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Xref: bloom-picayune.mit.edu rec.puzzles:18136 news.answers:3068 Newsgroups: rec.puzzles,news.answers Path: bloom-picayune.mit.edu!snorkelwacker.mit.edu!usc!wupost!uunet!questrel!chris From: uunet!questrel!chris (Chris Cole) Subject: rec.puzzles FAQ, part 1 of 15 Message-ID: <puzzles-faq-1_717034101@questrel.com> Followup-To: rec.puzzles Summary: This posting contains a list of Frequently Asked Questions (and their answers). It should be read by anyone who wishes to post to the rec.puzzles newsgroup. Sender: chris@questrel.com (Chris Cole) Reply-To: uunet!questrel!faql-comment Organization: Questrel, Inc. Date: Mon, 21 Sep 1992 00:08:26 GMT Approved: news-answers-request@MIT.Edu Expires: Sat, 3 Apr 1993 00:08:21 GMT Lines: 1557 Archive-name: puzzles-faq/part01 Last-modified: 1992/09/20 Version: 3 Instructions for Accessing rec.puzzles Frequently Asked Questions List INTRODUCTION Below is a list of puzzles, categorized by subject area. Each puzzle includes a solution, compiled from various sources, which is supposed to be definitive. EMAIL To request a puzzle, send a letter to uunet!questrel!faql-request containing one or more lines of the form: send <puzzle_name> For example, to request decision/allais.p, send the line: send decision/allais.p or just: send allais The puzzle will be mailed via return email to the address in your request's "From:" line. If you are unsure of this address, and cannot edit this line, then include in your message BEFORE the first "send" line the line: return_address <your_return_email_address> FTP The FAQL has been posted to news.answers. News.answers is archived in the periodic posting archive on pit-manager.mit.edu [18.172.1.27]. Postings are located in the anonymous ftp directory /pub/usenet/news.answers, and are archived by "Archive-name". Other subdirectories of /pub/usenet contain periodic postings that may not appear in news.answers. Other news.answers/FAQ archives (which carry some or all of the FAQs in the pit-manager archive) are: archive.cs.ruu.nl [131.211.80.5] in the anonymous ftp directory /pub/NEWS.ANSWERS (also accessible via mail server requests to mail-server@cs.ruu.nl) cnam.cnam.fr [192.33.159.6] in the anonymous ftp directory /pub/FAQ ftp.uu.net [137.39.1.9 or 192.48.96.9] in the anonymous ftp directory /usenet ftp.win.tue.nl [131.155.70.100] in the anonymous ftp directory /pub/usenet/news.answers grasp1.univ-lyon1.fr [134.214.100.25] in the anonymous ftp directory /pub/faq (also accessible via mail server requests to listserv@grasp1.univ-lyon1.fr), which is best used by EASInet sites and sites in France that do not have better connectivity to cnam.cnam.fr (e.g. Lyon, Grenoble) Note that the periodic posting archives on pit-manager.mit.edu are also accessible via Prospero and WAIS (the database name is "usenet" on port 210). CREDIT The FAQL is NOT the original work of the editor (just in case you were wondering :^). In keeping with the general net practice on FAQL's, I do not as a rule assign credit for FAQL solutions. There are many reasons for this: 1. The FAQL is about the answers to the questions, not about assigning credit. 2. Many people, in providing free answers to the net, do not have the time to cite their sources. 3. I cut and paste freely from several people's solutions in most cases to come up with as complete an answer as possible. 4. I use sources other than postings. 5. I am neither qualified nor motivated to assign credit. However, I do whenever possible put bibliographies in FAQL entries, and I see the inclusion of the net addresses of interested parties as a logical extension of this practice. In particular, if you wrote a program to solve a problem and posted the source code of the program, you are presumed to be interested in corresponding with others about the problem. So, please let me know the entries you would like to be listed in and I will be happy to oblige. Address corrections or comments to uunet!questrel!faql-comment. INDEX ==> analysis/bugs.p <== Four bugs are placed at the corners of a square. Each bug walks directly toward the next bug in the clockwise direction. The bugs walk with constant speed always directly toward their clockwise neighbor. Assuming the bugs make at least one full circuit around the center of the square ==> analysis/c.infinity.p <== What function is zero at zero, strictly positive elsewhere, infinitely differentiable at zero and has all zero derivitives at zero? ==> analysis/cache.p <== Cache and Ferry (How far can a truck go in a desert?) A pick-up truck is in the desert beside N 50-gallon gas drums, all full. The truck's gas tank holds 10 gallons and is empty. The truck can carry one drum, whether full or empty, in its bed. It gets 10 miles to the gallon. ==> analysis/cats.and.rats.p <== If 6 cats can kill 6 rats in 6 minutes, how many cats does it take to kill one rat in one minute? ==> analysis/e.and.pi.p <== Which is greater, e^(pi) or (pi)^e ? ==> analysis/functional/distributed.p <== Find all f: R -> R, f not identically zero, such that (*) f( (x+y)/(x-y) ) = ( f(x)+f(y) )/( f(x)-f(y) ). ==> analysis/functional/linear.p <== Suppose f is non-decreasing with f(x+y) = f(x) + f(y) + C for all real x, y. Prove: there is a constant A such that f(x) = Ax - C for all x. (Note: continuity of f is not assumed in advance.) ==> analysis/integral.p <== If f is integrable on (0,inf), and differentiable at 0, and a > 0, show: inf ( f(x) - f(ax) ) ==> analysis/period.p <== What is the least possible integral