A Conway Puzzle Solution (And Some Hints for the Other Puzzle)

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Two weeks ago, in honor of mathematician and puzzly spirit John Horton Conway, we shared two of his favorite brain teasers and challenged our fellow PuzzleNationers.

So today, we happily share the solution for puzzle #1, The Miracle Builders.

I had a window in the north wall of my house. It was a perfect square, 1 meter wide and 1 meter high. But this window never let in enough light. So I hired this firm, the Miracle Builders, who performed the impossible. They remodeled the window so it let in more light. When when they’d finished the window was a perfect square, 1 meter high and 1 meter wide.

How did they do it?

Both windows are perfect squares, 1 meter wide and 1 meter high. So how can there be a difference in the amount of light?

The trick of this puzzle is in the description. Although the original window was a perfect square, the dimensions of the square aren’t 1 meter by 1 meter. No, it was a square placed like a diamond, with one corner directly above its opposite. So the 1 meter dimensions were the diagonals, not the sides.

All the Miracle Builders had to do was build a square window in the usual arrangement (two sides horizontal, two sides vertical) with dimensions of 1 meter by 1 meter. That creates a larger window (with a diagonal of √2m) and allows more light.

Very tricky indeed.


We had several solvers who successfully cracked the Miracle Builders puzzle, but there was less success with puzzle #2, The Ten Divisibilities.

So, in addition to the original puzzle, we’re going to post some solving hints for those intrepid solvers who want another crack at the puzzle.

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…]

Here’s a few hints that should help whittle down the possibilities for any frustrated solvers:

-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.

Good luck, and happy puzzling!


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Answers to Our Thanksgiving Logic Puzzle

We’re halfway to Christmas already, but remember Thanksgiving? It wasn’t all that long ago, we swear!

We celebrated the holiday by posting a fun little logic puzzle for our fellow puzzlers and PuzzleNationers. And we’re overdue to post the solution to our little dinner dilemma!

So, without further ado, let’s get to work!


Four girls — Emma, Taylor, Madison, and Morgan — are waiting for the Thanksgiving dinner.

Each is a different age (8, 9, 10, or 11) and looking forward to eating a different Thanksgiving staple (turkey, mashed potatoes, stuffing, or pumpkin pie).

Can you puzzle out the age and favorite Thanksgiving food of each girl from the clues below?

  • Madison is looking forward to eating turkey.
  • The girl who likes pumpkin pie is one year younger than Morgan.
  • Emma is younger than the girl that loves turkey.
  • The girl who likes stuffing is two years older than Morgan.

So where do we start? Simple. We start with Morgan.

Why Morgan? Because we have two clues connected to her that mention ages, clues 2 and 4.

There is a girl one year younger than Morgan and a girl two years older. Since the ages are 8, 9, 10, and 11, that means Morgan must be 9 years old.

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Now let’s look at clue 3. The girl who loves turkey is either age 9 or 10, since we already have foods for the other ages. Emma is younger than that girl. The only way Emma can be younger than age 9 or 10 is to be 8 years old.

So let’s fill that part in.

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Sticking with turkey-related clues, we can now look at clue 1. If Madison is the one who likes turkey, she has to be age 10, because that’s the only age in the chart with both the girl’s name and the favorite food uncompleted.

And by process of elimination, that means Morgan likes mashed potatoes and Taylor likes stuffing.

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How did you do, fellow puzzlers? Did you solve the logic puzzle in time for turkey dinner? Let us know in the comments section below! We’d love to hear from you.


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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 Puzzle for Thanksgiving!

Happy Thanksgiving, PuzzleNationers!

Today is a day for celebrating with family and friends, and giving thanks for all the good things in our lives. And 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.

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!


Four girls — Emma, Taylor, Madison, and Morgan — are waiting for the Thanksgiving dinner.

Each is a different age (8, 9, 10, or 11) and looking forward to eating a different Thanksgiving staple (turkey, mashed potatoes, stuffing, or pumpkin pie).

Can you puzzle out the age and favorite Thanksgiving food of each girl from the clues below?

  • Madison is looking forward to eating turkey.
  • The girl who likes pumpkin pie is one year younger than Morgan.
  • Emma is younger than the girl that loves turkey.
  • The girl who likes stuffing is two years older than Morgan.

Best of luck unraveling our little food-filled mystery!


Oh, but before we go, don’t forget about the Deal of the Day!

Every single day through the end of 2019, we’ll be offering a special deal for our puzzle apps!

We’re talking sales, discounts, special promotions, the works! And the best part? It’s something exciting and different every single day!

Check out today’s Deal of the Day!

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It’s our Ruby Value Pack, offering 150 terrific crossword puzzles of all difficulties for your puzzling pleasure!

