February 2005 Games

You know the drill, folks.

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Welcome to the Unofficial Calculatrivia Discussion Place!

Hello Calculatrivia fans!

The time has come. Bob Lodge sent me the answer key last night. I've replaced the "TBA"s with the answers he provided.

I've used white on white (except for Y and E) for the answers. (I made the answers visible today, 2/5, since it's come to my attention that search engines are frequently programmed to ignore websites that use the same color for text and background. Seems that's a dirty search optimization trick, and I want to stay in good with Google.)

Update (3/24/04): Welcome GAMES readers learning about this site from the May issue. For all, here's a Word document (84 KB) from Bob Lodge that walks through the calculation steps. Enjoy!

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Whither the Unofficial Calculatrivia Discussion Place?

First, thank you to everyone who's engaged in this lively discussion that developed out of thin air! This has been a very exciting week to watch this little site unfold, and I'm sure it will continue in the days to come.

Before you all disperse into the ether, JM and I would like to know your thoughts about the destiny of the site. We'll certainly keep Calculatrivia discussion up - no fear - especially since Bob's said he'll submit the URL to GAMES.

Now that all you GAMES mag fans are here, what more, if anything, would you like to see? Shall we set up a new front page discussion for each issue of GAMES? Are there other puzzles you'd like to talk about, but haven't found an online forum? Anything else come to mind? It's been a pleasure, and now that GAMES has a modicum of online presence, we'd like to foster it. Let us know what you think.

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Michael's Calculatrivia Fan Fiction letter

Michael sent me a copy of his Calculatrivia Fan Fiction letter to post here. It's a diary of his experience doing the puzzle, and will no doubt reveal some shared frustration and joys! Click "continue reading" below, or here to view it in MS Word.

January 12, 2004

Dear Mr. Lodge,

I commend you on your efforts of creating the intricate latticework you call Ultimate Calculatrivia. However, since you shanghaied so much of my personal time, including the bulk of my two weeks off over the Holidays, I feel the need to return the favour, and I implore you to read my note decrying your twisted, torturous, recursive, circuitous, beastly behemoth of a contest.

Start Me Up

Having taken hiatus from entering GAMES contests since “The 100” (from GAMES’ 100th issue) some 10 years ago (and I am only a puppy at 33 years of age), I thought this puzzle, tricky as it seemed, would be my reasonable rebirth into the world of structured problem-solving for money. I now know that “The 100” was a veritable Candyland compared to your torture chamber. I have systematically broken down my approach and results for you. I don’t particularly care how busy you are…I insist that you read my Calculatrivia Diary.

The beginning. I discovered the puzzle, and made a commitment to solve it. I low-balled my abilities to my wife, boring her with blather about its shrewd construction and arcane references, and how I’d never get through it. Of course, this was so that she might, in my own fantasy world, think me her intellectual hero when I finally cracked the thing with my dizzying intellect and preposterously good research abilities.

First Cut is the Deepest

My first read-through isolated many challenges, not least of which was that I was a 0-for-42 based on information that at the time resided in my brain (not being a fan of the show “COPS”, and all). After a couple of hours of reading and trying to get my head around the puzzle, I decided to label the questions, and thus began my plan of attack. There were six questions that I labeled ‘Impossible’, four as ‘Incomprehensible’, and an additional seven ‘Not Enough Information’. There was also Ω, which naturally I recognized as being insoluble until the other 41 were crack’d. That left me 24 questions, 16 of which I labeled as ‘Manageable’ and eight as ‘Very Hard’. I felt I needed to put a major dent into these 24 in order to have a chance at this. I set to work.

Many of the answers in my ‘Manageable’ and ‘Very Hard’ piles fell quite quickly. Dragster time records, years for frightening solar eclipses, Herbie Love Bugs, Magic Squares, celebrity tattoos…answers started appearing with great frequency. Unbeknownst to me, a couple of them I was annotating erroneously (such as 477 milliseconds, rather than 4477 milliseconds). But progress was upon me. After six days and seven nights, I found myself with answers for all of the ‘Manageables’ and five of the ‘Very Hards’, plus had cracked several codes, performed some pretty versatile mathematics, plugged in some variables, and had recorded answers to 31 questions. [Five of those answers, at the time, were wrong]. Cadenzas and composites and scruples were past me, but I figured the worst was yet to come.

Take this Job and Shove it

With 11 to go, I felt at an impasse. And I presumed that there would be some people to get them all and then correctly solve for X, so I had to make something happen, or give in. There would be no point in submitting a solution that I knew was incomplete. As per my normal routine, I popped on to my rec.puzzles nexus on the Net, to see if there were any others out there, in need of a nudge or just camaraderie (“lone nuts”, as David, a brilliant and wry fellow solver who eventually became my lifeline, would later tag us as). There had been a couple of web posts, referring either to help in finding George Starbuck poetry, the melody to a certain entertainer’s theme song, and a typo in the contest’s equation. I posted a comment or two, and then I culled the email addresses of the interested parties. I began exchanging rants, theories, and musings about this contest with my four virtual kindreds, but did not really exchange much information. My plan was to establish these contacts, but to ‘go it alone’ until I was desperate.