period of the sum of functions of periods 3 and 6? ==> analysis/rubberband.p <== A bug walks down a rubberband which is attached to a wall at one end and a car moving away from the wall at the other end. The car is moving at 1 m/sec while the bug is only moving at 1 cm/sec. Assuming the rubberband is uniformly and infinitely elastic, will the bug ever reach the car? ==> analysis/series.p <== Show that in the series: x, 2x, 3x, .... (n-1)x (x can be any real number) there is at least one number which is within 1/n of an integer. ==> analysis/snow.p <== Snow starts falling before noon on a cold December day. At noon a snowplow starts plowing a street. It travels 1 mile in the first hour, and 1/2 mile in the second hour. What time did the snow start falling?? ==> analysis/tower.p <== A number is raised to its own power. The same number is then raised to the power of this result. The same number is then raised to the power of this second result. This process is continued forever. What is the maximum number which will yield a finite result from this process? ==> arithmetic/7-11.p <== A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11. He was curious that the cost was the same as the store name, so he inquired as to how the figure was derived. The clerk said that he had simply multiplied the prices of the four ==> arithmetic/clock/day.of.week.p <== It's restful sitting in Tom's cosy den, talking quietly and sipping a glass of his Madeira. I was there one Sunday and we had the usual business of his clock. ==> arithmetic/clock/thirds.p <== Do the 3 hands on a clock ever divide the face of the clock into 3 equal segments, i.e. 120 degrees between each hand? ==> arithmetic/consecutive.product.p <== Prove that the product of three or more consecutive natural numbers cannot be a perfect square. ==> arithmetic/consecutive.sums.p <== Find all series of consecutive positive integers whose sum is exactly 10,000. ==> arithmetic/digits/all.ones.p <== Prove that some multiple of any integer ending in 3 contains all 1s. ==> arithmetic/digits/arabian.p <== What is the Arabian Nights factorial, the number x such that x! has 1001 digits? How about the prime x such that x! has exactly 1001 zeroes on the tail end. (Bonus question, what is the 'rightmost' non-zero digit in x!?) ==> arithmetic/digits/circular.p <== What 6 digit number, with 6 different digits, when multiplied by all integers up to 6, circulates its digits through all 6 possible positions, as follows: ABCDEF * 1 = ABCDEF ABCDEF * 3 = BCDEFA ==> arithmetic/digits/divisible.p <== Find the least number using 0-9 exactly once that is evenly divisible by each of these digits? ==> arithmetic/digits/equations/123456789.p <== In how many ways can "." be replaced with "+", "-", or "" (concatenate) in .1.2.3.4.5.6.7.8.9=1 to form a correct equation? ==> arithmetic/digits/equations/1992.p <== 1 = -1+9-9+2. Extend this list to 2 - 100 on the left side of the equals sign. ==> arithmetic/digits/equations/383.p <== Make 383 out of 1,2,25,50,75,100 using +,-,*,/. ==> arithmetic/digits/extreme.products.p <== What are the extremal products of three three-digit numbers using digits 1-9? ==> arithmetic/digits/googol.p <== What digits does googol! start with? ==> arithmetic/digits/labels.p <== You have an arbitrary number of model kits (which you assemble for fun and profit). Each kit comes with twenty (20) stickers, two of which are labeled "0", two are labeled "1", ..., two are labeled "9". You decide to stick a serial number on each model you assemble starting ==> arithmetic/digits/nine.digits.p <== Form a number using 0-9 once with its first n digits divisible by n. ==> arithmetic/digits/palindrome.p <== Does the series formed by adding a number to its reversal always end in a palindrome? ==> arithmetic/digits/palintiples.p <== Find all numbers that are multiples of their reversals. ==> arithmetic/digits/power.two.p <== Prove that for any 9-digit number (base 10) there is an integral power of 2 whose first 9 digits are that number. ==> arithmetic/digits/prime/101.p <== How many primes are in the sequence 101, 10101, 1010101, ...? ==> arithmetic/digits/prime/all.prefix.p <== What is the longest prime whose every proper prefix is a prime? ==> arithmetic/digits/prime/change.one.p <== What is the smallest number that cannot be made prime by changing a single digit? Are there infinitely many such numbers? ==> arithmetic/digits/prime/prefix.one.p <== 2 is prime, but 12, 22, ..., 92 are not. Similarly, 5 is prime whereas 15, 25, ..., 95 are not. What is the next prime number which is composite when any digit is prefixed? ==> arithmetic/digits/reverse.p <== Is there an integer that has its digits reversed after dividing it by 2? ==> arithmetic/digits/rotate.p <== Find integers where multiplying them by single digits rotates their digits. ==> arithmetic/digits/sesqui.p <== Find the least number where moving the first digit to the end multiplies by 1.5. ==> arithmetic/digits/squares/leading.7.to.8.p <== What is the smallest square with leading digit 7 which remains a square when leading 7 is replaced by an 8? ==> arithmetic/digits/squares/length.22.p <== Is it possible to form two numbers A and B from 22 digits such that A = B^2? Of course, leading digits must be non-zero. ==> arithmetic/digits/squares/length.9.p <== Is it possible to make a number and its square, using the digits from 1 through 9 exactly once? ==> arithmetic/digits/squares/three.digits.p <== What squares consist entirely of three digits (e.g., 1, 4, and 