Puzzles in Pop Culture: Square One TV

Puzzles in Pop Culture is all about chronicling those moments in TV, film, literature, art, and elsewhere in which puzzles play a key role. In previous installments, we’ve tackled everything from The West Wing, The Simpsons, and M*A*S*H to MacGyver, Gilmore Girls, and various incarnations of Sherlock Holmes.

And in today’s edition, we’re jumping into the Wayback Machine and looking back at the math-fueled equivalent of Sesame Street: Square One TV!

[The intro to Square One TV, looking more than a little dated these days.]

This PBS show ran from 1987 to 1994 (although reruns took over in 1992), airing five days a week and featuring all sorts of math-themed programming. Armed with a small recurring group of actors, the writers and producers of Square One TV offered many clever (if slightly cheesy) ideas for presenting different mathematical concepts to its intended audience.

Whether they were explaining pie charts and percentages with a game show parody or employing math-related magic tricks with the aid of magician Harry Blackstone, Jr., the sketches were simple enough for younger viewers, but funny enough for older viewers.

In addition to musical parodies performed by the cast, several famous musicians contributed to the show as well. “Weird Al” Yankovic, Bobby McFerrin, The Fat Boys, and Kid ‘n’ Play were among the guests helped explain fractions, tessellations, and other topics.

[One of the many math-themed songs featured on the show.]

Two of the most famous recurring segments on Square One TV were Mathman and Mathcourt. (Sensing a theme here?)

Mathman was a Pac-Man ripoff who would eat his way around an arcade grid until he reached a number or a question mark (depending on this particular segment’s subject).

For instance, if he came to a question mark and it revealed “3 > 2”, he could eat the ratio, because it’s mathematically correct, and then move onward. But if he ate the ratio “3 < 2”, he would be pursued by Mr. Glitch, the tornado antagonist of the game. (The announcer would always introduce Mr. Glitch with an unflattering adjective like contemptible, inconsiderate, devious, reckless, insidious, inflated, ill-tempered, shallow, or surreptitious.)

Mathcourt, on the other hand, gave us a word problem in the form of a court case, leaving the less-than-impressed district attorney and judge to establish whether the accused (usually someone much savvier at math than them) was correct or incorrect. As a sucker for The People’s Court-style shenanigans, this recurring segment was a personal favorite of mine.

But from a puzzle-solving standpoint, MathNet was easily the puzzliest part of the program. Detectives George Frankly and Kate Tuesday would use math to solve baffling crimes. Whether it was a missing house, a parrot theft, or a Broadway performer’s kidnapping, George and Kate could rely on math to help them save the day.

These segments were told in five parts (one per day for a full week), using the Dragnet formula to tackle all sorts of mathematical concepts, from the Fibonacci sequence to calculating angles of reflection and refraction.

These were essentially word problems, logic problems, and other puzzles involving logic or deduction, but with a criminal twist. Think more Law & Order: LCD than Law & Order: SVU.

Granted, given all the robberies and kidnappings the MathNet team faced, these segments weren’t aiming as young or as silly as much of Square One TV‘s usual fare, but they are easily the most fondly remembered aspect of the show for fans and casual viewers alike.

Given the topic of Tuesday’s post — the value of recreational math — it seemed only fitting to use today’s post to discuss one of the best examples of math-made-fun in television history.

Square One TV may not have been nearly as successful or as long-lasting as its Muppet-friendly counterpart, but its legacy lives on in the hearts and memories of many puzzlers these days.


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(More Than) 5 Questions: Escape the Room edition!

Welcome to a very special edition of 5 Questions!

Usually, 5 Questions is simply that: five individual questions answered by our guest. But this time around, we’ve ditched the 5 Q format in lieu of a more relaxed, conversational interview. I hope you enjoy!


Escape the Room games started as a video-game phenomenon, but have since moved into the real world with great success as teams are tasked with physically finding clues and solving puzzles in order to escape!

[Darcy, right, poses with another solver, complete with
deerstalker and Meerschaum pipe a la Sherlock Holmes.]

Penny Dell Puzzles social media coordinator (and friend of the blog) Darcy recently tackled the challenge posed by Mission Escape Games, and she was gracious enough to take the time out to answer some questions about this intriguing puzzle-solving experience.

So without further ado, let’s get to it in a very special edition of 5 Questions!


