollhouse. Thick punch-out boards provide the floor, roof, and various pieces of furniture for the house, and an envelope full of different materials await eager solvers to challenge their minds with mechanical puzzles, riddles, deduction, and outside-the-box thinking.

Furniture, walls, ceiling, floor… every inch of the playspace is utilized in some form or fashion, creating one of the most immersive escape room game experiences I’ve ever played. Heck, some puzzle apps aren’t this engaging, and that’s with no physical barriers or restrictions when it comes to the puzzles.

One of the hardest things to replicate from the escape room experience is the tactile sensation of puzzle solving. The sheer joy and satisfaction of physically manipulating pieces, moving objects, finding secrets, fitting pieces together, and completing tasks is very difficult to simulate in miniature.

But this game has that solving fun in SPADES. Virtually every piece has to be handled or used in some way, and getting to play around with these pieces puts all sorts of solving skills to the test, whether it’s jigsaw-style puzzling, pattern recognition, brain teasers, or logical deduction.

And anyone who experienced their fair share of escape rooms knows the feeling of dealing with puzzles in stages. Some of the game pieces and items you find are relevant to the puzzles at hand, while others must be tucked aside or saved to be carried forward into different areas. The Cursed Dollhouse is no different, offering puzzles for each room in the house as well as information and game pieces to keep with you that will prove vital later.

It can be a bit overwhelming to have so much at hand at once, but it’s immensely satisfying to slowly assign different pieces to their particular puzzles and eliminate them one by one. It’s like whittling down the puzzliest to-do list of all time, and it’s great fun.

They’ve even added a new spin to a classic puzzler’s tool.

Anyone who has bent their brain with one of ThinkFun’s earlier Escape the Room games, as well as readers of yesterday’s post, will be familiar with one of the key solving elements: the decoder ring.

Utilizing a system of symbols for every puzzle, the decoder ring even has a locking feature to add a touch more suspense to the proceedings. Once you’ve turned each wheel and lined up your symbols, you slide the locking lever to the side, and several small windows open in the center of the disc. If the symbols revealed match the puzzle symbol, you’ve got the correct solution!

It’s a nice little touch that adds a lot to an age-old solving trope, and seeing the faces of younger solvers light up when the ring confirms their solve is a terrific moment of puzzling to treasure.

Similar to the Exit: The Game products, The Cursed Dollhouse also has a guidebook. It offers descriptions of the narrative as you progress and instructions on when you can proceed. For younger solvers, it’s a solid framework for the sometimes chaotic and undirected energy of escape room-style solving.

The Cursed Dollhouse offers fewer moments of frantic running around, but you won’t miss it; you’ll be too busy poring over every inch of the house and the gameplay pieces to miss all the skittering about you’re used to.

Be careful, though; younger solvers and older alike should be wary of the tape and sticky substances holding many of the various gameplay elements in the house in place. I worried on more than one occasion that I might damage one of the gamepieces just trying to free it. They’ve traded a bit of user-friendliness in service to keeping the puzzle elements in their places.

The game also offers an online resource to print and recreate any puzzle elements you manipulate or destroy in the course of your solve, so that you can reset the game for other players. It’s a nice touch that ensures more players get a chance to tackle this devious series of puzzles, and also helps mitigate a price point that’s a little higher than the average at-home escape room set.

The webpage also offers solving hints and solutions for any puzzles that flummox you, complete with visuals and videos, so you can not only progress forward, but learn precisely how the puzzle works (so if you encounter a similar puzzle in the future, you’ll know what to do).

I really can’t say anymore with giving something away, so I can only hope this review has managed to convey just how impressed I am by this puzzle game. The amount of thought, detail, and care that has gone into it is staggering, only matched by the ingenuity and deviousness of the puzzle designers. It brings the escape room experience home like never before, and young solvers and older alike will find plenty to enjoy in this meticulously crafted package.

Plus it’s gloriously spooky, which makes it perfect for fall and Halloween solving.

Escape the Room: The Cursed Dollhouse will be available on October 1st from Amazon for $42.99, and it’s worth every penny.


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Kickstarter Roundup!

Oh yes, it’s that time again.

For years now, crowdfunding platforms like Kickstarter and Indiegogo have been hotbeds of innovative puzzle and game design, and I’m always happy to spread the word about worthy projects that I think will delight and intrigue my fellow PuzzleNationers.

So let’s take a look at some projects that are currently seeking funding and see if any pique your interest! (This time around, we’ve got twice as many recommendations as usual! So much puzzly potential!)


atoz crossword

The first is a project by Fireball Crosswords and Fireball Newsflash Crosswords constructor Peter Gordon, entitled A-to-Z Crosswords Volume 2: More Petite Pangram Puzzles.