9)? ==> arithmetic/digits/squares/twin.p <== Let a twin be a number formed by writing the same number twice, for instance, 81708170 or 132132. What is the smallest square twin? ==> arithmetic/digits/sum.of.digits.p <== Find sod ( sod ( sod (4444 ^ 4444 ) ) ). ==> arithmetic/digits/zeros/factorial.p <== How many zeros are in the decimal expansion of n!? ==> arithmetic/digits/zeros/lsd.factorial.p <== What is the least significant non-zero digit in the decimal expansion of n!? ==> arithmetic/digits/zeros/million.p <== How many zeros occur in the numbers from 1 to 1,000,000? ==> arithmetic/magic.squares.p <== Are there large squares, containing only consecutive integers, all of whose rows, columns and diagonals have the same sum? How about cubes? ==> arithmetic/pell.p <== Find integer solutions to x^2 - 92y^2 = 1. ==> arithmetic/prime/arithmetic.progression.p <== Is there an arithmetic progression of 20 or more primes? ==> arithmetic/prime/consecutive.composites.p <== Are there 10,000 consecutive non-prime numbers? ==> arithmetic/sequence.p <== Prove that all sets of n integers contain a subset whose sum is divisible by n. ==> arithmetic/sum.of.cubes.p <== Find two fractions whose cubes total 6. ==> arithmetic/tests.for.divisibility/eleven.p <== What is the test to see if a number is divisible by eleven? ==> arithmetic/tests.for.divisibility/nine.p <== What is the test to see if a number is divisible by nine? ==> arithmetic/tests.for.divisibility/seven.p <== What is the test to see if a number is divisible by 7? ==> arithmetic/tests.for.divisibility/three.p <== Prove that if a number is divisible by 3, the sum of its digits is likewise. ==> combinatorics/coinage/combinations.p <== How many ways are there to make change for a dollar? Count combinations of coins, not permuations. ==> combinatorics/coinage/dimes.p <== "Dad wants one-cent, two-cent, three-cent, five-cent, and ten-cent stamps. He said to get four each of two sorts and three each of the others, but I've forgotten which. He gave me exactly enough to buy them; just these dimes." How many stamps of each type does Dad want? ==> combinatorics/coinage/impossible.p <== What is the smallest number of coins that you can't make a dollar with? I.e., for what N does there not exist a set of N coins adding up to a dollar? It is possible to make a dollar with 1 current U.S. coin (a Susan B. Anthony), 2 coins (2 fifty cent pieces), 3 coins (2 quarters and a fifty cent piece), ==> combinatorics/color.p <== An urn contains n balls of different colors. Randomly select a pair, repaint the first to match the second, and replace the pair in the urn. What is the expected time until the balls are all the same color? ==> combinatorics/full.p <== Consider a string that contains all substrings of length n. For example, for binary strings with n=2, a shortest string is 00110 -- it contains 00, 01, 10 and 11 as substrings. Find the shortest such strings for all n. ==> combinatorics/gossip.p <== n people each know a different piece of gossip. They can telephone each other and exchange all the information they know (so that after the call they both know anything that either of them knew before the call). What is the smallest number of calls needed so that everyone knows everything? ==> combinatorics/grid.dissection.p <== How many (possibly overlapping) squares are in an mxn grid? ==> combinatorics/subsets.p <== Out of the set of integers 1,...,100 you are given ten different integers. From this set, A, of ten integers you can always find two disjoint subsets, S & T, such that the sum of elements in S equals the sum of elements in T. Note: S union T need not be all ten elements of ==> cryptology/Beale.p <== What are the Beale ciphers? ==> cryptology/Feynman.p <== What are the Feynman ciphers? ==> cryptology/Voynich.p <== What are the Voynich ciphers? ==> cryptology/swiss.colony.p <== What are the 1987 Swiss Colony ciphers? ==> decision/allais.p <== The Allais Paradox involves the choice between two alternatives: A. 89% chance of an unknown amount 10% chance of $1 million ==> decision/division.p <== N-Person Fair Division If two people want to divide a pie but do not trust each other, they can still ensure that each gets a fair share by using the technique that one ==> decision/dowry.p <== Sultan's Dowry A sultan has granted a commoner a chance to marry one of his hundred daughters. The commoner will be presented the daughters one at a time. ==> decision/envelope.p <== Someone has prepared two envelopes containing money. One contains twice as much money as the other. You have decided to pick one envelope, but then the following argument occurs to you: Suppose my chosen envelope contains $X, then the other envelope either contains $X/2 or $2X. Both cases are ==> decision/exchange.p <== At one time, the Mexican and American dollars were devalued by 10 cents on each side of the border (i.e. a Mexican dollar was 90 cents in the US, and a US dollar was worth 90 cents in Mexico). A man walks into a bar on the American side of the border, orders 10 cents worth of beer, and tenders a Mexican dollar ==> decision/newcomb.p <== Newcomb's Problem A being put one thousand dollars in box A and either zero or one million dollars in box B and presents you with two choices: ==> decision/prisoners.p <== Three prisoners on death row are told that one of them has been chosen at random for execution the next day, but the other two are to be freed. One privately begs the warden to at least tell him the name of one other prisoner who will be freed. The warden relents: 