superprismatic Posted August 17, 2009 Report Share Posted August 17, 2009 The polynomial X23+X+1 can be expressed as the product of 2 factors. If the powers of X, excluding the constant term, in one of these factors is converted into letters (1=A, 2=B, etc.), it is observed that these letters can be anagrammed into a three-word phrase meaning, with a certain stretch of the imagination, "a peculiarity of a seat in a church gallery." What is the phrase? SUPERPRISMATIC CLARIFICATION: Perhaps the word "powers" should be replaced by "exponents" to better nail down the intent of the puzzle. SUPERPRISMATIC OBSERVATION: Walter Penney did not have access to computer algebra software! Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted August 17, 2009 Report Share Posted August 17, 2009 (edited) The polynomial X23+X+1 can be expressed as the product of 2 factors. If the powers of X, excluding the constant term, in one of these factors is converted into letters (1=A, 2=B, etc.), it is observed that these letters can be anagrammed into a three-word phrase meaning, with a certain stretch of the imagination, "a peculiarity of a seat in a church gallery." What is the phrase? SUPERPRISMATIC CLARIFICATION: Perhaps the word "powers" should be replaced by "exponents" to better nail down the intent of the puzzle. SUPERPRISMATIC OBSERVATION: Walter Penney did not have access to computer algebra software! No computer algebra software was used in the solving of this puzzle. Though for most practical purposes, I did the same algorithm that an algebra software would have used. x23 + x + 1 = (x 2 + x + 1) * ( x21 - x20 + x18 - x17 + x15 - x14 + x12 - x11 + x9 - x8 + x6 - x5 + x3 - x2 + 1 ) The exponents that make up the anagram must be (21 20 18 17 15 14 12 11 9 8 6 5 3 2), which correspond to the following letters. "u" "t" "r" "q" "o" "n" "l" "k" "i" "h" "f" "e" "c" "b" Here's where I need a tag team. I'm not much of an anagram person, so feel free to jump here. Edited August 17, 2009 by bushindo Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 loft/bench/quirk Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted August 17, 2009 Report Share Posted August 17, 2009 loft/bench/quirk Good teamwork. I have never been good at anagrams, so I'd like to know how you did it so quick. Is there a particular algorithm or approach that you use to construct/deconstruct anagrams? Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted August 17, 2009 Report Share Posted August 17, 2009 Belch Fork Quint Belch Font Quirk Blench Fork Quit Blench Oft Quirk Bench Folk Quirt Bench Fork Quilt Bench Loft Quirk Blotch Fen Quirk Herb Flock Quint Bilk Quench Fort Brink Clef Quoth Cob Elf Nth Quirk bonanova, I'd like to ask you the same question I asked tpaxatb. Is there a non-computer particular algorithm or approach that you use to construct/deconstruct anagrams? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2009 Report Share Posted August 17, 2009 bonanova, I'd like to ask you the same question I asked tpaxatb. Is there a non-computer particular algorithm or approach that you use to construct/deconstruct anagrams? (if you could call it a method <g>) I play a *lot* of scrabble. (OK, I may have been slightly exaggerating on the speed...it took about 15 mins or so ) For this one, the Qu is pretty obvious... In addition, you could see that you run out of vowels really quickly. I was operating under the assumption that no letter was repeating. so we're talking (discounting the U paired with the Q) 1 long word, 2 words (1 with 2 vowels and 1 with 1) or 3 words, each with one vowel (i discarded the "scrabble words" that are silly in the context of something like a walter penney puzzle <g>)... In any of the cases you realize that you will have more than one few consonant connectors. You're talking stuff like NT, LF, FT, CH, TH, LT, RK etc. I operated under the assumption that it was at least 2 words. When dealing with Qu, I tend (just habit, I guess) I look for words that START with QU. You can see rather quickly that QUI QUO QUE are your starters. Plus I had the puzzle in mind, and it happened that I was able to get quirk quickly (I ran through Quilt, Quick, Quench, (eliminated because of two vowels + u) and hit Quirk, which fit the puzzle. (although I was thrown and didn't see it right away because of the lack of "Y" I was looking for an adjective) that gave me: E O B C F H L N T Still operating under the assumption that there's two words left, I was still looking for consonant connectors.... CH, NT, FT, TH. I'm also looking for a word that