But in mid-December, with 9 clues still unsolved (and several of the ‘solved’ clues dubious, and as it turned out, wrong), I gave up, and forgot about your horrid beast of a riddle, wrapped in an enigma, wrapped in a hermetically sealed rubberized straitjacket sealed with mylar, protected by a secret entrance code written in Navajo with a pipe bomb attached, set to go off on February 2nd.

You’re the Inspiration

But with time off work for good behaviour in late December, I decided to take the puppy out for another run. Hundreds of repetitions of piano and synthesizer notes, to the 1-4-6-9 rhythm were yielding nothing (especially since I didn’t know about the Naka River and its Anka anagram at the time). My wife – y’know, the one I was hoping to impress – was getting irked with my infernal humming and key-punching, and said “why don’t you try switching it up an octave, or something”. Thirty seconds later, I had her in a headlock. I gave her a noogie, and I was back in the game.

Empty Garden (Hey, Hey Johnny)

Carson! Hay-ohhhhhhh! Soon Naka fell, to retrofit Clue beta. Then 99 gallons flooded open the door for the diagonal of the square bisecting the cylinder (and its ugly and seemingly improbably solution). All the information became available for the ‘number of stars’ question…my thoughts twinkled. Carson had been the key to getting me motivated and getting more hammers to fall. I thought it fitting that Johnny Carson was answer ‘J’. Leno is OK, but he’s no Johnny.

But what remained were brutally difficult questions. I was left with the ‘number of stars’ question, the octagon perimeter, the chess puzzle, the value of Bulgarian stamps, the George-flaming-Starbuck poem, the Motorola processor, and, of course, our good friend Ω.

A Hard Day’s Night

Brute force alone helped me crack the octagon. I kept looking at it and using every nugget of geometry and trigonometry I could remember, but I kept getting the useless equation 0 = 0. I knew it could be done with the information I had, but I just couldn’t crack it. Though I was a former math league captain in high school and a short-lived Math Major in university, the Law of Cosines had somehow sluiced through my memory banks, and onto the cutting room floor.

Once I re-discovered this formula, in what I was expecting to be a futile search of geometry websites (yes, there are geometry websites aplenty!), I knew it was the piece I needed. My all-nighter finally gave me a substantiated result. Success, in this venue and at this stage, is more about relief than celebration. Knocking answers off the list simply eased my tension. There was no celebration in the end zone.

Brilliant Disguise

From the early days of this contest, I had been reading every single solitary available reference to the late George Starbuck, and had scoured the books that were in our local University library – none of which had ever been checked out before. Perhaps not even opened. No luck. I exchanged futile emails with English professors, and eventually ordered two of Starbuck’s books – “Visible Ink” and “The Works” – from Amazon. No sign of butterflies or Scandinavian faeries to be found. Nothing even close. I was beginning to feel like an imbecile, and that this was to be the place that I would stumble and fall. I had some solace in the expectation that other puzzlers were having the same problems with this question. Until…

Andrew, a web acquaintance, told me that he had solved this question, that the poems in question were not in any of the books I had read, and in the world’s lamest hint, told me that the digits in the correct answer (including decimals) added up to be a prime number. Great – so the correct answer could be 20 or 3,426,761.8 or, really, anything. [And, not including the decimals.] What he didn’t tell me (damn him) was that there were no decimals, and that the poet in question of course, was not George Starbuck…the real poet was Winfield Townley Scott – a poet hidden in the original Starbuck offering. And so there is little surprise that there is no mention of Swedish angels or butterflies in Mr. Starbuck’s obscure dirges. In an “act of faith”, my true Calculatrivia sage and confidante (David), and another from my inner circle (Sandra), nudged me on the poetry, and I had it beat. Of course, 62,500 – the correct answer – did have digits that add up to the primal 13. Thanks for the hot tip, Andrew.

Bani and the Jets

The Romanian stamps question first appeared in my ‘Impossible’ list. I didn’t quite understand it, and there was so much other information required (and so little that I could find about Romanian stamps). It is the only question that I have not in any way corroborated (or even solved, really). Another question (lambda) pretty much forced the value, in bani, to equal 2,050. Had that been a stand-alone question, I don’t know how I possibly would have found it. I simply stopped looking for support for this answer, and took it as a given.

Saved by Zero

Everything I could find about the original cores of apples (the Motorola question) left me tossed-up between 68,000 and 6,800, but I really had no way of deciding between the two, and hoped that the formula itself would force one of them to be true. 6,800 seemed much more palatable, it brought my Ω level down considerably, and I felt quite certain that the pieces were starting to fit. So I dumped the final zero, locked in on 6,800, and felt one step closer to the prize.