'Susie will ==> decision/red.p <== I show you a shuffled deck of standard playing cards, one card at a time. At any point before I run out of cards, you must say "RED!". If the next card I show is red (i.e. diamonds or hearts), you win. We assume I the "dealer" don't have any control over what the order of ==> decision/rotating.table.p <== Four glasses are placed upside down in the four corners of a square rotating table. You wish to turn them all in the same direction, either all up or all down. You may do so by grasping any two glasses and, optionally, turning either over. There are two catches: you are ==> decision/stpetersburg.p <== What should you be willing to pay to play a game in which the payoff is calculated as follows: a coin is flipped until in comes up heads on the nth toss and the payoff is set at 2^n dollars? ==> decision/switch.p <== Switch? (The Monty Hall Problem) Two black marbles and a red marble are in a bag. You choose one marble from the bag without looking at it. Another person chooses a marble from the bag and it ==> decision/truel.p <== A, B, and C are to fight a three-cornered pistol duel. All know that A's chance of hitting his target is 0.3, C's is 0.5, and B never misses. They are to fire at their choice of target in succession in the order A, B, C, cyclically (but a hit man loses further turns and is no longer ==> english/acronym.p <== What acronyms have become common words? ==> english/ambiguous.p <== What word in the English language is the most ambiguous? What is the greatest number of parts of speech that a single word can be used for? ==> english/antonym.p <== What words, when a single letter is added, reverse their meanings? Exclude words that are obtained by adding an "a-" to the beginning. ==> english/behead.p <== Is there a sentence that remains a sentence when all its words are beheaded? ==> english/capital.p <== What words change pronunciation when capitalized (e.g., polish -> Polish)? ==> english/charades.p <== A ....... surgeon was ....... to operate because he had ....... ==> english/contradictory.proverbs.p <== What are some proverbs that contradict one another? ==> english/contranym.p <== What words are their own antonym? ==> english/element.p <== The name of what element ends in "h"? ==> english/equations.p <== Each equation below contains the initials of words that will make the phrase correct. Figure out the missing words. Lower case is used only to help the initials stand out better. ==> english/fossil.p <== What are some examples of idioms that include obsolete words? ==> english/frequency.p <== In the English language, what are the most frequently appearing: 1) letters overall? 2) letters BEGINNING words? 3) final letters? ==> english/gry.p <== Find three completely different words ending in "gry." ==> english/homographs.p <== List all homographs (words that are spelled the same but pronounced differently) ==> english/homophones.p <== What words have four or more spellings that sound alike? ==> english/j.ending.p <== What words and names end in j? ==> english/ladder.p <== Find the shortest word ladders stretching between the following pairs: hit - ace pig - sty four - five ==> english/less.ness.p <== Find a word that forms two other words, unrelated in meaning, when "less" and "ness" are added. ==> english/letter.rebus.p <== Define the letters of the alphabet using self-referential common phrases (e.g., "first of all" defines "a"). ==> english/lipograms.p <== What books have been written without specific letters, vowels, etc.? ==> english/multi.lingual.p <== What words in multiple languages are related in interesting ways? ==> english/near.palindrome.p <== What are some long near palindromes, i.e., words that except for one letter would be palindromes? ==> english/palindromes.p <== What are some long palindromes? ==> english/pangram.p <== A "pangram" is a sentence containing all 26 letters. What is the shortest pangram (measured by number of letters or words)? What is the shortest word list using all 26 letters in alphabetical order? In reverse alphabetical order? ==> english/phonetic.letters.p <== What does "FUNEX" mean? ==> english/piglatin.p <== What words in pig latin also are words? ==> english/pleonasm.p <== What are some redundant terms that occur frequently (like "ABM missile")? ==> english/plurals/collision.p <== Two words, spelled and pronounced differently, have plurals spelled the same but pronounced differently. ==> english/plurals/doubtful.number.p <== A little word of doubtful number, a foe to rest and peaceful slumber. If you add an "s" to this, great is the metamorphosis. ==> english/plurals/drop.s.p <== What plural is formed by DROPPING the terminal "s" in a word? ==> english/plurals/endings.p <== List a plural ending with each letter of the alphabet. ==> english/plurals/french.p <== What English word, when spelled backwards, is its French plural? ==> english/plurals/man.p <== Words ending with "man" make their plurals by adding "s". ==> english/plurals/switch.first.p <== What plural is formed by switching the first two letters? ==> english/portmanteau.p <== What are some words formed by combining together parts of other words? ==> english/potable.color.p <== Find words that are both beverages and colors. ==> english/rare.trigraphs.p <== What trigraphs (three-letter combinations) occur in only one word? ==> english/records/pronunciation/silent.p <== What words have an exceptional number of silent letters? ==> english/records/pronunciation/spelling.p <== What words have exceptional ways to