Category: Uncategorized

Here’s a fun little brainteaser I saw that I thought I’d share with y’all:

Rearrange the letters of the four words in each set to form four new words that rhyme. For example, given the words BEARD, HERDS, DAIS, and ADDER, you would anagram them to spell BREAD, SHRED, SAID, and DREAD.

1. ONSET, NEWS, WRONG, HORNET
[spoiler /Show Answer/ /Hide Answer/]STONE, SEWN, GROWN, THRONE[/spoiler]

2. CURES, SOWER, SEVER, STEER
[spoiler /Show Answer/ /Hide Answer/]CURSE, WORSE, VERSE, TERSE[/spoiler]

3. DUNE, WELD, CURED, TWEEDS
[spoiler /Show Answer/ /Hide Answer/]NUDE, LEWD, CRUDE, STEWED[/spoiler]

4. SINGER, ASPEN, VINES, SPINAL
[spoiler /Show Answer/ /Hide Answer/]REIGNS, PANES, VEINS, PLAINS[/spoiler]

5. RANGED, ENLARDS, DACRON, DARNED
[spoiler /Show Answer/ /Hide Answer/]GANDER, SLANDER, CANDOR, DANDER[/spoiler]

6. BUSIER, SOLE, HOSES, WIVES
[spoiler /Show Answer/ /Hide Answer/]BRUISE, LOSE, SHOES, VIEWS[/spoiler]

I was very lucky to grow up during the Golden Age of Video Arcade Games. I always loved pinball machines since I was very young, so when video games became popular in the late 70s and early 80s, I was hooked.

My earliest video game memory is wandering away from my parents’ camper at the campground in Rainbow Springs State Park and heading up to the community center just to play Sea Wolf. I still remember where all of my favorite video games were located – arcades in shopping malls, single machines in convenience stores, games lining the walls of smoky pool halls, and more. I was never an expert at playing any of them in particular – I just loved the whole electronic gaming experience.

As I graduated from high school and joined The Real World(tm), coin-op video games began to be overtaken by the power of home machines. The Nintendo NES had just been released, followed by the Super NES, Sega Genesis, and more. The allure of the coin-op games began to fade.

To honor that bygone era, I’ve started a new series of geocaching puzzles called Arcade Classics. The Arcade Classics series is not a quest (such as my PS101 Series) – all of the puzzles are of the completely standalone solve-at-your-desk variety. They’re on the easyish end of the difficulty spectrum and will take solvers to interestingly relevant places I’ve discovered on my trips around town.

Enjoy!

-eP

PS: If you want to experience that coin-op goodness for yourself, you can do so right at home. The freeware application called the Multiple Arcade Machine Emulator, or MAME, lets you play all of those old games on your Windows computer at home.

PPS: If you like classic video games, you’ll LOVE these YouTube videos: Pong, Space Invaders, Pole Position, Tetris

http://www.youtube.com/watch?v=fK7-4jQYkEg

(Editor’s Note – This is part of an amazing (but non-puzzle-related) playlist which you can view by clicking here. -eP)

I’m on a particular self-imposed geocaching quest – to complete the Florida-Style Alphabet Soup Challenge using nothing but puzzle caches.

I mentioned this quest to lorriebird and that I had no caches (neither found nor unfound) that I could use for the letters K or Z. Since she knew that I would be traveling to her area soon for an event cache, she graciously hid two appropriately-named puzzle caches for me to find – Ken(Ken) Moves to Naples and Zany Brainy Word Nerd (aka ZBWN).

I zipped through KenKen fairly quickly and took a cursory look at ZBWN. I tried a few ideas that have worked in other caches, but I couldn’t discover a pattern that made sense to me. I put it aside and went onto a few other caches, returning to ZWBN every now and then.

But as the weeks went by, I started to panic: “What if I don’t solve it before the event? Unless I figure it out, I’m going to be the laughing stock of every puzzlehead south of I-4!” And yet, other people seemed to be cracking it in mere seconds – every Found It log entry on ZBWN that claimed how easily each cacher solved it deflated my oversized ego more and more.

Finally, after the event cache and just as I was about to leave, one of the other cachers asked if he could give me a hint for ZBWN. I finally broke down and said yes, only to discover that I had the solution in front of me the entire time – it was one of the very first things I tried – and I was too blind to see it.

In my defense, I had a very good reason – it was because I’ve attempted too many puzzles like it in the past and they clouded my opinion of what the solution would be.

