Puzzly Romance Strikes Again!

For some reason, people simply do not associate puzzles with romance. And that’s ridiculous.

In this blog alone, we’ve documented several examples of puzzly romance, including several proposals delivered with the help of our friends at Penny Dell Puzzles.

Pop culture also has its fair share of romantic moments where puzzles play a huge part. The West Wing shared a moment of hilarious, quiet domesticity between the president and the first lady where a crossword was involved. Parks and Rec celebrated Valentine’s Day with a puzzle-filled scavenger hunt.

And last week Brooklyn Nine-Nine — already familiar to PuzzleNationers for their seesaw puzzle episode — added its own unforgettable moment of puzzly romance to the pile of evidence.

[Image courtesy of Indiewire.]

The episode in question, entitled “HalloVeen,” has the officers and detectives of the 99th Precinct engaging in their annual Halloween heist to determine who is the craftiest and most brilliant member of the squad.

As the players double-cross, triple-cross, and outmaneuver each other with increasingly ridiculous and circuitous plans to acquire this year’s MacGuffin — a championship belt in the style of pro wrestling — both the players and the viewers are surprised by one player’s long con…

Jake has used the heist to propose to his girlfriend, fellow detective Amy.

Although there’s a lot of clever plotting in this episode, that’s not the puzzly moment. That comes later, as the characters each share a story explaining when they planted the idea of proposing in Jake’s head.

Jake replies that none of them are correct. It turns out, it was a quiet moment at home with Amy that convinced him:

[Image courtesy of Heroes and Heartbreakers.]

It’s not dramatic or overscripted or full of fireworks. It’s an everyday moment with the woman he loves. It’s nerdy and funny and silly and idiosyncratic. It’s simple. It feels genuine.

All thanks to a typo in a crossword.

Ain’t love grand?


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Fix These Sixes!

[Image courtesy of Daily Brain Teaser.]

It’s a new year, and I’ve already got a new math puzzle for you. A friend discovered this one and sent it my way in the hopes that I’d be able to crack this diabolical brain teaser.

Fellow puzzlers and PuzzleNationers, this is the Sixes puzzle.

0 0 0 = 6

1 1 1 = 6

2 2 2 = 6

3 3 3 = 6

4 4 4 = 6

5 5 5 = 6

6 6 6 = 6

7 7 7 = 6

8 8 8 = 6

9 9 9 = 6

The goal is to make all of the above equations true by adding mathematical symbols.

And, naturally, there are rules.

  • You can use as many mathematical symbols as you want for each equation
  • You are not allowed to use letters, so spelling out functions like “cos” is out
  • You are not allowed to add digits of any kind, so no turning a “2” into a “12”
  • The result has to be exactly 6 ( not 6.0000000000000001 or 5.999999999999999 )
  • Square roots are allowed
  • You are not allowed to change “=” to “≠” (not equal to) or manipulate the result in any way

Take a crack at it, then scroll down past the dice to see how it’s done.

Last warning before answers!

[Image courtesy of The Progzilla Files.]

Let’s start by knocking out the easiest one.

2 2 2 = 6 can be resolved as 2+2+2=6.

6 6 6 = 6 can be resolved as 6+6-6=6 or 6-6+6=6.

They get a little trickier from here, involving multiple operations.

3 3 3 = 6 can be resolved as 3×3-3=6, becoming 9-3=6.

Fractions also come into play for a few of these equations. (This can also be represented as division.)

5 5 5 = 6 can be resolved as 5+(5/5)=6, becoming 5+1=6.

7 7 7 = 6 can be resolved as 7-(7/7)=6, becoming 7-1=6.

[Image courtesy of TAF.org.]

Okay, we’re halfway there, and now the square root rule gives us a hint regarding how to resolve the 4 equation.

4 4 4 = 6 can be 4+4-(√4)=6, becoming 8-2=6.

And this formula gives us a way to crack the 8 equation.

8 8 8 = 6 can be resolved as 8-√(√(8+8))=6, becoming 8-√(√16)=6, becoming 8-(√4)=6, becoming 8-2=6.