The project is easy to explain, but mindblowing to think about. Every single day for 24 WEEKS, you get a 9×11 crossword puzzle that contains all 26 letters. The puzzles range from easy to medium in difficulty, arrive by email, and are constructed by Gordon and professional puzzler Frank Longo.

This is a very cool project that deserves your support — they’re a little more than a third of the way there, with 9 days to go — and you should definitely check it out!

puzzle postcard

The next project is Puzzle Postcards: Season Two by the Enigma Emporium.

Last year, Wish You Were Here was part of our Holiday Puzzly Gift Guide, and it’s fantastic to see that the Enigma Emporium is Kickstarting another puzzle postcard mystery this year.

Essentially, an entire mystery is concealed within a handful of postcards, challenging you to mine them for every scrap of information as you uncover a series of coded messages. It’s spycraft in an envelope, very clever stuff.

Already funded with 12 days to go — and carrying a solid track record of previous successful Kickstarter projects behind them — I cannot recommend this one highly enough. I loved Wish You Were Here, as well as the follow-up series.

fuzzies

For a change of pace, our next project is The Fuzzies.

Basically, this is a Jenga-style dexterity game, but made out of little fuzzy balls instead of pieces of wood. And instead of choosing which piece you remove and place on top, that is determined by a deck of cards instead.

I don’t know how it works — actually staying upright in the first place — but apparently it does.

This family-friendly game has already tripled its funding goal with 29 days to go, so it might be right up your alley.

enigmas

The next project we’re sharing today is the ENIGMAS deck of puzzle playing cards.

David Kwong — constructor, magician, and all-around puzzly fellow — has masterminded a puzzle mystery and a series of hidden messages and ciphers, all contained within a deck of cards.

ENIGMAS marries some of the ideas from his Enigmatist show — specifically the historical aspects — with an ingenious puzzle hunt to create an intriguing solving situation. Plus, once you’ve cracked all the puzzly elements, you’ve still got a beautiful deck of cards to enjoy.

This project has blasted well past its funding goal, and with 9 days to go, they’ve added a special limited-run deck of red cards (to compliment the standard blue deck) that will only be offered to Kickstarter backers and never sold in stores. With a pedigree like David’s, you can’t go wrong!

sherlock

Our next project is bigger and no less ambitious. It’s Sherlock’s Mysteries: An Interactive Puzzle Adventure (not to be confused with another Sherlock-based Kickstarter running right now).

Combining board game and escape room elements, this project contains 10 mysteries (described as chapters) that combine into one interwoven narrative where you try to save the life of Sherlock Holmes!

By combining murder mystery-style solving with puzzles like ciphers and deduction puzzles, this project definitely tries to encapsulate the experience of being the Great Detective from the comfort of your own home.

About halfway to its goal with 21 days left, this project isn’t a lock (given the price tag of $135 to experience the entire story), but it’s definitely worth a look. (I’m especially intrigued by the fact that certain levels offer “refill kits” that allow the experience to be played more than once!)

shivers

For something just as puzzly but more immersive from a roleplaying point of view, there’s The Shivers.

In this game, someone has gone missing in the house owned by the Shivers family, and you play one of the family members trying to solve the mystery and defeat dangerous foes at work in various sinister and creepy scenarios.

This gameplay is bolstered by pop-up 3-D models of the various rooms of the house, bringing the setting and different stories to life right before your eyes.

This is a very clever combination of puzzle hunt, roleplaying game, and pop-up book that I’ve never really seen before, and like some of these other projects, it has blown past its funding goal with strong support from interested gamers and puzzlers.

legacy

Following the escape room/puzzle mystery at home template, Legacy: Quest for a Family Treasure is our next project to discuss.

You receive a black box in the mail, and inside, you discover in your estranged father’s will that there is a family treasure hidden somewhere in Europe. And you’ll have to unravel secrets of the past in order to secure your future.

This immersive mystery involves audio and video clues, physical evidence to pore over, and even incorporates Internet searching into the gameplay. I’ve been thoroughly impressed with the level of depth and attention to detail in this one, and clearly I’m not the only one, as the project has already met and surpassed its funding goal with 10 days to go.

The familial element adds a neat twist to the mystery-at-home genre, and I suspect this project will do very well.

labyrinth

The last project we’ll be sharing today is The Labyrinth: An Immersive Multi-Platform Puzzle Challenge.

There’s a lot of stuff included in this one: puzzle boxes, ciphers, maps, tools. They’re sending you a CRATE full of material here. The goal is to move through the various chambers of a labyrinth, solving puzzles as you go.

