Tag Archives: Magic Square

The Search for the Greatest Palindrome

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[Palindrome, written as an ambigram.]

Palindromes are a classic — and challenging — form of wordplay. Essentially, you’re trying to come up with phrases or entire sentences that read the same backwards and forwards.

Although palindromes have been around for a very long time — dating back to magic squares — they’ve gained additional prominence in recent years. The 2017 World Palindrome Championship was determined alongside the American Crossword Puzzle Tournament the same year. They have their own awards ceremony: The SymmyS Awards. There was even a documentary on the subject.

Palindrome creation was a popular pastime in Bletchley Park during the off-time of the codebreakers and staff. And those palindromic magic squares we referenced earlier? It was once believed that they held magical properties and served as incantations to ward off threats both spiritual and physical.

Musician, parodist, and wordsmith “Weird Al” Yankovic, no stranger to palindromes himself, once said that “the writing of a brilliant palindrome is a small miracle, and that, I think, deserves to be honored more than a lot of the stupid and inconsequential things we often celebrate in our culture.”

They’re an integral part of puzzle history.

But why do I have palindromes on the brain today? Because I’ve been trying to figure out which one is the best one ever created.

It’s a tricky topic, extremely subjective. What parameters do I use to choose the palindrome in the top spot?

The most famous one is either “Madam, I’m Adam” or “a man, a plan, a canal… Panama!”

I prefer the latter. It’s not just thematically appropriate to its subject, but it’s also a univocalic, a sentence using only one vowel. There’s a lot of linguistic legerdemain going on here.

It has been expanded upon, of course. I’ve seen this wordier version around:

A man, a plan, a canoe, pasta, heros, rajahs, a coloratura, maps, snipe, percale, macaroni, a gag, a banana bag, a tan, a tag, a banana bag again (or a camel), a crepe, pins, Spam, a rut, a Rolo, cash, a jar, sore hats, a peon, a canal — Panama!

Do I go by sheer length? Some palindromes are incredibly long, but are mostly nonsense.

My friend Troy recently shared this lengthy palindrome with me:

Dennis, Nell, Edna, Leon, Nedra, Anita, Rolf, Nora, Alice, Carol, Leo, Jane, Reed, Dena, Dale, Basil, Rae, Penny, Lana, Dave, Denny, Lena, Ida, Bernadette, Ben, Ray, Lila, Nina, Jo, Ira, Mara, Sara, Mario, Jan, Ina, Lily, Arne, Bette, Dan, Reba, Diane, Lynn, Ed, Eva, Dana, Lynne, Pearl, Isabel, Ada, Ned, Dee, Rena, Joel, Lora, Cecil, Aaron, Flora, Tina, Arden, Noel, and Ellen sinned.

It makes more sense than the Panama one, but just barely. It’s a thinly disguised list, that’s all.

So, is narrative coherence a necessity for the best palindrome ever?

World Champion Palindromist Mark Saltveit claims that his first palindrome was “Resoled in Saratoga, riveting in a wide wale suit, I use law, Ed. I, wan, ignite virago, tar a snide loser.”

It’s lengthy, and it mostly makes sense. But Saltveit rarely worries about that. One of his most famous creations is this borderline nonsensical concoction:

Devil Kay fixes trapeze part; sex if yak lived.

Sure, it manages to use Xs and a Z, but it’s gibberish. I much prefer his winner from the First World Palindrome Championship in 2012:

I tan. I mull. In a way, Obama, I am a boy, a wan Illuminati.

The Bletchley Park palindromists demanded some level of coherence. One of the most impressive produced there was “Doc, note, I dissent. A fast never prevents a fatness. I diet on cod.”

It’s certainly impressive, and feels like it could be spoken casually.

Maybe the ideal palindrome walks the tightrope of cleverness, innovation, length, and coherence.

Although it’s quite short, I do enjoy this existential one from the 2018 SymmyS Awards: “Am I man-made? Damn! Am I, Ma?”

I’ve pored over dozens and dozens of palindromes, trying to find one that best represents the wordplay and the art form. And I’ve made my choice.

In my humble, puzzly opinion as a self-appointed adjudicator of palindromic magnificence, I choose Anthony Etherin’s “The Failed Cartographer” as the best palindrome I’ve ever seen.

Please enjoy this wistful, almost operatic bit of wordplay:

Demand a hill, at solid nadir…. Damn it! One morn I saw I was in Rome,
not in Madrid, and I lost all I had named…

Magical.