So, Darcy, correct me if I’m wrong, but your friend invited you to be locked in a room with her, with only your wits and cunning to help you both escape within a certain amount of time? How did this come about?

As unfavorable as it may seem, it was actually a birthday gift. My husband bought me tickets to Mission Escape Games in NYC, and we went with a group of friends.

Oh, so how many of you could be in a given escape room? (I’m assuming there is more than one.)

There are a few rooms. We had 9 people in our room. Our group was teamed up with another group to find out what happened to Dr. Jekyll before Mr. Hyde showed up.

All the other rooms have other themes, and the owners try to change up the challenges frequently. That’s so people can keep coming back and playing something fresh, but also so others who have played won’t give away the secrets of how to escape

So your group and another team are all in a room together. What does the room look like? Is there someone there to guide you and answer questions, or are you on your own?

You’re on your own! We were told that we had an hour to escape and to look everywhere — and they mean everywhere — for clues. We walked into a small Victorian-era room with a fireplace and other period props and just started searching. We upended tables, took out drawers, you name it.

Many clues didn’t make sense at first, but as the game progressed, we realized every clue was there for a reason. There was also a small TV screen in the corner of the room that very ominously counted down your time.

But as we found out, the TV screen served a dual purpose. We had someone watching us the entire time who would provide clues, if necessary, through the screen.

Can you give us an example of some of the clues you found, and how they made more sense as the game progressed?

Not to give too much away, but we found a key that seemed to have no relevance at first, since it didn’t open the only door in the room. We soon discovered our little room was not as small as it seemed.

Most clues turned out to be more than they seemed at first. There were a lot of puzzles solved by trying to find out what was missing, rather than where something was hiding.

You said that the people running the game could give you clues through the television. Could you elaborate on that?

If we got stuck, we could ask for a hint. At one point, we were all standing over a chess board, befuddled because we knew it needed to come into play, we just didn’t know how. After discussing chess moves for a while, the TV screen showed us a poem using the words “King,” “Queen,” and “Knight.”

This reminded us that much earlier, we had found a deck of cards, so we knew that the deck of cards and the chess board were both necessary to solving that part of the puzzle.

How long did you have to escape?

One hour.

And did you?

Technically, no. But we came so close, our “handler” gave us an extra two minutes to finish.

Do you feel like a bigger or smaller group would have helped more?

You know, at first I wasn’t so sure about working with complete strangers, but by the end of the mission, I felt that every single person contributed in some way.

In my case, the more people present, the more knowledge brought to the table. For instance, I’m terrible with numbers, but others in the group used their very strong math skills to keep us afloat. My strength is in brain teasers and optical illusions, so I could help identify some of the riddles and visual tricks.

So you would definitely go again?

Absolutely! We had such a good time! We made new friends and, despite not escaping in time, we still felt very proud of ourselves.


Many thanks to Darcy for her time and her story about Mission Escape Games! You can check out her social media skills on the Facebook and Twitter accounts for Penny Dell Puzzles!

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A ten-digit brain teaser to melt your mind!

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

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

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

Enjoy!


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

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

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


[Image courtesy of Wikipedia.]

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

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

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

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

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

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

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

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

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

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

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

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

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

[Sorry guys, you’re out.]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Let’s return to those starting formulas.

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

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

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

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

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

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

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

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

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

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

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

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

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

So, here are our options at this point:

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

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

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

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

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

So ABCDEFGHIJ = 5736912480.


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

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Puzzles in Pop Culture: Sherlock Holmes (a.k.a. The puzzle is afoot!)

Mystery novels and stories are catnip to puzzlers, because they’re an entertaining way to exercise our deductive skills and enjoy puzzling outside our usual fare of apps, games, and paper puzzles.

And surely there’s no greater boon to the mystery-loving puzzler than the ongoing adventures of Sherlock Holmes in all his forms. Not only is there are series of feature films starring the Great Detective, but there are two television programs focusing on his singular brand of puzzling: Sherlock and Elementary.

[Note: I will be discussing both seasons of Elementary, seasons 1 and 2 of Sherlock, and the season 3 premiere. So consider this your spoiler alert.]

Beyond the normal whodunnit storytelling that frames both shows — a staple of the genre that traces back to the original Sir Arthur Conan Doyle stories and novels — there are smaller puzzles to unravel.

Perhaps the most famous from the Doyle canon is “The Adventure of the Dancing Men,” where Holmes solves a curious pictographic code in the hopes of preventing a heinous crime.