Below are 12 examples of just the sort of puzzle that kept me from solving ZBWN without a hint. I would strongly recommend that you solve ZBWN first before tackling these, or you will be as lost in the weeds as I was.

Good luck!

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The Last Word

Each of the 12 sets of words below has a common denominator, some unusual factor that is shared by the six words in the set. It’s up to you to determine what that factor is and identify which one of the three words after the list has it, too.

For example, given SEXES, MOM, DEIFIED, LEVEL, POP, and REDDER, with choices DIVINED, ROTATOR, and STARTS, you’d pick ROTATOR: All the words are spelled the same forward and back.

For how many of the following sets can you get the last word?

1. SETTEE, RACCOON, EMBARRASS, APPELLATION, BASSOON, SUFFRAGETTE
a. BEDROOM   b. PROPELLER   c. EGGSHELL   [spoiler /Show Answer/ /Hide Answer/]c. EGGSHELL – words with two pairs of double letters[/spoiler]

2. TEA, EYE, SEA, QUEUE, ARE, WHY
a. YOU   b. ATE   c. WEE   [spoiler /Show Answer/ /Hide Answer/]a. YOU – homophones of letters of the alphabet[/spoiler]

3. MUSEUM, EARLOBE, YEARLY, SEAMSTRESS, WILLOW, DOODAD
a. COCOON   b. ERASER   c. TABLET   [spoiler /Show Answer/ /Hide Answer/]c. TABLET – words that begin and end with the same letter[/spoiler]

4. YOUTH, THEMATIC, USHER, SHEIK, ITALICS, MEDIUM
a. THEATER   b. WEEVIL   c. DOMESTIC   [spoiler /Show Answer/ /Hide Answer/]b. WEEVIL – words beginning with a pronoun[/spoiler]

5. GIGGLING, REARRANGER, ASSESS, MINIMIZING, DIDDLED, PIZZAZZ
a. DEEDED   b. INTERMITTENT   c. CANDIDACY   [spoiler /Show Answer/ /Hide Answer/]b. INTERMITTENT – words with one letter appearing four times[/spoiler]

6. REVILED, STRESSED, REPAID, STAR, DRAWER, PARTS
a. VILE   b. REGARD   c. STINK   [spoiler /Show Answer/ /Hide Answer/]c. STINK – words that can be reversed to spell other words[/spoiler]

7. PREVIEW, TALLOW, SELECTION, GOLDEN, BRAIDED, CLAMP
a. TRACING   b. CASHEW   c. CONVERT   [spoiler /Show Answer/ /Hide Answer/]a. TRACING – words that become new words when the first letter is removed[/spoiler]

8. CIVIC, LIVID, MIX, MILL, VIVID, DILL
a. MIMIC   b. LICIT   c. MINIM   [spoiler /Show Answer/ /Hide Answer/]a. MIMIC – words consisting of letters that are Roman numerals[/spoiler]

9. BANANA, DEMONIC, FICKLE, HUMBUG, JABORANDI, LUCK
a. NEMESIS   b. NUDISM   c. MEGATION   [spoiler /Show Answer/ /Hide Answer/]b. NUDISM – words whose last letters immediately precede their first letters in the alphabet[/spoiler]

10. GEL, GROUP, PLACE, FIXED, RESOLUTE, ADJUST
a. USELESS   b. COLLECTION   c. AFGHAN   [spoiler /Show Answer/ /Hide Answer/]b. COLLECTION – synonyms of the word “set”[/spoiler]

11. RING, TOPS, MANATEE, WINDLESS, EARTH, ANGER
a. MATTER   b. TUNES   c. OUGHT   [spoiler /Show Answer/ /Hide Answer/]c. OUGHT – words that become new words when the last letter is moved to the front[/spoiler]

12. ACCEPT, BEGINS, ABHORS, CHINOS, BILLOW, EFFORT
a. ALMOST   b. BEFORE   c. CENSOR   [spoiler /Show Answer/ /Hide Answer/]a. ALMOST – words whose letters are in alphabetical order[/spoiler]

Not much content here – just a note to say that I’m back from my summer vacation and will resume my semi-regular quasi-updates to this blog shortly. I apologize for any panic or disturbance my lack of posting may have caused you.

If you like word puzzles (and who among us doesn’t, really?), you’ll love the Word Games forum over on Podcacher.com.

Yes, I know the past few posts have been a bit heavy on the plugging of Podcacher.com, but if you listened to the show and realized how aweome Sonny and Sandy are, you’d completely understand.