Can you think of a palindrome that better epitomizes the genre? Please share in the comments section below. We’d love to hear from you!

Oh, and as for my favorite palindrome? That’s easy. It’s a stupid one I wrote for a friend.

“My friend Sean has a really weird last name: Emantsaldriewyllaerasahnaesdnierfym.”

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PuzzleNation Product Review: IcoSoKu

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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.]

Most puzzles — whether we’re talking about puzzle boxes, jigsaw puzzles, physical brain teasers, or mechanical puzzles — operate under a simple premise: the puzzle arrives in one configuration, and it’s up to you to solve it and put it into a different configuration.

With puzzle boxes, you’re opening them. With jigsaws, you’re assembling the pieces. With physical brain teasers and mechanical puzzles, you’re separating them, freeing a given piece, or accomplishing a particular task. But in each case, they’ve arrived that way. You have been pitted against the designer.

Project Genius‘s IcoSoKu is something different. IcoSoKu challenges you to create your own puzzle, and then solve it.

The setup is elegant in its simplicity. It’s a puzzle ball consisting of a twenty-sided icosahedron base, twelve numbered pegs, and twenty triangular tiles with different combinations of pips at the corners.

To start, remove all of the tiles and all of the pegs from the icosahedron. Place the numbered pegs wherever you wish on the puzzle ball.

Then, you must figure out how to arrange the triangular tiles on the puzzle ball.

This is tougher than it seems. Each triangular tile has a different combination of pips in its corners. Some corners have none, while others have one, two, or three pips. And each corner neighbors a different numbered peg. Each numbered peg is surrounded by five corners, and the pips on each corner, when added together, should total the number on the peg.

And with numbers ranging from 1 to 12, you have to be both clever and careful in your tile placement. That peg labeled “1” can only have a single pip neighboring it, meaning that the other four tiles surrounding that peg should have empty corners.

[Three different looks at the same solved puzzle ball.]

IcoSoKu combines the deduction of placement puzzles like Minesweeper or Blackout! with the mathematical puzzling of a magic square or a Sudoku puzzle. And by making the puzzle three-dimensional, it places a healthy demand on your puzzly faculties. You’re constantly tipping and turning the puzzle ball, because you can never see the whole puzzle at once, making it much harder to manage your tiles and maintain a good sense of just how many of those valuable little pips you’ve already used.

And as soon as you’ve placed the final tile and searched the puzzle ball all over, confirming a successful solution… all you want to do is strip away all of the tiles and pegs to test your wits again.

Assigning pegs randomly creates a completely different solving experience from bundling all the large numbers together on one side and all the small numbers together on the other side of the ball. Although you will begin to spot certain patterns and techniques that will come in handy as you solve each successive permutation of the puzzle, you’ll still find IcoSoKu to be an engaging and satisfying challenge.

Plus there are other ways you can enjoy the puzzle after cracking it yourself. I challenged a fellow puzzler to a timed IcoSoKu solve-off! First, I arranged the pegs and timed how long it took her to solve the puzzle ball I’d devised. Then, she arranged the pegs and timed how long it took me to unravel the puzzle ball she’d created. It added a fun touch of competition and uncertainty to the solving experience, one that my patient solo-solving didn’t capture.

But whether you’re tackling IcoSoKu yourself or with a puzzly rival, you’ll find plenty to enjoy here. It’s a DIY puzzle, masterfully put together and waiting for you to execute.

IcoSoKu is available from Project Genius and other participating retailers, appropriate for solvers 9 and up!

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Cracking the GCHQ Christmas Card!

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As you may recall, my fellow puzzlers and PuzzleNationers, a few months ago, a government organization in England called the GCHQ — Government Communications Headquarters — released a puzzly Christmas card designed to tax even the savviest puzzle solvers.

They’ve finally released the answers to this mind-blowing series of puzzles, and I’d like to go over some of them with you. Partly to marvel at the puzzle wizardry necessary to solve this challenging holiday gift, and partly to gloat about the parts I managed to solve.

So let’s get to it!

Part 1 was a logic art puzzle where you have to deduce where to place black squares on an open grid in order to form a picture.

Each column and row has a series of numbers in it. These numbers represent runs of black squares in a row, so a 1 means there’s one black square followed by a blank square on either side and a 7 means 7 black squares together with a blank square on either side.