With 55 puzzles included — and an expected solve time of 8-10 hours — this is a breathtaking amount of puzzly paraphernalia. So there’s cost to consider here. The full puzzle costs $195 (there’s even a more expensive deluxe edition), so although that easily makes it the priciest project we’re discussing today, but also one of the most visually impressive.

And yet, with 14 days to go, they’ve already passed their funding goal nine times over. Check it out and see what you think of the expansive puzzle selection offered here.


Have any of these games or projects hooked you? Tell us which ones you’re supporting in the comments section below! And if there are any campaigns you’re supporting that we missed, let us know!

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PuzzleNation Product Review: Chicken War

chicken war header

[Note: I received a free copy of this game in exchange for a fair, unbiased review. Due diligence, full disclosure, and all that.]

The farm is no longer the quiet, idyllic escape you pictured when learning the sounds barnyard animals make. Instead, it has fallen to factional fury and un-cooped combat between various groups of chickens vying for victory. Such is the setting for ThinkFun‘s latest brain-training game, the colorful and crafty tile game Chicken War.

chickenwar1

There are two ways to win Chicken War. You can either be the last player standing or the first player to complete their army. To be the last player standing, your opponents’ leaders must be identified. To be the first player to complete your army, you have to have nine other chickens with two traits in common with your leader.

As you can see, Chicken War’s hybrid style of play combines the player observation of a game like Throw Throw Burrito or Scrimish with the deductive reasoning of a game like Clue.

chickenwar2

Each player is trying to recruit chickens for their army, and must do so in full view of the other players. This means that you have to strategize not only your recruitment process, but how to do so without revealing too much to your opponents. Plus you have to do all that while keeping an eye on your opponents’ efforts to recruit!

First, you select your leader from the ten starting chickens in your yard. Optimally, you’ll pick a leader where many of the other starting chickens already share two traits, which gives you a leg up in building your army.

chickenwar3

You’ll hide your leader token under that particular chicken to mark it, using your screen to do so away from the prying eyes of other players.

Remember, that’s two traits and only two traits in common.

chicken war trait

The four possible traits, as shown above, are weapon, shirt color, eyewear, and footwear. Each trait has three variations. For instance, shirt color can be blue, red, or green. Eyewear can be sunglasses, mask, or none.

(Keep those four traits in mind. Body type, pose, and style of tail are all irrelevant, but can be distracting.)

chickenwar9

As you can see here, the top two chickens have two traits in common: shirt color and eyewear. (Footwear and weapon differ.) The two bottom chickens have three traits in common: shirt color, eyewear, and footwear. Therefore, if 05 and 06 are leaders, 05 has a recruit, but 06 does not.

How do you recruit chickens? By drawing from the discard pile. You either keep the new chicken and discard one of the chickens from your yard, or you immediately discard the new chicken.

chickenwar4

The only other ways to recruit chickens are to use the two special tiles: steal and infiltrate.

Steal lets you take a chicken from another player’s yard and discard one of your unwanted chickens into the discard pile. This not only gives you a new chicken, but leaves your opponent one chicken short. This can be a strategic advantage, because any player with fewer than 10 chickens can’t lob an egg and cannot win the game, even if their remaining chickens all match the leader.

chickenwar8

Infiltrate allows you to swap one of your chickens with one of your opponents’ chickens. That player must then tell you one trait your chicken (the one placed in their yard) has with their leader. If there are no traits in common with the leader, they must tell you that instead. And if you accidentally trade for their leader, they must pick a new leader and start over. So in any case, you gain a new chicken and important knowledge about your opponent’s game.

If multiple players gang up on a single player, the Infiltrate card can prove very dangerous, eventually outing the player’s leader and making them easy pickings for an egg and elimination from the game. (This tactic is more likely to catch new players, as more experienced players would endeavor to repeat the same revealed trait over and over, whenever possible.)

So each turn, you must either draw a chicken from the discard pile or lob an egg.

chickenwar5

Lobbing one of your three eggs means you place your egg on a chicken in another player’s yard that you suspect is their leader. If you’re correct, that player is out.

But if you’re wrong, you lose an egg and have to discard two chickens from your yard, leaving yourself two chickens short of victory. (Also, as we stated before, you can’t win the game or lob an egg with fewer than 10 chickens in your yard.)

chickenwar6

The two methods of winning can often lead to two different styles of gameplay. Either a player focuses on their recruitment, hoping to be the first to complete their army, or they focus on eliminating another player by sussing out who their leader chicken is.

This adds a lot of variety to the game, particularly when it comes to repeat playthroughs. Figuring out your opponents’ tactics can inform your own, and yet, you don’t want to tip your hand.