spell sounds? ==> english/records/pronunciation/syllable.p <== What words have an exceptional number of letters per syllable? ==> english/records/spelling/longest.p <== What is the longest word in the English language? ==> english/records/spelling/most.p <== What word has the most variant spellings? ==> english/records/spelling/operations.on.words/deletion.p <== What exceptional words turn into other words by deletion of letters? ==> english/records/spelling/operations.on.words/insertion.and.deletion.p <== What exceptional words turn into other words by both insertion and deletion of letters? ==> english/records/spelling/operations.on.words/insertion.p <== What exceptional words turn into other words by insertion of letters? ==> english/records/spelling/operations.on.words/movement.p <== What exceptional words turn into other words by movement of letters? ==> english/records/spelling/operations.on.words/substitution.p <== What exceptional words turn into other words by substitution of letters? ==> english/records/spelling/operations.on.words/transposition.p <== What exceptional words turn into other words by transposition of letters? ==> english/records/spelling/operations.on.words/words.within.words.p <== What exceptional words contain other words? ==> english/records/spelling/sets.of.words/nots.and.crosses.p <== What is the most number of letters that can be fit into a three by three grid of words, such that no letter is repeated in any row, column or diagonal? ==> english/records/spelling/sets.of.words/squares.p <== What are some exceptional word squares (square crosswords with no blanks)? ==> english/records/spelling/single.words.p <== What words have exceptional lengths, patterns, etc.? ==> english/repeat.p <== What is a sentence containing the most repeated words, without: using quotation marks, using proper names, using a language other than English, ==> english/repeated.words.p <== What is a sentence with the same word several times repeated? ==> english/rhyme.p <== What English words are hard to rhyme? "Rhyme is the identity in sound of an accented vowel in a word...and of all consonantal and vowel sounds following it; with a difference in ==> english/self.ref.letters.p <== Construct a true sentence of the form: "This sentence contains _ a's, _ b's, _ c's, ...," where the numbers filling in the blanks are spelled out. ==> english/self.ref.numbers.p <== What true sentence has the form: "There are _ 0's, _ 1's, _ 2's, ..., in this sentence"? ==> english/self.ref.words.p <== What sentence describes its own word, syllable and letter count? ==> english/sentence.p <== Find a sentence with words beginning with the letters of the alphabet, in order. ==> english/snowball.p <== Construct the longest coherent sentence you can such that the nth word is n letters long. ==> english/spoonerisms.p <== List some exceptional spoonerisms. ==> english/states.p <== What long words have all bigrams either a postal state code or its reverse? ==> english/telegrams.p <== Since telegrams cost by the word, phonetically similar messages can be cheaper. See if you can decipher these extreme cases: UTICA CHANSON MIGRATE INVENTION ANNUAL KNOBBY SORRY IN FACTUAL BEEN CLOVER. ==> english/trivial.p <== Consider the free non-abelian group on the twenty-six letters of the alphabet with all relations of the form <word1> = <word2>, where <word1> and <word2> are homophones (i.e. they sound alike but are spelled differently). Show that every letter is trivial. ==> english/weird.p <== Make a sentence containing only words that violate the "i before e" rule. ==> english/word.boundaries.p <== List some sentences that can be radically altered by changing word boundaries and punctuation. ==> english/word.torture.p <== What is the longest word all of whose contiguous subsequences are words? ==> games/chess/knight.control.p <== How many knights does it take to attack or control the board? ==> games/chess/mutual.check.p <== What position is a stalemate for both sides and is reachable in a legal game (including the requirement to prevent check)? ==> games/chess/mutual.stalemate.p <== What's the minimal number of pieces in a legal mutual stalemate? ==> games/chess/queens.p <== How many ways can eight queens be placed so that they control the board? ==> games/chess/size.of.game.tree.p <== How many different positions are there in the game tree of chess? ==> games/cigarettes.p <== The game of cigarettes is played as follows: Two players take turns placing a cigarette on a circular table. The cigarettes can be placed upright (on end) or lying flat, but not so that it touches any other cigarette on the table. This continues until one person looses by not ==> games/connect.four.p <== Is there a winning strategy for Connect Four? ==> games/craps.p <== What are the odds in craps? ==> games/crosswords/cryptic/clues.p <== What are some clues (indicators) used in cryptics? ==> games/crosswords/cryptic/double.p <== Each clue has two solutions, one for each diagram; one of the answers to 1ac. determines which solutions are for which diagram. All solutions are in Chamber's and Webster's Third except for one solution ==> games/crosswords/cryptic/intro.p <== What are the rules for cluing cryptic crosswords? ==> games/go-moku.p <== For a game of k in a row on an n x n board, for what values of k and n is there a win? Is (the largest such) k eventually constant or does it increase with n? ==> games/hi-q.p <== What is the quickest solution of the game Hi-Q (also called Solitair)? For those of you who aren't sure