Square roots also come into play in solving the 9 equation.

9 9 9 = 6 can be resolved as (9+9)/(√9)=6, becoming 18/3=6.

Now, admittedly, at this point, I was stumped. I had two equations left, and no ideas regarding how to proceed.

0 0 0 = 6

1 1 1 = 6

So, I reached out to a mathematician pal of mine — the same one who helped me crack the diabolical Seesaw Puzzle from Brooklyn Nine-Nine — and he immediately knew what to do: use an exclamation point.

In mathematics, an exclamation point represents a factorial, the product of every positive number between the given number and zero.

For instance, 6! represents 6x5x4x3x2x1, or 720.

1 1 1 = 6 can now be resolved as (1+1+1)!=6, becoming 3!=6, becoming 3x2x1=6.

But what about 0 0 0 = 6?

Factorials to the rescue again! You see, 0! equals 1. So we can use the 1 equation as a template for this one.

0 0 0 = 6 can be resolved as (0!+0!+0!)!=6, becoming (1+1+1)!=6, becoming 3!=6, becoming 3x2x1=6.

And there you have it, the Sixes puzzle conquered with nothing but crafty math and puzzly skills. An excellent start to a new year of brain teaser challenges!


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At least there’s no giant boulder chasing you…

[Is this the way out or a costly dead end?]

We’ve tackled all sorts of brain teasers in the past. From the Brooklyn Nine-Nine desert island seesaw to several hat puzzles, from Cheryl’s birthday logic puzzle to a diabolical light switch puzzle, we have conquered all challengers thus far!

But never before have we confronted a puzzle with as much backstory as today’s contender. Ladies and gentlemen and PuzzleNationers of all sorts, today we battle the Temple Tunnel puzzle.

Imagine that you’re a professor leading a group of eight grad students on an expedition into a booby-trap-filled temple.

[No, not THAT professor.]

After two of the students bump into an altar, they activate a trap, sending everyone scrambling for the exits before the temple collapses all around you.

The group finds itself in a room with five tunnels and an hourglass detailing how much time you have to escape. One of them leads back to the altar and the other four are possible routes of escape. Unfortunately, you can’t remember which one it is!

All you remember is that it took approximately twenty minutes to get here from the exit. How do you determine which tunnel is the correct one, and get everyone to safety?

Oh wait, there’s one more little complication. That altar the students bumped into? It released the vengeful spirits of the temple’s king and queen, which have possessed two of your students. So you can’t trust what they say.

So how do you figure out which tunnel is the right one without being deceived by your two compromised students?

[Image courtesy of XKCD.com.]

*deep breath* Wow, that’s quite a setup! So let’s summarize:

  • You have an hour to escape, and four corridors to explore.
  • Each corridor will require 40 minutes to explore: 20 minutes to determine if it’s the exit, and 20 minutes back to report your findings.
  • Whatever groupings you break the team up into, you have two possible liars among them, and no way to determine which ones are the liars before sending them down a tunnel.

For a wonderful animated version of this puzzle, as well as its solution, check out the YouTube video below from TED-Ed:

Now, while the solution itself is quite clever, I can’t help but ask certain questions:

It says that the possessed students can’t harm the others, but can they mislead them with actions as well as words?

I’ve seen several proposed solutions that included not only sending groups down the tunnels, but instructing one or more of them to leave the temple immediately if they find the exit (meaning that not seeing them return would confirm they’d found the exit). But if the liars can simply stay at the dead end, that would be a false confirmation of finding the exit.

The video is ambiguous about this, because it says the spirits will lead them to their doom, but then it also says that the curse only affects their communication.

How does the group know you’re not one of the liars?

The solution is entirely dependent upon you being able to explore a tunnel alone, because that determines the groupings for the other three tunnels. If you have to take someone with you (either an honest student or a liar), that affects your ability to draw proper conclusions from the other groupings. And even if you find the exit, the student with you could lie about it, and there’s no way to prove the truth to the group definitively.