This is mostly a deduction puzzle — figuring out how to place all the strings of black squares with white spaces between them within the space allotted — but no image immediately emerged, which was frustrating. Once the three corner squares started to form though, I realized the answer was a QR code, and the puzzle started to come together nicely.

Part 2 was a series of six multiple-choice brain teasers. I’ll give you the first three questions, along with answers.

Q1. Which of these is not the odd one out?

A. STARLET
B. SONNET
C. SAFFRON
D. SHALLOT
E. TORRENT
F. SUGGEST

Now, if you stare at a list of words long enough, you can form your own patterns easily. Here’s the rationale the GCHQ used to eliminate the odd ones out:

STARLET is an odd one out because it does not contain a double letter.
SONNET is an odd one out because it has 6 letters rather than 7.
SAFFRON is an odd one out because it ends in N rather than T.
TORRENT is an odd one out because it starts with T rather than S.
SUGGEST is an odd one out because it is a verb rather than a noun.

SHALLOT is our answer.

Q2. What comes after GREEN, RED, BROWN, RED, BLUE, -, YELLOW, PINK?
A. RED
B. YELLOW
C. GREEN
D. BROWN
E. BLUE
F. PINK

After playing around with some associative patterns for a while, I realized that somehow these colors must equate to numbers. First I tried word lengths, but 5-3-5-3-4-___-6-4 didn’t make any sense to me. But then, it hit me: another time where colors and numbers mix.

Pool balls. Of course, the colors and numbers didn’t match, because this is a British puzzle, and they don’t play pool, they play snooker.

So the colored balls in snooker become the numbers 3, 1, 4, 1, 5, -, 2, 6. The numbers of Pi. And now the blank makes sense, because Pi reads 3.1415926, and there’s no 9 ball in snooker.

So the next number in the chain is 5, and 5 is the color BLUE.

Q3. Which is the odd one out?
A. MATURE
B. LOVE
C. WILDE
D. BUCKET
E. BECKHAM
F. SHAKA

This one came pretty quickly to me, as the names Oscar Wilde and Charlie Bucket leapt out. And if you follow the phonetic alphabet, you also get Victor Mature, Romeo Beckham, and Shaka Zulu. (I didn’t get Mike Love, however.)

Since Shaka Zulu was the only one where the phonetic alphabet word was the surname, not the first name, SHAKA is the odd one out.

(The other three questions included an encryption puzzle, a number pattern (or progressions puzzle), and a single-letter puzzle.)

Granted, since you could retake this part as many times as you wanted, you could luck your way through or brute force the game by trying every permutation. But managing to solve most of them made this part go much faster.

Part 3 consisted of word puzzles, and was easily my favorite section, because it played to some strengths of mine.

A. Complete the sequence:

Buck, Cod, Dahlia, Rook, Cuckoo, Rail, Haddock, ?

This sequence is a palindrome, so the missing word is CUB.

B. Sum:

pest + √(unfixed – riots) = ?

This one is a little more involved. To complete the formula, you need to figure out what numbers the words represent. And each word is an anagram of a French number. Which gives you:

sept + √(dix-neuf – trois) = ?

Dix-neuf is nineteen and trois is three, so that’s sixteen beneath a square root sign, which equals four. And sept (seven) plus four is eleven.

The French word for eleven is onze, and ZONE is the only anagram word that fits.

C. Samuel says: if agony is the opposite of denial, and witty is the opposite of tepid, then what is the opposite of smart?

This is a terrific brain teaser, because at first blush, it reads like nonsense, until suddenly it clicks. Samuel is Samuel Morse, so you need to use Morse Code to solve this one. I translated “agony” and tried reversing the pattern of dots and dashes, but that didn’t work.

As it turns out, you need to swap the dots and dashes, and that’s what makes “denial” read out. This also worked with “witty” and “tepid,” so when I tried it with “smart,” the opposite was OFTEN.

D. The answers to the following cryptic crossword clues are all words of the same length. We have provided the first four clues only. What is the seventh and last answer?

1. Withdraw as sailors hold festive sing-song
2. It receives a worker and returns a queen
3. Try and sing medley of violin parts
4. Fit for capture
5.
6.
7. ?

Now, I’m not a strong cryptic crossword solver, so this part took FOREVER. Let’s work through it one clue at a time.

1. Withdraw as sailors hold festive sing-song

The word WASSAIL both reads out in “withdraw as sailors hold” and means “festive sing-song.”