what the game looks like: ==> games/jeopardy.p <== What are the highest, lowest, and most different scores contestants can achieve during a single game of Jeopardy? ==> games/knight.tour.p <== For what board sizes is a knight's tour possible? ==> games/nim.p <== Place 10 piles of 10 $1 bills in a row. A valid move is to reduce the last i>0 piles by the same amount j>0 for some i and j; a pile reduced to nothing is considered to have been removed. The loser is the player who picks up the last dollar, and they must forfeit ==> games/othello.p <== How good are computers at Othello? ==> games/risk.p <== What are the odds when tossing dice in Risk? ==> games/rubiks.clock.p <== How do you quickly solve Rubik's clock? ==> games/rubiks.cube.p <== What is known about bounds on solving Rubik's cube? ==> games/rubiks.magic.p <== How do you solve Rubik's Magic? ==> games/scrabble.p <== What are some exceptional scrabble games? ==> games/square-1.p <== Does anyone have any hints on how to solve the Square-1 puzzle? ==> games/think.and.jump.p <== THINK & JUMP: FIRST THINK, THEN JUMP UNTIL YOU ARE LEFT WITH ONE PEG! O - O O - O / \ / \ / \ / \ O---O---O---O---O ==> games/tictactoe.p <== In random tic-tac-toe, what is the probability that the first mover wins? ==> geometry/K3,3.p <== Can three houses be connected to three utilities without the pipes crossing? _______ _______ _______ | oil | |water| | gas | ==> geometry/bear.p <== If a hunter goes out his front door, goes 50 miles south, then goes 50 miles west, shoots a bear, goes 50 miles north and ends up in front of his house. What color was the bear? ==> geometry/bisector.p <== If two angle bisectors of a triangle are equal, then the triangle is isosceles (more specifically, the sides opposite to the two angles being bisected are equal). ==> geometry/calendar.p <== Build a calendar from two sets of cubes. On the first set, spell the months with a letter on each face of three cubes. Use lowercase three-letter abbreviations for the names of all twelve months (e.g., "jan", "feb", "mar"). On the second set, ==> geometry/circles.and.triangles.p <== Find the radius of the inscribed and circumscribed circles for a triangle. ==> geometry/coloring/cheese.cube.p <== A cube of cheese is divided into 27 subcubes. A mouse starts at one corner and eats through every subcube. Can it finish in the middle? ==> geometry/coloring/dominoes.p <== There is a chess board (of course with 64 squares). You are given 21 dominoes of size 3-by-1 (the size of an individual square on a chess board is 1-by-1). Which square on the chess board can you cut out so that the 21 dominoes exactly cover the remaining ==> geometry/construction/4.triangles.6.lines.p <== Can you construct 4 equilateral triangles with 6 toothpicks? ==> geometry/construction/5.lines.with.4.points.p <== Arrange 10 points so that they form 5 rows of 4 each. ==> geometry/construction/square.with.compass.p <== Construct a square with only a compass and a straight edge. ==> geometry/cover.earth.p <== A thin membrane covers the surface of the earth. One square meter is added to the area of this membrane. How much is added to the radius and volume of this membrane? ==> geometry/dissections/circle.p <== Can a circle be cut into similar pieces without point symmetry about the midpoint? Can it be done with a finite number of pieces? ==> geometry/dissections/hexagon.p <== Divide the hexagon into: 1) 3 indentical rhombuses. 2) 6 indentical kites(?). 3) 4 indentical trapezoids. ==> geometry/dissections/square.70.p <== Since 1^2 + 2^2 + 3^2 + ... + 24^2 = 70^2, can a 70x70 sqaure be dissected into 24 squares of size 1x1, 2x2, 3x3, etc.? ==> geometry/dissections/square.five.p <== Can you dissect a square into 5 parts of equal area with just a straight edge? ==> geometry/duck.and.fox.p <== A duck is swimming about in a circular pond. A ravenous fox (who cannot swim) is roaming the edges of the pond, waiting for the duck to come close. The fox can run faster than the duck can swim. In order to escape, the duck must swim to the edge of the pond before flying away. Assume that ==> geometry/earth.band.p <== How much will a band around the equator rise above the surface if it is made one meter longer? ==> geometry/ham.sandwich.p <== Consider a ham sandwich, consisting of two pieces of bread and one of ham. Suppose the sandwich was dropped into a machine and spindled, torn and mutiliated. Is it still possible to divide the ham sandwich with a straight knife cut such that both the ham and the bread are ==> geometry/hike.p <== You are hiking in a half-planar woods, exactly 1 mile from the edge, when you suddenly trip and lose your sense of direction. What's the shortest path that's guaranteed to take you out of the woods? Assume that you can navigate perfectly relative to your current location and ==> geometry/hole.in.sphere.p <== Old Boniface he took his cheer, Then he bored a hole through a solid sphere, Clear through the center, straight and strong, And the hole was just six inches long. ==> geometry/ladders.p <== Two ladders form a rough X in an alley. The ladders are 11 and 13 meters long and they cross 4 meters off the ground. How wide is the alley? ==> geometry/lattice/area.p <== Prove that the area of a triangle formed by three lattice points is integer/2. ==> geometry/lattice/equilateral.p <== Can an equlateral triangle have vertices at integer lattice points? ==> geometry/rotation.p <== What is the smallest rotation that returns an object to its original state? ==> geometry/smuggler.p <== Somewhere