Why not just ask each student individually a question the ancient king or queen wouldn’t know the answer to?

Presumably the spirits of ancient royalty wouldn’t know about the latest episode of NCIS or which version of Windows we’re up to.

In any case, this was a delightful mind-bender, one that has stumped many an intrepid solver. How did you do? Tell us in the comments below!


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A New Year’s Eve Countdown!

It’s New Year’s Eve, and we are literally counting down the hours until 2016, so why not celebrate the end of 2015 with a little countdown of our own?

Here are my 10 favorite blog posts from 2015!


#10 Rubik ‘Round the World

One of the most amazing things about the world today is how interconnected we all are. The Internet has made it easily to not only keep in touch with far-flung friends, but to forge new, meaningful friendships and connections with staggering ease.

And I confess, I am a total sucker for those heartwarming clickbait videos that spread the message that we are all the same. (The one of that guy doing the same dance in countries across the world comes to mind.) So seeing people from all over the world solve a Rubik’s Cube one move at a time…what can I say? It got me.

#9 Holiday Puzzly Gift Guide

Every year, one of my favorite activities is putting together our Holiday Puzzly Gift Guide. I get to include the best products sent to me for review by top puzzle and game companies, mix in some of my own favorites, and draw attention to terrific constructors, game designers, and friends of the blog, all in the hopes of introducing solvers (and families of solvers) to quality puzzles and games.

#8 Music and Puzzles

Talking about how puzzles are relevant to daily life is one of my favorite subjects for blog posts. Brain health, stress relief, the long-term benefits of puzzle solving…we’ve discussed all these topics and more during my time as lead blogger.

This year I continued that tradition with this post about how listening to music can make you a more effective solver. It’s always interesting for me to do some research and really delve into a topic — especially scientific ones because they’re often so drastically misreported or misinterpreted by mainstream outlets — and give the PuzzleNation audience the straight story.

#7 The Dress

One of the most bizarre moments of 2015 was when someone shoved their iPhone in my face and asked me what color a dress was. It wasn’t until a few moments later that I found out this was a big thing on the Internet that people were vociferously debating.

The chance to explain exactly what was going on in the photo through one of my favorite puzzly mediums — the optical illusion — was too much fun to resist, and it resulted in one of the year’s most popular, most shared blog posts.

#6 The American Crossword Puzzle Tournament

Although it’s a highlight of the puzzly calendar every year, this year’s ACPT was extra special for me because it was the first I attended in person.

Not only did I get to meet a lot of top names in crosswords — in many cases, finally getting a chance to put names to faces after many emails and tweets exchanged — but I got to enjoy the Big Fight feel of seeing so many friends and puzzlers test their mettle against some great puzzles.

#5 A Puzzly Wedding Proposal

Our friends at Penny Dell Puzzles pulled off one heck of a puzzly coup when an intrepid fellow puzzler asked them for help proposing to his girlfriend with a special Escalators puzzle.

I reached out to the lucky fiancé and got his permission to share the story with the PuzzleNation readership, and as I learned more about who was involved and how they’d managed to make it happen, I just became more and more enamored with the story. I have no doubt that years from now, this will still be one of my favorite blog posts.

#4 Max Reviews the Boston Festival of Indie Games

Guest bloggers are nothing new to PuzzleNation Blog, as Sherri regularly pops in with her app reviews, but Max Galpern pushed things to another level with his appearances throughout the year. Not only did he pioneer our first video review (with assistance from Fred), but he took over the blog for an entire day with his review of the Boston Festival of Indie Games.

Here’s hoping we can get Max back for 2016 a few times, though I suspect he’ll be in high demand.

#3 Will Sudoku

We do a lot of reviews (board game and card game reviews, puzzle reviews, tournament reviews, app reviews, etc.) and I thoroughly enjoy introducing new puzzly products and events to my fellow PuzzleNationers and sharing my thoughts on them.