Don’t forget to keep your eyes peeled across all our social media (Facebook and Twitter especially!) for new announcements each and every day for the rest of the year!

Happy Thanksgiving and happy solving!


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

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!

PuzzleNation Product Review: Domino Maze

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

What is it about dominoes that makes watching them fall such a satisfying experience? Is it the meticulous prep work required for a domino display? The balance and hand-eye coordination required to place each one? The danger of upsetting the whole thing before all the pieces are in place? The potential energy harnessed and ready to be unleashed as soon as the last domino is set up?

Whatever it is, it makes for one heck of a conclusion to a logic puzzle.

The creative minds at ThinkFun have conjured up a delightful twist on their traditional complete-the-path brand of logic puzzles, incorporating not just gravity, but the click-clack cacophony of a chain reaction in a new challenge for younger puzzlers and more experienced ones alike.

In today’s product review, we’re taking a look at Domino Maze.

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[One Challenge Card’s preset pieces in place. Note the three gates, each already balanced to topple over when the domino path crosses through.]

Domino Maze builds on the usual domino-stacking skills and tricks — splitting the path, making sharp turns, redirecting kinetic energy — by adding sequential gates that your domino path must pass through in order to complete each challenge.

The gates are numbered one through three, indicating the order in which you must hit your targets. (The gates are carefully balanced, so when a domino hits the target, the weight on top flips over, raising the numbered flap high AND knocking over the next domino in your chain.)

Similar to other ThinkFun games, the puzzle includes Challenge Cards, which increase in difficulty as you work your way through the deck. Beginner and Intermediate Challenges give way later to Advanced and Expert puzzles that will have you wracking your brain to employ the required number of dominoes, build your path, and hit the gates in precise order.

Note: Be aware that you need a completely flat surface for this game. The grooves will hold the domino, but the slightest mistake could send them tumbling. That’s particularly true when the staircases are involved. There’s no need to add a level of frustration beyond the natural challenge of the game by fighting gravity AND the designers’ puzzles.

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The Beginner-level cards are your introduction to the puzzle, taking you through the motions of how to place the dominoes, utilizing the numerous grooves in both the base and the elevated platform. As you proceed, the game adds new wrinkles to the game, like using the two pivot pieces (allowing you to change direction in a single move), splitting your path with the diagonal grooves.

That elevated platform is an especially devious and clever addition, since it not only requires more dominoes (to traverse one or both of the staircases that connects the platform to the base), but requires multi-dimensional thinking, like starting your path underneath the platform versus atop the platform. In this manner of solving, Domino Maze echoes other top-down logic puzzles in the ThinkFun library like Gravity Maze and Roller Coaster Challenge.

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[Two different angles of the same Challenge Card, mid-solve.]

You also slowly develop a sense of what I call “domino math,” the ability to look at the number of dominoes you have to work with, and immediately limit your choices and potential solutions based on what you know. For instance, three dominoes in a straightaway can cover half the board, but it costs three dominoes to make a 90-degree turn in one square, so you begin to recognize where resources MUST go vs. where they COULD go.

That’s a huge benefit down the line, when your dominoes (through splits and other maneuvers) must maximize their usefulness. It seems daunting when you look at a Challenge Card and see that you have to place 18 dominoes, but honestly, that’s less intimidating than looking at a card with gates scattered all over, and seeing you only have seven or eight dominoes to work with.

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But whether you’re a younger puzzler just getting started with logics, an experienced puzzler who likes the idea of combining a little hand-eye coordination with your solving, or a domino enthusiast looking for a new challenge, you’re bound to find the ever-escalating gameplay of Domino Maze to be a treat. (And just imagine the challenging pathways you could construct with two sets. Or a Rube Goldberg device made of ThinkFun puzzles.)

Watching those dominoes fall and those gates flip with the push of a single fingertip is a very fun and satisfying way to confirm that your puzzling skills are up to snuff. Plus there’s the sound, and the tactile sense of accomplishment with a path well-deduced and well-built.

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Very few puzzles offer that kind of fanfare for a proper solve, and the logical foundation behind cause-and-effect is rarely as enjoyable as it is in Domino Maze.

Domino Maze is available from ThinkFun and other participating retailers.


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PuzzleNation Product Review: Invasion of the Cow Snatchers

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

Nobody does deduction and logic puzzle games quite like the folks at ThinkFun. We’ve wielded lasers, electrical circuits, robots, and even putty in order to conquer some of their most recent and diabolical puzzles. But they always have some new tricks up their sleeves, and their latest offering is positively magnetic.

So join us as we give the full PuzzleNation Blog review treatment to Invasion of the Cow Snatchers, a puzzle game all about bringing species together… with magnets.

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The challenge is deceptively simple: you’re an alien, and your job is to maneuver your UFO around the farm and pick up all of the cows, then finally the bull, before leaving the area.

