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!

Nice going! But how did you settle on the last digits of each pair?

The pattern of a word can be represented by a sequence of numbers indicating single and repeated letters. For example, the pattern of BOYCOTT is 1234255 since the second letter is the same as the fifth; the last two letters are the same and the other letters are all different. The patterns of two ten- letter words each containing only seven different letters, are added, treating the pattern representations as ten-digit numbers. The result is 2464870348. What are the words?

An automatic card shuffler always rearranges the cards the same way if the setting is the same. A set of twelve cards bearing the letters GOLDENBINARY [/code] is put through the machine, and the cards, in the order in which they emerge, are put through again. They come out [code] ANINOYGREDBL What message did the cards convey after the first operation, assuming the setting is left unchanged?

When I did the puzzle, I stumbled on the same T. It turns out to be correct. There is another explanation for the apparent conflict!

The Answer is ALAUZRNQNLI No, sorry. But I see that you used the equivalents in my example. The example is only there to show you how the system works. You do not know the table of equivalents for the actual problem. Also, the answer is an actual 11-letter common English word.

The letters of the alphabet plus "space" are to be replaced by the 27 permutations of the numbers 1, 2, 3, repetitions allowed. These numerical equivalents are to be written in a column below each letter and taken off horizontally in groups of three, proceeding from the end of one row to the beginning of the next. As a final step these groups of three are to be reconverted into letters using the same equivalents. By this method MATHEMATICS becomes MGACNFMCOTM and another eleven- letter word becomes NFASOICAOTO. What is the second word? SUPERPRISMATIC EXAMPLE: Suppose we use the following equivalents: A = 3,3,3 B = 1,3,1 C = 2,2,3 D = 1,1,1 E = 2,2,2 F = 1,2,1 G = 2,3,2 H = 2,1,1 I = 1,3,2 J = 1,2,2 K = 3,1,3 L = 2,3,3 M = 2,3,1 N = 3,2,3 O = 3,3,2 P = 3,1,1 Q = 3,2,1 R = 1,3,3 S = 2,1,3 T = 3,3,1 U = 1,2,3 V = 3,2,2 W = 3,1,2 X = 1,1,2 Y = 1,1,3 Z = 2,1,2 "space" = 2,2,1 [/code] The phrase "Bad Juju" becomes: [code] BAD JUJU 13121111 33122222 13112323 Pulling numbers off by rows then converting to letters, we get: B (1,3,1) H (2,1,1) Y (1,1,3) W (3,1,2) E (2,2,2) S (2,1,3) X (1,1,2) N (3,2,3) [/code] and so, BHYWESXN is the cypher.

A certain quotation containing 26 letters is written below a normal alphabet and a third line is generated by writing below each letter in the second line the letter which is below it in the first line. If, for example, A in the first line has a B below it in the second line, any A in the second line will have a B below it in the third line. Thus: "Give me liberty or give me death" will lead to the sequence: LBDMYMTBIMVMTRVLBDMYMEMGMI [/code] Another 26-letter quotation treated in the same way yields the third line: [code] YIYVNEASLROEEEEUAIYVAUAUAL What does it say? SUPERPRISMATIC EXPANDING THE EXAMPLE: ABCDEFGHIJKLMNOPQRSTUVWXYZ GIVEMELIBERTYORGIVEMEDEATH LBDMYMTBIMVMTRVLBDMYMEMGMI [/code] SUPERPRISMATIC'S REQUEST: If you solve this, please describe how you did it. My method is not very slick, so I'd like to see a better one -- perhaps one using a result from Group Theory, e.g.

N electric light bulbs numbered 1 to N are arranged in a circle and are so wired that pressing the switch to turn on (off) any light also turns on (off) the adjacent lights. At present all lights are off and it is desired to turn on only the first light. What sequence of switches should be activated? (Assume that N is not a multiple of 3) SUPERPRISMATIC CLARIFICATION: Pressing the switch for light K will change the state of lights K-1, K, and K+1 (mod N). So, if those lights were (ON,ON,OFF) then pressing that switch will change it to (OFF,OFF,ON). SUPERPRISMATIC'S QUESTION: Are there any on-off patterns of lights which are NOT achievable from the all off condition using some sequence of switch pushing? SUPERPRISMATIC'S OTHER QUESTIONS: Is it always possible to get from any particular on-off pattern to any other with some sequence of switch pushing? Is this essentially different than my previous question?

and for the record im dumb again Good work! You got it! I suppose I made a typo because it should have been "an hour later" instead of "an gour later". But, you have my admiration for this nice solution! Nice!