[I later found out that the formula forced them both false, and started me into a guessing game, a downward spiral, and finally, an epiphany.]

Wasted Days and Wasted Knights

The chess puzzle came to me in the middle of the night. I’ve never had a chess puzzle come to me in the middle of the night before. I had spent many hours trying to make unorthodox first moves, and always ended up awarding a kingly escape route. The late night synaptical explosion sent me rushing to the chessboard. I don’t know if I have ever felt more powerful than banishing that little horsie into the corner.

I Want Your X

I finally settled on 76 for the number of stars in question C, mostly because it made for a decent exponent in the formula (“the monster equation” according to David). And so I created a formula-based spreadsheet to enter the numbers, hoping it would spit out a rational and very satisfying X. With tooling and retooling, X equaled anything from
–1099.342986732 to 213,423.34298798, but definitely nothing taut, recognizable, or mildly satisfying. Something (or somethings) was wrong. Some exchanges of thoughts with David led him to scream a cyber eureka, but still left me as Clueless Joe Jackson. Unwittingly, I still had 6 wrong answers, whereas I thought I had only 2 (including the ultimate Ω).

Clue T was wrong. Clue I was wrong. As were Clues G, K and ι. And of course, Ω was a million minims away. But I didn’t know…couldn’t know…which ones were off-kilter, or why. I began to use the equation as a way to help solve the clues. A quick review corrected G to 4477. I saw my solution to T not fitting into the puzzle, so I attacked the question again, and eventually found a number that reduced much of the top part of the second parenthesis down to something digestible.

Then I got some smart advice from David. “Given the ungodly messiness of answer E – which IS correct – and given the way E appears in the monster equation (three times), and given the promise that everything will work out to a rational number, what is the ONLY POSSIBLE way to make that happen, without leaving behind any leftover one-third or two-third roots?” This led me to research K again, looking for more possibilities, and found 6,502. The new answer made a lot of things disappear. David’s advice, however cryptic it might have been, had shown me a glimmer of how to make certain variables vanish, and allow all of the third roots to come together for a mathematical ménage-a-trois. Their bodies became one, and I washed all the roots and pi’s and horrific looking numbers right out of my hair.

Runnin’ Down a Dream

Suddenly my spreadsheet’s X – for the first time – displayed a clearly rational answer: 10.15.

I shouted. “I’ve got it, honey”. My wife smirked and snorted (to my chagrin), but rather than the expected ticker-tape parade, she posed “are you back?” I told her I had a bit of cross-referencing to do, and I had to formally compile my answer, but that married life, and the last 2 days of vacation, was back on stream.

But, of course, the answer is not 10.15. I was not back. Clue K was still wrong. Clue I was still wrong. The whole thing, in fact, was still very wrong. And the error in these two variables (I and K) did not have alarm bells attached – Ω worked, and my X was rational.

American Pi

In true puzzlers’ fashion, my New York pal David and I gave each other tips and clues, rather than answers. After much parrying over the meaning of the word ‘widdershins’, we seemed to agree that the correct answer to K was 368π, just slightly different that our original assertion. This brought my X (and presumably his) to a tidy 11.2. The answer, however attractive, was still horribly wrong. But we both believed ourselves to have a perfect score, and glory among the numerate of the world would be ours.

The Rising

I was all ready to send my answers to GAMES, and await my cheque, when a stray note came from David. “The other variable”, it said, “that could be wrong and still lead us to a wrong rational answer is I, but we’re pretty confident that’s 14, right?” I responded that I had confirmed Clue I, that the date was February 29, 1876, and that the answer was certainly 14. So not to worry.

But something was eating at me. I remembered an exchange with Sandra, my other compadre, in which she had said that Clue I was 15, and I had pleasantly informed her that she was off her rocker. I forced myself to look closer, and what I saw was the most devious and sinister question of the lot. As if you, Mr. Lodge, had warped history just to pin a smelly red herring on my door.

You have undoubtedly snookered many people on this question. Most normal people conclude that once a ship has sunk, it’s no longer afloat. But now and then, ships are raised – re-floated if you will – and then re-sunk with honour (but not very often on the day before a new state enters the Union). The synchronization of the questions, and the brilliance of the red herring was quite a feat. I is 15, not 14. And but for a triple take, and an innocent ‘are we sure’ from David, you had me.

Good Riddance (Time of My Life)

But I think I have got you beat. Ten and seven-eighths, Lodge. Ten and seven-eighths.

It’s Hip to be Square

Now I wonder if you will begin your threeupmanship and show me what other undetected sniveling trick you placed in the puzzle, to make the answer eleven and forty-three-sixty seconds, or some such. Or can I (and good ol’ David) bask in our ability to combine detective work, logic, trust, dogged determination, and an over-riding embrace of all things clever to bust this open?

Thanks. Truly, thanks.

Michael Pickard

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Open forum

For general discussion about the contest.

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Answer: 2132

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Answer: 49

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Answer: 76

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Answer: 362880

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