And both Sherlock and Elementary frequently return to this cryptographic trope, for both dramatic tension and storytelling twists and turns.

Episode 2 of Sherlock, “The Blind Banker,” has a cryptographic mystery at the heart of the story, one that echoes “The Adventure of the Dancing Men” and its similarly perilous stakes.

Codebreaking is also at the core of the season 2 premiere, “A Scandal in Belgravia,” as Sherlock attempts increasingly complex ways of cracking the code of Irene Adler’s phone. (There’s a marvelous scene where he introduces a dummy phone in order to copy her keystrokes is foiled when Irene realizes the dummy phone is a fake, and in turn types in a fake passcode. It’s a terrific exchange of gamesmanship.)

The cipher used in the season 3 premiere, “The Empty Hearse,” is another prime example, and one that quick-witted viewers could solve alongside Sherlock, as he and Mary decipher the message and pursue Watson’s kidnappers.

Elementary has had its fair share of codes as well. The season 2 episode “The Diabolical Kind” featured numerous techniques for coding information — from hidden spaces in seemingly innocuous drawings to elaborate letter-shifting codes akin to the Caesar cipher — all of which Holmes unraveled with ease. (Sadly, the puzzlers in the audience aren’t given much opportunity to crack the codes themselves.)

But each show has also played on the natural human ability to find meaningless patterns in chaos and interpret them as hidden messages. Sherlock‘s season 2 episode “The Hounds of Baskerville” had Watson chasing down a Morse Code message that turned out to be nothing more than flashes of light.

And Elementary‘s most recent episode had an excellent sequence where Watson read too much into a former mobster’s statement about “a mutt” who would be “in the ground tomorrow.” (Watson suspected the “mutt” referenced a suspect’s mixed ancestry, while “in the ground tomorrow” would point toward the suspect’s Jewish heritage and burial traditions.) Holmes correctly dismissed both as red herrings.

Both Sherlock and Elementary had a bit of fun exploring characters fixating on small clues, only to be misled. It’s an intriguing path to take when the main character of each show bases so many conclusions on similarly minuscule bits of data.

With such a richness of Sherlockian material on television these days, both mystery fans and puzzlers have plenty to sate their appetites.

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PuzzleNation Book Review: The Riddle of the Labyrinth

Welcome to the fifth installment of PuzzleNation Book Reviews!

All of the books discussed and/or reviewed in PNBR articles are either directly or indirectly related to the world of puzzling, and hopefully you’ll find something to tickle your literary fancy in this entry or the entries to come.

Let’s get started!

Our book review post this time around — our first nonfiction book review — features Margalit Fox’s work The Riddle of the Labyrinth: The Quest to Crack an Ancient Code.

When archaeologist Arthur Evans unearthed the first of hundreds of preserved tablets from a dig on the island of Crete, he had no idea he was unveiling a puzzle that would last for decades.

Linear B.

It has all the trappings of a classic mystery: an exotic setting, an uncrackable code, a cast of brilliant and curious people brought together to solve it, and a final, world-changing deductive leap to the finish. The Riddle of the Labyrinth is the story of how the conundrum of Linear B was resolved, framed by the life stories of the three people most responsible for conquering a 50-year mystery.

The Riddle of the Labyrinth is terrific, a perfect fusion of historical writing and investigative reporting that presents an incredible mental and deductive achievement as a slow-boil mystery, and by doing so, rewrites the established narrative to spread the credit around.

The writing is meticulous and painstakingly detailed, allowing the reader to truly understand, sometimes graphic by graphic, how each breakthrough in the solving process was made, and just how phenomenal the detective work involved truly was.

I’ve written about real-life examples of codecracking in the past, but they all pale in comparison to the enormity and complexity of what Alice Elizabeth Kober and Michael Ventris accomplished when they unraveled the riddle of Linear B.

It’s impressive in the extreme that Fox was able to make some high-level deduction and linguistic skill so easily understood by the average reader. Even fans of cryptograms and other codebreaking-style puzzles could learn a great deal from Kober’s techniques and Fox’s wonderfully thorough and easily-parsed step-by-step analysis.

By citing examples like The Dancing Men from the famous Sherlock Holmes story, Fox provides great shortcuts for the reader, removing none of the wonder of Kober and Ventris’ accomplishments while still clearing away so much potential confusion.

In short, this is science writing, history writing, and storytelling in top form. What a treat.

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