on the high sees smuggler S is attempting, without much luck, to outspeed coast guard G, whose boat can go faster than S's. G is one mile east of S when a heavy fog descends. It's so heavy that nobody can see or hear anything further than a few feet. Immediately ==> geometry/table.in.corner.p <== Put a round table into a (perpendicular) corner so that the table top touches both walls and the feet are firmly on the ground. If there is a point on the perimeter of the table, in the quarter circle between the two points of contact, which is 10 cm from one wall and 5 cm from ==> geometry/tesseract.p <== If you suspend a cube by one corner and slice it in half with a horizontal plane through its centre of gravity, the section face is a hexagon. Now suspend a tesseract (a four dimensional hypercube) by one corner and slice it in half with a hyper-horizontal hyperplane through ==> geometry/tetrahedron.p <== Suppose you have a sphere of radius R and you have four planes that are all tangent to the sphere such that they form an arbitrary tetrahedron (it can be irregular). What is the ratio of the surface area of the tetrahedron to its volume? ==> geometry/tiling/rational.sides.p <== A rectangular region R is divided into rectangular areas. Show that if each of the rectangles in the region has at least one side with rational length then the same can be said of R. ==> geometry/tiling/rectangles.with.squares.p <== Given two sorts of squares, (axa) and (bxb), what rectangles can be tiled? ==> geometry/tiling/scaling.p <== A given rectangle can be entirely covered (i.e. concealed) by an appropriate arrangement of 25 disks of unit radius. Can the same rectangle be covered by 100 disks of 1/2 unit radius? ==> geometry/tiling/seven.cubes.p <== Consider 7 cubes of equal size arranged as follows. Place 5 cubes so that they form a Swiss cross or a + (plus). ( 4 cubes on the sides and 1 in the middle). Now place one cube on top of the middle cube and the seventh below the middle cube, to effectively form a 3-dimensional ==> group/group.01.p <== AEFHIKLMNTVWXYZ BCDGJOPQRSU ==> group/group.01a.p <== 147 0235689 ==> group/group.02.p <== ABEHIKMNOPTXZ CDFGJLQRSUVWY ==> group/group.03.p <== BEJQXYZ DFGHLPRU KSTV CO AIW MN ==> group/group.04.p <== BDO P ACGJLMNQRSUVWZ EFTY HIKX ==> group/group.05.p <== CEFGHIJKLMNSTUVWXYZ ADOPQR B ==> group/group.06.p <== BCEGKMQSW DFHIJLNOPRTUVXYZ ==> induction/hanoi.p <== Is there an algorithom for solving the hanoi tower puzzle for any number of towers? Is there an equation for determining the minimum number of moves required to solve it, given a variable number of disks and towers? ==> induction/n-sphere.p <== With what odds do three random points on an n-sphere form an acute triangle? ==> induction/paradox.p <== What simple property holds for the first 10,000 integers, then fails? ==> induction/party.p <== You're at a party. Any two (different) people at the party have exactly one friend in common (the friend is also at the party). Prove that there is at least one person at the party who is a friend of everyone else. Assume that the friendship relation is symmetric and not reflexive. ==> induction/roll.p <== An ordinary die is thrown until the running total of the throws first exceeds 12. What is the most likely final total that will be obtained? ==> induction/takeover.p <== After graduating from college, you have taken an important managing position in the prestigious financial firm of "Mary and Lee". You are responsable for all the decisions concerning take-over bids. Your immediate concern is whether to take over "Financial Data". ==> logic/29.p <== Three people check into a hotel. They pay $30 to the manager and go to their room. The manager finds out that the room rate is $25 and gives $5 to the bellboy to return. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so ==> logic/ages.p <== 1) Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim. 2) Eight years ago, Mary was half as old as Jane will be when Jane is one year ==> logic/bookworm.p <== A bookworm eats from the first page of an encyclopedia to the last page. The bookworm eats in a straight line. The encyclopedia consists of ten 1000-page volumes. Not counting covers, title pages, etc., how many pages does the bookworm eat through? ==> logic/boxes.p <== Which Box Contains the Gold? Two boxes are labeled "A" and "B". A sign on box A says "The sign on box B is true and the gold is in box A". A sign on box B says ==> logic/calibans.will.p <== ---------------------------------------------- | Caliban's Will by M.H. Newman | ---------------------------------------------- ==> logic/camel.p <== An Arab sheikh tells his two sons that are to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days, ask a wiseman for advise. After hearing the advice they jump on the ==> logic/centrifuge.p <== You are a biochemist, working with a 12-slot centrifuge. This is a gadget that has 12 equally spaced slots around a central axis, in which you can place chemical samples you want centrifuged. When the machine is turned on, the samples whirl around the central axis and do their thing. ==> logic/children.p <== A man walks into a bar, orders a drink, and starts chatting with the bartender. After a while, he learns that the bartender has three children. "How old are your children?" he asks. "Well," replies the bartender, "the product of their ages is 72." The man thinks for a ==> logic/condoms.p <== How can you have mutually safe sex with three women with only two condoms? ==> logic/dell.p <== How