Once I had one or two playthroughs behind me, I really started getting invested in the gameplay and trying to get into my opponents’ heads. (Also, there’s something delightfully demented about these chickens all being armed with “weapons” we would use to make breakfast from their eggs. That’s a nice touch.)

chickenwar7

Although it makes for a tense, enjoyable one-on-one game, the full potential of Chicken War comes alive with all four players involved. It forces to split your attention, retain a lot of information, and constantly adapt your strategy to an ever-shifting landscape.

As you can see, there’s a surprising amount of thought, strategy, and complexity behind this so-called guessing game, and it makes Chicken War a terrific gateway game to other board games in the same style, but with more complex rulesets or player choices. War is hell, but Chicken War is healthy brain-fueled fun.

[Chicken War is available from ThinkFun and other retail outlets.]


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Answer to the Fiendish Second Conway Puzzle, The Ten Divisibilities!

John_H_Conway_2005_(cropped)

Last month, in honor of mathematician and puzzly spirit John Horton Conway, we shared two of his favorite brain teasers and challenged our fellow PuzzleNationers to crack them.

Two weeks ago, we shared the solution to puzzle #1The Miracle Builders, and offered a few hints for puzzle #2, The Ten Divisibilities.

Now that we’ve heard from a few solvers who either conquered or got very close to conquering the second puzzle, we happily share both the solution and how we got there.


The Ten Divisibilities

I have a ten digit number, abcdefghij. Each of the digits is different, and:

  • a is divisible by 1
  • ab is divisible by 2
  • abc is divisible by 3
  • abcd is divisible by 4
  • abcde is divisible by 5
  • abcdef is divisible by 6
  • abcdefg is divisible by 7
  • abcdefgh is divisible by 8
  • abcdefghi is divisible by 9
  • abcdefghij is divisible by 10

What’s my number?

[To clarify: a, b, c, d, e, f, g, h, i, and j are all single digits. Each digit from 0 to 9 is represented by exactly one letter. The number abcdefghij is a ten-digit number whose first digit is a, second digit is b, and so on. It does not mean that you multiply a x b x c x…]

And here are the hints we offered to help:

-If you add all the digits in a number, and the total is divisible by 3, then that number is also divisible by 3.
-If the last two digits of a number are divisible by 4, then that number is divisible by 4.
-If the last three digits of a number are divisible by 8, then that number is divisible by 8.


The solution is 3816547290.

So, how do we get there?

First, we use process of elimination.

Any number divisible by 10 must end in a zero, so j = 0.

Any number divisible by 5 must end in a zero or a five, so e = 5 (because each digit only appears once).

That gives us abcd5fghi0.

But that’s not all we know.

If a number is divisible by an even number, that number must itself be even. So that means b, d, f, and h must all be even numbers (i.e. some combination of 2, 4, 6, and 8). That also means that a, c, g, and i must all be some combination of the remaining odd numbers (1, 3, 7, and 9).

That’s a lot of information that will come in handy as we solve.

So, where to next? Let’s look at one of those even-numbered spots.

We’ve been told that abcd is divisible by 4. But any number is divisible by 4 if the last two digits are divisible by 4. So that means cd is divisible by 4.

So, if c is odd, d is even, and cd is divisible by 4, that limits the possibilities somewhat. cd must be 12, 16, 32, 36, 72, 76, 92, or 96.

So d is either 2 or 6.

That will be helpful in figuring out def. And knowing def is the key to this entire puzzle.


One of the clues we offered in our last post was that if the sum of a number’s digits is divisible by 3, then that number is also divisible by three. We know abc is divisible by 3, so that means a + b + c is also divisible by 3.

And if something is divisible by 6, then it’s also divisible by 3, so a + b + c + d + e + f is divisible by 3.

Here’s where things get a little tricky. Since a + b + c + d + e + f is divisible by 3, and a + b + c is divisible by 3, then when you subtract a + b + c from a + b + c + d + e + f, the result, d + e + f would also be divisible by 3.

Why is that helpful? Because it means we can look at def instead of abcdef, and we know a lot about def right now.

d is either 2 or 6. e is 5. f is either 2, 4, 6, or 8. And the sum of d + e + f is divisible by 3.

So that gives us two possibilities to deal with, either 2 + 5 + f, where the sum is divisible by 3, or 6 + 5 + f, where the sum is divisible by 3.

Since each number is only used once, that’s six possible equations:

  • 2 + 5 + 4 = 11
  • 2 + 5 + 6 = 13
  • 2 + 5 + 8 = 15
  • 6 + 5 + 2 = 13
  • 6 + 5 + 4 = 15
  • 6 + 5 + 8 = 19

Only 258 and 654 have sums divisible by 3, so they’re our two possibilities for def.