Sounds easy, right? You’re a member of an advanced alien species, you can travel the galaxy. Picking up a few curious Earth creatures should be a cakewalk.

Well, obviously, the crew at ThinkFun already thought of that. And you’ll have plenty of obstacles to navigate and overcome before you can complete your task. Not only is there a silo you can never pass over, but there are barriers of varying heights that can impede your path.

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[Here, we’ve captured one cow, so we can pass over the green row of crops. In the second pic, we’ve captured our second cow. In the background, you can see the silo (which we can’t pass at all) and the white fence, which we can pass over with up to 2 cows.]

For instance, if you’ve already captured one cow, you can’t carry it over a barn wall, but you can carry it over the row of crops. (The walls allow between 0 and 3 cows to be carried over them, depending on their height.)

Note: Be aware that you need a completely flat surface for this game. The magnets are powerful, and they’re liable to shift and move when the UFO comes near. The bull is especially prone to this.

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Each Challenge Card requires you to navigate the grid in a specific way in order to capture all of the cows and be successful. After all, once a cow is captured, you can’t drop it. Demanding that the bull be collected last adds another wrinkle to the gameplay, since you cannot pass over the bull until all of the cows are collected, which requires creative thinking and good planning.

Honestly, I can’t think of another ThinkFun puzzle to date that requires this much movement or utilizes the full space of the board as effectively as Invasion of the Cow Snatchers.

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[Continuing the challenge card from above, we pass over the white fence, pick up our third cow, and pass over the hay bales, before rounding the corner, capturing the bull last, and making our escape.]

Finally, you have to escape the board, and there are no walls that allow you to pass with more than three captured cow tokens, so your escape route also has to be considered.

The Challenge Cards increase in difficulty as you work your way through the deck. Easy and Medium Challenges give way later to Hard and Super Hard puzzles that will have you wracking your brain to stealthily maneuver your UFO around the farm setting.

This is probably my favorite design I’ve seen from ThinkFun. The clever use of magnets, the plastic casing that separates the UFO from the rest of the board, and the impressive variety of challenges they’ve conjured with relatively few obstacles makes for a game with tons of replay value and puzzles that are always engaging, never frustrating. You KNOW there’s a path to victory. You just have to be cagey enough to find it.

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Oh, and remember how I said you can’t drop any of the cows? Well, you can if you accept the challenge of the twenty Genius level Challenge Cards that are also included. These cards utilize everything you’ve learned up to this point, but add crop circles where you can drop off cows (but not the bull) temporarily.

Why? Because it’s not just about capturing all of the cows, then the bull, then escaping. Now you must capture the cows in a very specific order. (Suddenly, the color coding of the cow tokens becomes more than a fun design choice. It becomes an integral part of the puzzle.)

This new gameplay option completely reinvents the concept. Before, it didn’t matter what in order you captured the cows, only that you got them all. It almost feels like you’re starting over from scratch, because the walls aren’t the primary obstacle anymore (though they can still offer some intriguing challenges to this new gameplay model).

The crop circles are another delightfully tongue-in-cheek addition to the already fun design of the game, playing nicely on the alien abduction gimmick.


All in all, I was thoroughly impressed by ThinkFun’s latest logic puzzle game. The concept is hilarious, the colorful and clever pieces make for fun reactive gameplay, and the puzzles are harder than you’d expect. Watching the cows fly up and snap! against the plastic as the UFO captures them never gets old!

It’s simple enough for the youngest puzzlers to get into, but there’s plenty here for parents and older puzzlers as well. (Some of the Genius level Challenge Cards really tax your brainpower!)

[Invasion of the Cow Snatchers is for ages 6 and up, available from ThinkFun and other participating retailers.]


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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 Deduction Puzzle for Independence Day!

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[Image courtesy of NWI Times.]

It’s Independence Day, and is there any better way to celebrate the history of America than with a little deduction puzzle based on some classic American symbols? I hardly think so!

Good luck and Happy Fourth of July!


To celebrate America’s birthday, a group of five enthusiastic vexillologists — devotees of the study of flags — decided to stage five days of presentations about different flags from American history.

Each person presented a different flag’s history each day (the thirteen-star flag, the fifty-star flag, the Don’t Tread on Me flag, the Marine Corps flag, or the Coast Guard flag), and the presentations were performed in a different order each day (first, second, third, fourth, or fifth).

Each vexillologist presented one flag per day, and none of them repeated a flag presentation across the five days. Similarly, none of the flag presentations happened in the same order each day. So, for instance, if a flag was first in the order on July 3rd, it wouldn’t be first in the order any other day.

Can you complete the schedule of flag presentations below?

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Are you having any puzzly celebrations for Independence Day? 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!

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!