FYI – Puzzlehead.org along with the PS101 series and the Lamp Skirt Micros 101 Final Exam were mentioned on the May 17, 2009, episode of Podcacher’s podcast (starting at about 12:40 into the podcast). Whoo-hoo! Thanks, Sonny and Sandy!

Podcacher is a great service, one to which all puzzleheads and geocachers should subscribe.

It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
-Pierre de Fermat, 1637

Pierre de Fermat was a French lawyer and mathematician who lived from 1601 to 1665, and his work has formed the foundation of many advanced areas of mathematics. His work on maxima, minima, and tangents to curves formed the basis of differentiation. His work on reducing general power functions to the sums of geometric series was influential to Newton and Liebnitz in their development of the fundamental theorem of calculus. Fermat’s work with Blaise Pascal formed the basis of the theory of probability. His principle of least time lead to the principle of least action and the development of classical physics. Fermat was instrumental in establishing the basis upon which modern scientific and mathematical understanding is derived.

However, he was not always as rigorous as one might like. Although he dabbled in mathematics, he always considered himself an amateur. He communicated most of his work to his friends in letters, often with little or no proof of his assertions. Many mathematicians doubted several of his claims, especially given the difficulty of some of the problems he attempted to solve and the tools available to him with which to solve them.

His most famous assertion was made in a note he scribbled in the margin of the book Arithmetica by the Greek philosopher and mathematician Diophantus. The assertion concerns the equation a^n + b^n = c^n (where “^” means “to the power of”). While solutions for the case of n=2 were well known since the time of the ancient Greeks, Fermat asserted that for any other integer greater than 2 there were no numbers a, b, and c that could make this equation true. This assertion has come to be known as Fermat’s Last Theorem, as it was the last of his unproven assertions to remain unproven.

The most tantalizing part of his assertion was the quote at the end: I have discovered a truly marvelous proof of this, which this margin is too narrow to contain. For over 350 years, mathematicians searched in vain for this elusive proof. Fermat challenged his peers to prove the cases of n=3 and n=4, but he himself offered no proof of those cases. Euler proved the case for n=3 in 1770, n=5 was proved by others around 1825, and n=7 was proved in 1839.

Additional proofs were developed in the 1800s for 6 ,10, and 14. Sophie Germain proved that Fermat’s Last Theorem was true for any prime number p such that the expression 2p+1 was also prime (such values of p are called “Sophie Germain primes”). By 1993, computer-based proofs had been used to demonstrate the truth of Fermat’s Last Theorem for all values up to 4 million. But the proof of the general case of n>2 remained unproven.

Mathemetician Andrew Wiles was one of many to become enamored at a young age with the search for Fermat’s marvelous little proof. He described the problem this way: “Here was a problem, that I, a ten year old, could understand and I knew from that moment that I would never let it go. I had to solve it.”. Wiles worked on the proof off and on for years, with no success. Eventually he abandoned work on proving the theorem and went on to other areas of research, specifically into the advanced mathematical concept of modular elliptic curves. (Don’t ask me what they are – I’ve read about them a bunch and still don’t understand them.)

In 1985, mathematician Jean-Pierre Serre asserted that if a special case of the theorem concerning elliptic curves called the Taniyama-Shimura Conjecture was true, then Fermat’s Last Theorem would have to be true. In 1986, Ken Ribet proved this assertion which transformed the proof of Fermat’s Last Theorem into the proof of the Taniyama-Shimura Conjecture. This development meant that Andrew Wiles’ dream of proving Fermat’s Theorem was now a matter of proving one of the most important conjectures in his particular area of mathematics specialization.

Wiles’ search for a proof was renewed in earnest. Wiles worked for years on the proof in secret, starting in the summer of 1986. He dedicated all of his research time to proving Taniyama-Shimura. He compared the proof to walking into a giant mansion where all of the lights were turned out – you wander around in one room, feeling your way around the walls and the furniture, until eventually you find the light switch. Once you turn on the switch, the room is illuminated, and you can make your way to the next room. Repeat this process long enough, and eventually the entire mansion will be lit.

In a series of lectures presented at the Isaac Newton Institute for Mathematical Sciences over three days from June 21-23, 1993, Wiles presented his proof to the world. As he began lecturing on day one, word spread quickly through the mathematics community that his work might be the long-awaited proof of Fermat’s Last Theorem. On the third day, after finishing his proof and stating that his proof implied the correctness of Fermat’s Last Theorem, he concluded by saying, “I think I’ll stop here.” For his proof, delivered 354 years after the original theorem was posited, he not only received a standing ovation, but a host of other awards and accolades.