We’ll have to try both of them to see which is the correct choice. How do we do that?

Let’s start with the assumption that def is 258.


That would mean our answer is abc258ghi0. We know b and h have to be even numbers, and only 4 and 6 are left as options. Since fewer numbers are divisible by 8 than by 2, let’s look at abc258gh.

One of the other hints we offered was that if the last three digits of a number are divisible by 8, then the whole number is divisible by 8.

So that means if abc258gh is divisible by 8, then 8gh is divisible by 8. That’s much more manageable.

So, f is 8, h is 4 or 6, and g is either 1, 3, 7, or 9. That gives us eight possibilities for 8gh: 814, 834, 874, 894, 816, 836, 876, and 896.

Dividing each of these by 8 reveals only two possible choices: 816 and 896. That means, in this scenario, h is 6, b is 4, and our number is a4c258g6i0.

What’s next? Well, remember that trick we did with abcdef before? We’re going to do it again with abcdefghi.

Any number divisible by 9 is divisible by 3. Our rule of sums tells us that a + b + c + d + e + f + g + h + i is also divisible by 3. And since a + b + c + d + e + f is divisible by 3, subtracting it means that g + h + i is also divisible by 3.

With 816 and 896 as our possibilities for fgh, that means our possibilities for ghi are 16i and 96i. That gives us the following possibilities: 163, 167, 169, 961, 963, 967, where the sum of our answer must be divisible by 3.

  • 1 + 6 + 3 = 10
  • 1 + 6 + 7 = 14
  • 1 + 6 + 9 = 16
  • 9 + 6 + 1 = 16
  • 9 + 6 + 3 = 18
  • 9 + 6 + 7 = 22

963 is the only one that works, which gives us a4c2589630. With only 1 and 7 remaining as options, our possible solution is either 1472589630 or 7412589630.

But, if you divide either 1472589 or 7412589 by 7 — which is faster than running every one of the 10 conditions through a calculator — neither divides cleanly. That means 258 is incorrect.


I know that was a lot of work just to eliminate one possibility, but it was worth it. It means 654 is correct, so our solution so far reads abc654ghi0.

And we can use the same techniques we just employed with 258 to find the actual answer.

We know b and h have to be even numbers, and only 2 and 8 are left as options. Again, since fewer numbers are divisible by 8 than by 2, let’s look at abc654gh.

4gh is divisible is 8. So, f is 4, h is 2 or 8, and g is either 1, 3, 7, or 9. That gives us eight possibilities for 4gh: 412, 432, 472, 492, 418, 438, 478, and 498.

Dividing each of these by 8 reveals only two possible choices: 432 and 472. That means b is 8, and our number is a8c654g2i0.

Now, let’s look at ghi.

With 432 and 472 as our possibilities for fgh, that means our possibilities for ghi are 32i and 72i. That gives us the following possibilities: 321, 327, 329, 721, 723, 729, where the sum of our answer must be divisible by 3.

  • 3 + 2 + 1 = 6
  • 3 + 2 + 7 = 12
  • 3 + 2 + 9 = 14
  • 7 + 2 + 1 = 10
  • 7 + 2 + 3 = 12
  • 7 + 2 + 9 = 18

Okay, that leaves us four possibilities for ghi: 321, 327, 723, and 729.

Stay with me, folks, we’re so close to the end!

Let’s look at our four possibilities:

  • a8c6543210 (79)
  • a8c6543270 (19)
  • a8c6547230 (19)
  • a8c6547290 (13)

Next to each number, I’ve placed the only digits missing in each scenario, two for each.

That means there are only 8 possible ways to arrange the remaining numbers:

  • 7896543210
  • 9876543210
  • 1896543270
  • 9816543270
  • 1896547230
  • 9816547230
  • 1836547290
  • 3816547290

So let’s do what we did last time, and divide each chain at the seventh number by 7.

  • 7896543 / 7
  • 9876543 / 7
  • 1896543 / 7
  • 9816543 / 7
  • 1896547 / 7
  • 9816547 / 7
  • 1836547 / 7
  • 3816547 / 7

Only one of the chains can be cleanly divided by 7, and it’s 3816547.

Which means the solution for abcdefghij is 3816547290.


I know this was a monster of a solve — it rivals our Brooklyn Nine-Nine seesaw puzzle solution in complexity — but it’s one that every one of our fellow PuzzleNationers are capable of puzzling out.

How did you do on this diabolical brain teaser, folks? Let us know in the comments section below. We’d love to hear from you!


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