Just for grins, I went through all 3,628,800 possible assignments of digits to letters. Only one solution popped out. I realize that I could have gone through a much smaller number given the constraints that could be surmised, put the program only took a few minutes to write and under a second to run.

Spacing isn't a decoy. It's just used to make it easy to read the text. Other than that, spaces aren't used. Look at my "To be..." example above and you can see that spaces don't matter. Oh, I see what you mean now! In the "To be..." example, the letters just happened to come out in groups of 5. I guess that is confusing. But, just ignore spacing.

Not the way I read the puzzle. I suppose it's an 8 by 8 square because 56 letters + 8 numbers would just fit.

Perhaps the "To be.." example will be enlightening: 6 S T I O N O 3 B E T H R N 2 O T T H E Q 5 U E T O B E 1 O A T I S T 4 [/code] So the beginning of the quote (the first 5 letters) goes from right-to-left in the row containing the 1. The next five letters go in the cow containing 2, etc. Then, you pull out first (from top to bottom) from the column containing the 1. I hope this clears it up.

The numbers 1 to N are written in scrambled order in the diagonal cells of an N by N square (from upper left to lower right). A message is written horizontally in this square, starting in the row in which the 1 appears, then 2, etc. It is then taken out vertically, taken in columns in the order indicated by the numbers. Using this method with N=6 and the sequence 6,3,2,5,1,4, the quotation "To be or not to be, that is the question" becomes O T T U T T B Q B I S N E O T N H T E O I E O E S O R H T A [/code] Read the following: [code] U W D G O C A Y N E B F F R E S N N A U E D D H S I C R O E A A R U L U O O O N O S M A L M M N U R I A R M I T

A repairman fixing a typewritter accidentally rearranged the electric wiring so that each key printed a letter other than the one shown on the key (actually the letters were wired in pairs so that if, for example, on striking A a Z were printed, then on striking Z an A would be printed). A list of 9-letter words was being typed on this typewriter and ten words were written before the error was discovered. These ten words appeared as: A J E Y F Z E W A A N M K C G C W A C Q Q A H C E W A C X H C S X E X W G W E C Z I E G A G W Z A X K F K G H A W A Z Q C X A I D E K O O A K Z O F Z W D T C W D Z A O A Z A X I A [/code] What were the original ten words?

Just in case we get a visit from a resident of Krypton (usually called Superman) who is evil, it behooves us to stock up on kryptonite so as to have some way to check his super powers. I have found a chemical reaction which produces kryptonite. Unfortunately, I am unable to balance this particular chemical equation. Please help me by balancing this equation. You can Google "balancing chemical equations" and get some pretty good explanations. Please help so that we can be prepared! Here is the unbalanced equation: Te16Ni18O8 + Te3PtY + Ni20Pt14Kr3 + O4Y13Kr3 + Te8Kr5 + Ni4O4 --> Kr6Y17Pt9O8Ni16Te16

Upper case i.

The Fabulous Gazeeka Box converts letters into their binary equivalents (A=00001, B=00010, etc.), scrambles these 5-bit groups -- always in the same way -- and outputs the results as reconstituted letters. A certain word fed into the F.G.B. comes out NYVRTBKPIJ. Can you unscramble this?

The letters of a certain phrase are numbered in alphabetical order. Then each letter is advanced in the normal alphabetical sequence an amount equal to its number. (A follows Z.) By means of this scheme "Be a sport" is converted into DHBZUSXB, since the sequence of numbers is 2 3 1 7 5 4 6 8. How about UHFIZBBJFOJ?

Well, actually nothing ever actually converges until way, way out there at infinity. So, you are actually relying on a guess that this thing converges to (1+2*x+3*x^2)/6. If it differed by a small amount from this, the solutions may have been 25.00001, -25.6666678 say.

By that remark, I guess you're intrigued by this little problem. I never thought about it, but I guess if the convergent value were something like 321+87i, there may be some fruitful puzzling there! What next? Quaternions?