has something to do with church seat. At first I thought pew, but obviously no P or W (<g>)...Some quick rearranging gave me BENCH (actually I saw BENCH because I had previously seen QUENCH) So now I have O L F T - Only thing that makes sense is LOFT. Now, I wouldn't have gotten it without the letters (qualify: it would have taken me a LOT longer...you did the "hard" part Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted August 17, 2009 Report Share Posted August 17, 2009 (edited) (if you could call it a method <g>) I play a *lot* of scrabble. (OK, I may have been slightly exaggerating on the speed...it took about 15 mins or so ) For this one, the Qu is pretty obvious... In addition, you could see that you run out of vowels really quickly. I was operating under the assumption that no letter was repeating. so we're talking (discounting the U paired with the Q) 1 long word, 2 words (1 with 2 vowels and 1 with 1) or 3 words, each with one vowel (i discarded the "scrabble words" that are silly in the context of something like a walter penney puzzle <g>)... In any of the cases you realize that you will have more than one few consonant connectors. You're talking stuff like NT, LF, FT, CH, TH, LT, RK etc. I operated under the assumption that it was at least 2 words. When dealing with Qu, I tend (just habit, I guess) I look for words that START with QU. You can see rather quickly that QUI QUO QUE are your starters. Plus I had the puzzle in mind, and it happened that I was able to get quirk quickly (I ran through Quilt, Quick, Quench, (eliminated because of two vowels + u) and hit Quirk, which fit the puzzle. (although I was thrown and didn't see it right away because of the lack of "Y" I was looking for an adjective) that gave me: E O B C F H L N T Still operating under the assumption that there's two words left, I was still looking for consonant connectors.... CH, NT, FT, TH. I'm also looking for a word that has something to do with church seat. At first I thought pew, but obviously no P or W (<g>)...Some quick rearranging gave me BENCH (actually I saw BENCH because I had previously seen QUENCH) So now I have O L F T - Only thing that makes sense is LOFT. Now, I wouldn't have gotten it without the letters (qualify: it would have taken me a LOT longer...you did the "hard" part That's a wonderful approach. Thanks for the description, I learned a lot from it. Edited August 17, 2009 by bushindo Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 18, 2009 Report Share Posted August 18, 2009 That's a wonderful approach. Thanks for the description, I learned a lot from it. No problem (hehe I was just thinking that I feel honored now that someone actually learned from me...all these puzzles recently have been making me delve into math/comp sci recesses I haven't touched in years,since I don't deal with them daily.?) And this set of puzzles has been driving me batty I think (for me) the biggest help for this one (for me at least)...were the QU, the limited vowels, and the clues about the word...getting "quirk" helped ALOT Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 18, 2009 Report Share Posted August 18, 2009 bonanova, I'd like to ask you the same question I asked tpaxatb. Is there a non-computer particular algorithm or approach that you use to construct/deconstruct anagrams? Just what comes to mind when I look. My parents were addicted to a game called anagrams. It seems some people are gifted in that area - a glance at letters scattered on the table is all they need. I didn't inherit the gift, but I do play a decent game of Boggle... and spent several years as an editor, so I'm kind of a word guy. I looked up [wordsmith.org] the solutions, posted them, then decided it didn't add anything to the discussion and deleted it. You replied before I hit the button ... Quote Link to comment Share on other sites More sharing options...
Question
superprismatic
The polynomial X23+X+1 can be
expressed as the product of 2 factors.
If the powers of X, excluding the
constant term, in one of these factors
is converted into letters (1=A, 2=B,
etc.), it is observed that these letters
can be anagrammed into a three-word
phrase meaning, with a certain stretch
of the imagination, "a peculiarity of a
seat in a church gallery." What is the
phrase?
SUPERPRISMATIC CLARIFICATION: Perhaps
the word "powers" should be replaced
by "exponents" to better nail down the
intent of the puzzle.
SUPERPRISMATIC OBSERVATION: Walter
Penney did not have access to computer
algebra software!
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