A Pair of Brain Teasers From Your Fellow PuzzleNationers!

[Image courtesy of SharpBrains.com.]

We love brain teasers here at PuzzleNation Blog. Whether they’re riddles, logic problems, math puzzles, or challenging bits of wordplay, we take on all comers here.

We’ve solved some doozies in the past, like the Brooklyn Nine-Nine seesaw brain teaser, the diabolical long division brain teaser, and the curious way to tell time brain teaser.

In April 2019, we did a whole week of brain teasers while your friendly neighborhood blogger was at a convention. Last year, we honored the life of mathematician and puzzle icon John Horton Conway by sharing two of his favorite brain teasers.

There’s a long, proud PuzzleNation Blog tradition of cracking whatever brain teasers come our way, whether we find them ourselves, stumble across them in pop culture, or receive them from our marvelous PuzzleNationers when asked for solving assistance.

A friend of the blog discovered two brain teasers in a book of riddles and puzzles during a bookshelf cleanout recently, and they sent them our way to share with you!

We’ll post them below, and share the solutions next week! Good luck, fellow puzzlers!


Brain Teaser #1: There is a three digit number. All three digits are different. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?

Brain Teaser #2: When asked about his birthday, a man said, “The day before yesterday, I was only 25, and next year I will turn 28.” This is true only one day in a year – what day was he born?

Have you unraveled either of these brain teasers? Let us know in the comments section below! We’d love to hear from you.


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Puzzles in Pop Culture: Brooklyn Nine-Nine (Plus Will Shortz!)

[Image courtesy of FOX.com.]

In our Puzzles in Pop Culture series, we’ve featured shows as diverse as Gilmore Girls, NCIS: New Orleans, The West Wing, Hell’s Kitchen, and Parks and Recreation.

But oddly enough, the puzzliest show in the series has proven to be Brooklyn Nine-Nine, FOX’s hit sitcom about a New York precinct and its oddball collection of detectives. Not only did they pose a diabolical seesaw brain teaser in one episode, but crosswords were at the heart of another key moment in the show just last year.

And today’s post marks the show’s third appearance. Join us as we delve into “The Puzzle Master,” episode 15 of season 5.


The episode opens with detective Amy Santiago passing the sergeant’s exam and doing a dorky dance. Good start.

[Image courtesy of Spoiler TV.]

Her fiance, fellow detective Jake Peralta, has a doozy of a last case for he and Amy to solve as detectives. He presents her with a serial arson case that seem to be connected to the Saturday crossword puzzle. Amy, as a crossword fiend, is overjoyed.

Two different buildings have been set ablaze on two consecutive Saturdays, each with a puzzle left at the crime scene. The only other clue is a note sent to the puzzle’s “author” — not constructor, oddly — Melvin Stermley.

Amy immediately geeks out, mentioning that Stermley once created a puzzle where every word in the grid was the word “puzzle” in a different language. Jake then mentions that Stermley himself is coming in to help them with the case.

[Image courtesy of Brooklyn Nine-Nine Wiki.]

While Jake expects Melvin Stermley to be “a massive dork,” he turns out to be a handsome Hollywood tough guy type. Jake is instantly jealous. (For a nice bit of insider fun, Stermley is played by David Fumero, the husband of Melissa Fumero, who plays Amy Santiago.)

Amy has set up a display with both of Stermley’s puzzles connected to the fires, and the trio begin searching for leads. When Jake asks if he has the typical physique of a puzzler, he mentions that each puzzle only pays a couple hundred bucks, so he makes most of his money modeling. (No doubt a common response you’d get from any top constructor, right, folks?)

They read over the arsonist’s letter again: “Your clues I discombulate, to teach you to conjugate. The fool who fails to validate will watch as I conflagrate.”

Stermley suggests that they look at the answer grids of his puzzles for clues. Amy then jumps to anagramming some of the answer words. (The puzzler notes that Amy Santiago anagrams to “o, nasty amiga” and Jake Peralta to “eat a jerk, pal.”) Amy and Vin decide to split up the odd and even clues, leaving Jake out.

[Image courtesy of Spoiler TV.]

Getting nowhere with the anagrams, they wonder if “conjugate” in the arsonist’s letter means they should focus on the verbs, “the second best form of speech, after prepositions.” Jake suggests a different path, starting with possible suspects who don’t like Stermley, and the puzzler mentions the crossword night he’s hosting at a local bar. “It’s a total puz-hang,” according to Amy, and a good place to start looking.