But it’s rare that we get the first shot at introducing a brand-new never-before-seen puzzle or product, and that’s what separates the Will Sudoku post from many others. Serving as the debut outlet for a new puzzle was great fun and very exciting, one of those rarities that made 2015 such a terrific year.

#2 Brooklyn Nine-Nine and Island Seesaws

Brain teasers were a big part of 2015 for the blog, since several challenging ones went viral this year. But I don’t think any of them taxed my brain — both to solve AND to explain how to solve — like the island seesaw brain teaser from an episode of Fox’s sitcom Brooklyn Nine-Nine did.

It is an epic-length blog post — one I needed a mathematician friend of mine to help me write — but it broke down a tough puzzle bit-by-bit and explained every step. In a year of brain-melting puzzle posts, it still stands out.

#1 Announcing Free Daily Puzzles for the Penny Dell Crosswords App

I almost put announcing the Android release for the App here instead — because so many people had been asking about it for so long — but in the end, the free daily puzzle announcement won out, and not simply because it was a terrific new feature for the App, one that I feel would draw a lot of new eyes to the product.

Getting to interview Fred and talk about not just what we’ve been working on for years, but where we were headed in the future, made it feel like a special event for the PuzzleNation Team as a whole. Plus it was a chance to introduce all of you to another member of the team, something I hope to do more of in 2016.

It may sound self-serving or schlocky to talk about our flagship product as #1 in the countdown, but it’s something that we’re all extremely proud of, something that we’re constantly working to improve, because we want to make it the absolute best it can be for the PuzzleNation audience. That’s what you deserve.

Thanks for spending 2015 with us, through logic problems and love stories, through dresses and debuts, through Rubik’s Cubes and revelations. We’ll see you in 2016.


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Puzzles in Pop Culture: Brooklyn Nine-Nine

In previous editions of Puzzles in Pop Culture, we’ve explored opinions about crosswords, embarked on scavenger hunts with sitcom characters, and even saved New York with brain teasers alongside John McClane in Die Hard with a Vengeance. But it’s rare when a movie or TV show poses a puzzler and leaves it to the audience to solve it.

In “Captain Peralta,” a recent episode of the Fox police sitcom Brooklyn Nine-Nine, a subplot featured Captain Holt posing a brain teaser to his fellow officers.

There are 12 men on an island. 11 weigh exactly the same amount, but one of them is slightly lighter or heavier. You must figure out which.

The island has no scales, but there is a seesaw. You can only use it three times.

With Beyonce tickets going to the person who solved the puzzle, the competition was fierce. Rosa suggested using the seesaw to threaten the men into confessing. Amy and Terry suggested that the first seesaw ride involve putting six men on one side and six on the other, which Captain Holt quickly said wouldn’t work.

As it turns out, Holt was hoping one of his officers would solve the puzzle for him, since he’s been unable to crack it for years. The episode ended without providing the audience with a solution.

Thankfully, your friends here at PuzzleNation Blog would never leave you high and dry like that. Let’s get puzzling!

Now, this WOULD be a simple logic problem if you knew you were looking for someone lighter or you knew you were looking for someone heavier. In that case, a 3×3 ride, 4×4 ride, or even the 6×6 ride Amy and Terry suggested, would eliminate part of the field immediately, and the remaining two uses could determine the heavy person or the light person.

Unfortunately, in Captain Holt’s puzzle, you don’t know if the person is heavier or lighter, which makes this more difficult. For instance, if you knew you were looking for someone heavier, you could immediately eliminate anyone on the side of the seesaw higher in the air. But if you don’t know if the subject in question is lighter or heavier, then you could have a heavier person on one side or a lighter person on the other.

Diabolical.

But, with some careful deduction, you CAN solve this puzzle.

First, let’s identify our 12 castaways with the letters A through L. Now let’s divide them into three groups of four: ABCD, EFGH, and IJKL.

For the first seesaw ride, let’s weigh ABCD vs. EFGH.