His proof is not at all the “marvelous proof” that Fermat had envisioned – it uses mathematical techniques that were not developed until the 20th century and beyond. At the time the proof was presented, there were only a handful of people in the world that had any potential of understanding it. Most likely, Fermat believed that he had found a proof using only 17th century methods, and the potential existence of such a proof is what has driven mathematicians for years to seek its solution.

Wiles journey has been documented in many books and television specials. His own description of his journey contains many words of advice not only for mathematicians, but for puzzle-solvers everywhere, including:

• I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.
• Certainly one thing that I’ve learned is that it is important to pick a problem based on how much you care about it.
• Always try the problem that matters most to you.
• Just because we can’t find a solution doesn’t mean that there isn’t one.
• When I got stuck and I didn’t know what to do next, I would go out for a walk. I’d often walk down by the lake. Walking has a very good effect in that you’re in this state of relaxation, but at the same time you’re allowing the sub-conscious to work on you.
• Well, some problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they’re extremely hard to solve.
• That particular odyssey is now over. My mind is now at rest.

Wikipedia has a marvelous description of the proof – the proof itself is over 200 pages long. It also has a number of references to other articles, books, and TV shows to learn more about the proof.

Of course, the best pop culture reference to the proof is in Tom Lehrer’s timeless classic That’s Mathematics (YouTube).

In 1912, the Collegio Romano (now known as the Pontifical Gregorian University) faced a financial crisis. Short on cash, the school decided to raise funds through a discreet sale of a portion of the holdings in its library. Polish-American book dealer Wilfrid M. Voynich acquired 30 of the texts, which included what has become one of the most studied and least understood books in history – a book now known as the Voynich Manuscript.

This 272-page hand-written book (of which only 240 pages remain) is filled with writing in an unknown language as well as beautiful illustrations. So far, no one has managed to decipher the text or ascertain its meaning.

The language in which the text is written is perhaps the most mysterious part of the entire book. There are over 170,000 unique glyphs (or “letters”) in the text, and an alphabet of approximately 20-30 glyphs would account for nearly the entire text. The glyphs are arranged into approximately 35,000 words of varying length that seem to follow some basic rules of spelling similar to other known languages – certain glyphs must appear in each word (as vowels do in English), some glyphs can never follow others, and some symbols may be doubled while others may not. Some words are quite common, while others appear sporadically or only once. But the letter frequency, word frequency, and word relationships are unlike those in any other known language – it is far more complicated than a simple substitution cipher.

The book is organized into 17 groups of 16 pages each, divided into six major sections of different style and subjects (as indicated by the illustrations) on matters that appear to be herbal, astronomical, biological, cosmological, pharmaceutical, and instructive. The relationship between the illustrations and the text is uncertain.

The book’s history is also somewhat uncertain. By the style of dress of people depicted in the illustrations, most historians believe the book was written between 1450 and 1520. The earliest reference to the book was in a letter written in 1639 by Georg Baresch, an obscure alchemist living in Prague, to Jesuit scholar Anathasius Kircher at Collegio Romano asking for assistance in deciphering “this Sphynx that had been taking up space uselessly in [his] library for many years.” Kircher acquired the book in 1666 after Baresch’s death.

There is no mention of the book for the next 200 years, although it was likely kept at the library of Collegio Romano. When the forces of King Victor Emmanuel II of Italy captured Rome in 1870, the college moved much of its library collection to the Italian countryside for protection.

After Voynich’s death in 1930, the book made its way through the hands of various book collectors and dealers who were unable to find a buyer for it. In 1969, the book was donated to Yale University.

Fortunately, Yale has made high-res scans of the entire Voynich Manuscript avaialble online. Click here to take your own tour of the book’s secrets.

Many theories abound about the book’s authorship, content, purpose, and language. My favorite one was postulated by the folks over at XKCD.

I just upgraded the site to WordPress 2.8, which was released yesterday. WordPress describes the 2.8 release as a “fit and finish” release, meaning they fixed a bunch of bugs and cleaned up some annoyances in the user interface.

You shouldn’t notice anything different on the site other than it should generate pages somewhat faster. The Dashboard looks a bit different here and there, but it also looks mostly the same. (Most of the changes are visible only to administrators.)

If you notice anything that’s behaving too oddly (other than the site administrator), please let me know.