2. It receives a worker and returns a queen

The word ANTENNA both “receives” and is formed by “a worker” (ANT) and “returns a queen” (ANNE, reading backward).

3. Try and sing medley of violin parts

The word STRINGY is both an anagram of “try” and “sing” and a violin part (STRING).

4. Fit for capture

The word SEIZURE means both “fit” and “capture.”

Those four answers read out like this:

WASSAIL
ANTENNA
STRINGY
SEIZURE

And with three more answers to go, it seemed only natural that three more seven-letter answers were forthcoming. Plus, when you read the words spelling out downward, you notice that the first four letters of WASSAIL, ANTENNA, STRINGY, and SEIZURE were spelling out.

If you follow that thought, you end up with the start of a 7×7 word square:

 WASSAIL
ANTENNA
STRINGY
SEIZURE
ANNU___
INGR___
LAYE___

And the only seven-letter word starting with INGR that I could think of was INGRATE.

WASSAIL
ANTENNA
STRINGY
SEIZURE
ANNU_A_
INGRATE
LAYE_E_

And if the last word is LAYERED…

WASSAIL
ANTENNA
STRINGY
SEIZURE
ANNU_AR
INGRATE
LAYERED

Then the missing word must be ANNULAR. The original question asked for the last word though, so our answer is LAYERED.

This brings us to Part 4, Number Puzzles, where I must confess that I finally tapped out, because I could only figure out the first of the three progressions involved.

Fill in the missing numbers.

A. 2, 4, 8, 1, 3, 6, 18, 26, ?, 12, 24, 49, 89, 134, 378, 656, 117, 224, 548, 1456, 2912, 4934, 8868, 1771, 3543, …

B. -101250000, -1728000, -4900, 360, 675, 200, ?, …

C. 321, 444, 675, 680, 370, 268, 949, 206, 851, ?, …

In the first one, you’re simply multiplying by 2 as you go.

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, and so on.

But you begin to exclude every other number as you move into double-digits, triple-digits, quadruple-digits, and beyond.

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, and so on.

So the answer, 512, becomes the real answer, 52.

But, as I said, I couldn’t crack the other two, and I’m already exhausted just running through these four sections!

And, based on the answers they released recently, Part 5 only got more mindbending from there.

As a matter of fact, not a single entrant managed to get every answer in Part 5 correct. Prizes were awarded to the three people who came closest however, and it turns out a staggering 30,000+ people made it to Part 5. Color me impressed!

This was, without a doubt, the most challenging puzzle suite I have ever seen, and I offer heartfelt kudos to anyone in the PuzzleNation Blog readership who even attempted it!

You’re welcome to try it out for yourself, though. I highly recommend using this link from The Telegraph, which allows you to skip to the next part if you get stumped.

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These puzzles deliver!

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Puzzles are all around us. They’re in our newspapers and on our phones, they’re lurking in math problems and board games and children’s toys.

But as it turns out, according to an article forwarded to me by puzzler and friend of the blog Cathy Quinn, they’re also on our stamps.

At least in Macau, that is.

Late last year, Macau Post released the latest stamps in their Science and Technology series. Previous editions have featured the Golden Ratio, Fractals, and Cosmology, but this time around, they selected a topic near and dear to the hearts of many puzzlers:

Magic squares.

For the uninitiated, a magic square is a grid where the numbers within add up to the same total in every row, column, and diagonal.

Our friends at Penny/Dell Puzzles utilize patterns like this in their Anagram Magic Square puzzle, where a word to anagram accompanies each number in the diagram, eventually spelling out a bonus phrase or quotation.

But at its core, a magic square is about cleverly balancing every element until you reach a harmonious arrangement. It’s a curiously meditative sort of puzzle solving, and I can see how it would appeal to the meticulous nature of stamp collectors worldwide.

Here are the six stamps currently available through Macau Post.

There’s a classic 4×4 magic square grid in the upper left and an ancient Latin palindrome in the upper right, as well as part of a 4th-century Chinese palindromic poem in the lower left and a geometric puzzle in the lower right where the pieces in the inner squares can make all of the designs in the outer squares.

Not only that, but three additional stamps will be released this year, making a total of nine themed stamps, and wouldn’t you know it? The stamps themselves can be arranged to form a magic square when assembled, based on the values printed in the corner of each stamp.

Just another sign that puzzle magic is alive and thriving all across the world.

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