There are three possible outcomes:

  • They balance, meaning we can eliminate all eight of them and our mystery person is in IJKL.
  • ABCD sinks while EFGH rises, meaning there’s a heavier person in ABCD or a lighter person in EFGH, so we can eliminate IJKL.
  • EFGH sinks while ABCD rises, meaning there’s a heavier person in EFGH or a lighter person in ABCD, so we can eliminate IJKL.

OUTCOME 1: They balance

For the second seesaw ride, we’ll take IJK and weigh them against any three of the eliminated people — let’s say ABC — because we know they weigh the same.

OUTCOME 1-1: if IJK balances against ABC, we know that L is our guy. For the third seesaw ride, weigh L against A to determine if L is lighter or heavier.

OUTCOME 1-2: if IJK sinks, one of them is heavier than ABC. For the third seesaw ride, weigh I against J. If they balance, K is the heavy one. If I or J sinks, he’s the heavy one.

OUTCOME 1-3: if IJK rises, one of them is lighter than ABC. For the third seesaw ride, weigh I against J. If they balance, K is the light one. If I or J rises, he’s the light one.


OUTCOME 2: ABCD sinks while EFGH rises

For the second seesaw ride, we have eight possible suspects — four heavy, four light — so we mix up the two previous groupings in order to eliminate some suspects. We’ll take E, F, and A and weigh them against G, B, and L. That’s two from the lighter side and one from the heavier vs. one from the lighter, one from the heavier, and one we know is standard.

Again, there will be three possible outcomes:

OUTCOME 2-1: If EFA balances with GBL, they’re all eliminated, leaving either H as a lighter person or either C or D as a heavier person. For the third seesaw ride, weigh C against D. If they balance, H is lighter. If they don’t, whichever is heavier is our guy.

OUTCOME 2-2: If EFA sinks, either A is heavy (because E and F were on the lighter side before) or G is light (because B was on the heavier side and L has already been eliminated), and we can eliminate C, D, and H. For the third seesaw ride, weigh G against L. If they balance, A is heavy. If they don’t, then G is light.

OUTCOME 2-3: If EFA rises, either B is heavy (because G was on the lighter side and L has already been eliminated) or either E or F is light (because A was on the heavier side), and we can eliminate C, D, and H. For the third seesaw ride, weigh E against F. If they balance, then B is heavy. If they don’t, whichever is lighter is our guy.


OUTCOME 3: EFGH sinks while ABCD rises

For the second seesaw ride, we have eight possible suspects — four heavy, four light — so we mix up the two previous groupings in order to eliminate some suspects. We’ll take A, B, and E and weigh them against C, F, and L. That’s two from the lighter side and one from the heavier vs. one from the lighter, one from the heavier, and one we know is standard.

Again, there will be three possible outcomes:

OUTCOME 3-1: If ABE balances with CFL, they’re all eliminated, leaving either D as a lighter person or either G or H as a heavier person. For the third seesaw ride, weigh G against H. If they balance, D is lighter. If they don’t, whichever is heavier is our guy.

OUTCOME 3-2: If ABE sinks, either E is heavy (because A and B were on the lighter side) or C is light (because F was on the heavier side and L has already been eliminated), and we can eliminate D, G, and H. For the third seesaw ride, weigh C against L. If they balance, E is heavy. If they don’t, then C is light.

OUTCOME 3-3: If ABE rises, either F is heavy (because B was on the lighter side and L has already been eliminated) or either A or B is light (because E was on the heavier side), and we can eliminate D, G, and H. For the third seesaw ride, weigh A against B. If they balance, then F is heavy. If they don’t, whichever is lighter is our guy.


This was one whopper of a brain teaser, to be sure, and I’m not surprised it stumped even the likes of the impressive Captain Holt. But, as a special treat, if you’d like to see the Captain himself explain the solution, go here and check out the embedded video. Enjoy.

Of course, it doesn’t answer the real question: who cares about weight? Why aren’t they building a boat to escape the island?

Thanks for visiting PuzzleNation Blog today! You can share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and be sure to check out the growing library of PuzzleNation apps and games!