While waiting in line outside the bar, Jake is disappointed no one is dressed like The Riddler. Amy points out someone wearing crossword-patterned pants. (Again, a common sight at the ACPT.) They chat with one of the other people in line, a woman who jokingly refers to Stermley as her future husband.

[Image courtesy of Spoiler TV.]

Before anyone can enter, they have to solve one of Stermley’s puzzles. Amy is tasked with anagramming the phrase “MEET A BRAINIER STUD, A” into the name of a place in the world. (Jake’s jealousy is piqued by the anagrammed message, of course.)

She quickly solves it — UNITED ARAB EMIRATES — and heads inside. But when Jake tries to follow, he discovers he has to solve a puzzle of his own to get in. The phrase “SAD ANUS LOSER, I GO IN” must be anagrammed into a film based on a classic book. Cut to Jake sneaking into the bathroom, because he couldn’t solve the anagram.

(It was DANGEROUS LIAISONS, by the way.)

While Jake waits in the bathroom for his pants to dry — he stepped into the toilet while climbing down from the window — two puzzle fans come in, discussing Stermley’s mad puzzle skills and how “Sam” must be pissed, as Stermley replaced him doing the Saturday crossword, bumping him down to work in Parade Magazine.

They mention Sam’s toughest clue, “a 5-letter word for a game popular in nursing homes,” to which Jake replies “BINGO.”

[Image courtesy of AV Club.]

Jake mentions it to Stermley, who says Sam Jepson is one of his best friends and has been out of town for weeks. Jake still thinks Jepson is a solid lead.

Amy and Stermley, meanwhile, have realized that both targeted buildings were at the intersection of numbered streets, and those numbered intersections also point to letters in Stermley’s puzzles: M and A. They plan to build a trap into Stermley’s next puzzle to catch the arsonist.

When given a choice between Jake’s approach and Stermley’s, Amy opts to go with the puzzle trap.

Back at the precinct, Amy has determined that the most common letters in people’s names that follow MA are L, X, R, and T — Malcolm, Max, Mark, and Matthew, for example — so Stermley constructs a puzzle using only one of each of those letters. (A pretty daunting challenge, but definitely doable — especially if the cryptic-style crossword grid on the board behind Amy is the puzzle in question. It would have fewer intersections.)

Amy plans to stake out the intersections for each of those four letters, assigning one of them to Jake. (Jake, meanwhile, makes a secret plan to have Charles stake out Sam Jepson’s apartment.)

[Image courtesy of Spoiler TV.]

Charles spots Sam on the move — played by crossword guru Will Shortz, no less! — and Jake leaves his assignment to intercept. He and Charles follow Sam, who sits at a corner and eats soup, then calls his Mom. It turns out he has been out of town, only having returned tonight — and his marriage proposal was rejected. Bummer.

Jake returns to his assigned intersection, and the building is on fire. He has missed the arsonist.

Amy is understandably upset with Jake when they’re back at the office. Jake confesses he’s jealous of Stermley and doesn’t want Amy to wake up one day, regretting not marrying someone as smart as her. She reassures him that he’s a brilliant detective and that’s why she wants to marry him.

[Image courtesy of FOX.com.]

Jake has a epiphany, realizing that the arsonist’s name isn’t what’s being spelled out, it’s the word MARRY. (The word “conjugate” in the letter also pointed to marriage.)

And who wants to marry Stermley?

The woman in line at the bar on crossword night.

Jake and Amy bring the woman in, and it turns out the full message she intended to spell out with her fires was “MARRY ME OR ELSE I WILL KILL YOU, YOURS FOREVER, HELEN GERBELSON.”

That would take SO MANY FIRES. (I imagine she’d have to burn down several buildings more than once, given the sheer repetition of letters and the relatively few options for numbered streets.)

But, in the end, the arsonist has been caught, thanks to the power of puzzles and good police work.

[Image courtesy of Lauren Leti’s Twitter.]

Overall, I thought this was a very fun episode of the show. The anagram gags were the puzzly highlight, though I confess, I thought they’d do more with the Will Shortz cameo.

Here’s hoping there’s a crime at the Brooklyn Nine-Nine equivalent of the ACPT next year!

Also, as someone who has seen ARSON in a thousand grids, it is funny to see someone finally link the word and the act in a puzzly way.


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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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