can I solve logic puzzles (e.g., as published by Dell) automatically? ==> logic/elimination.p <== 97 baseball teams participate in an annual state tournament. The way the champion is chosen for this tournament is by the same old elimination schedule. That is, the 97 teams are to be divided into pairs, and the two teams of each pair play against each other. ==> logic/family.p <== Suppose that it is equally likely for a pregnancy to deliver a baby boy as it is to deliver a baby girl. Suppose that for a large society of people, every family continues to have children until they have a boy, then they stop having children. ==> logic/flip.p <== How can a toss be called over the phone (without requiring trust)? ==> logic/friends.p <== Any group of 6 or more contains either 3 mutual friends or 3 mutual strangers. Prove it. ==> logic/hundred.p <== A sheet of paper has statements numbered from 1 to 100. Statement n says "exactly n of the statements on this sheet are false." Which statements are true and which are false? What if we replace "exactly" by "at least"? ==> logic/inverter.p <== Can a digital logic circuit with two inverters invert N independent inputs? The circuit may contain any number of AND or OR gates. ==> logic/josephine.p <== The recent expedition to the lost city of Atlantis discovered scrolls attributted to the great poet, scholar, philosopher Josephine. They number eight in all, and here is the first. ==> logic/locks.and.boxes.p <== You want to send a valuable object to a friend. You have a box which is more than large enough to contain the object. You have several locks with keys. The box has a locking ring which is more than large enough to have a lock attached. But your friend does not have the key to any ==> logic/mixing.p <== Start with a half cup of tea and a half cup of coffee. Take one tablespoon of the tea and mix it in with the coffee. Take one tablespoon of this mixture and mix it back in with the tea. Which of the two cups contains more of its original contents? ==> logic/number.p <== Mr. S. and Mr. P. are both perfect logicians, being able to correctly deduce any truth from any set of axioms. Two integers (not necessarily unique) are somehow chosen such that each is within some specified range. Mr. S. is given the sum of these two integers; Mr. P. is given the product of these ==> logic/riddle.p <== Who makes it, has no need of it. Who buys it, has no use for it. Who uses it can neither see nor feel it. Tell me what a dozen rubber trees with thirty boughs on each might be? ==> logic/river.crossing.p <== Three humans, one big monkey and two small monkeys are to cross a river: a) Only humans and the big monkey can row the boat. b) At all times, the number of human on either side of the river must be GREATER OR EQUAL to the number of monkeys ==> logic/ropes.p <== Two fifty foot ropes are suspended from a forty foot ceiling, about twenty feet apart. Armed with only a knife, how much of the rope can you steal? ==> logic/same.street.p <== Sally and Sue have a strong desire to date Sam. They all live on the same street yet neither Sally or Sue know where Sam lives. The houses on this street are numbered 1 to 99. ==> logic/self.ref.p <== Find a number ABCDEFGHIJ such that A is the count of how many 0's are in the number, B is the number of 1's, and so on. ==> logic/situation.puzzles.outtakes.p <== The following puzzles have been removed from my situation puzzles list, or never made it onto the list in the first place. There are a wide variety of reasons for the non-inclusion: some I think are obvious, some don't have enough of a story, some involve gimmicks that annoy me, ==> logic/situation.puzzles.p <== Jed's List of Situation Puzzles History: original compilation 11/28/87 ==> logic/smullyan/black.hat.p <== Three logicians, A, B, and C, are wearing hats, which they know are either black or white but not all white. A can see the hats of B and C; B can see the hats of A and C; C is blind. Each is asked in turn if they know the color of their own hat. The answers are: ==> logic/smullyan/fork.three.men.p <== Three men stand at a fork in the road. One fork leads to Someplaceorother; the other fork leads to Nowheresville. One of these people always answers the truth to any yes/no question which is asked of him. The other always lies when asked any yes/no question. The third person randomly lies and ==> logic/smullyan/fork.two.men.p <== Two men stand at a fork in the road. One fork leads to Someplaceorother; the other fork leads to Nowheresville. One of these people always answers the truth to any yes/no question which is asked of him. The other always lies when asked any yes/no question. By asking one yes/no question, can you ==> logic/smullyan/integers.p <== Two logicians place cards on their foreheads so that what is written on the card is visible only to the other logician. Consecutive positive integers have been written on the cards. The following conversation ensues: A: "I don't know my number." ==> logic/smullyan/liars.et.al.p <== Of a group of n men, some always lie, some never lie, and the rest sometimes lie. They each know which is which. You must determine the identity of each man by asking the least number of yes-or-no questions. ==> logic/smullyan/painted.heads.p <== While three logicians were sleeping under a tree, a malicious child painted their heads red. Upon waking, each logician spies the child's handiwork as it applied to the heads of the other two. Naturally they start laughing. Suddenly one falls silent. Why? ==> logic/smullyan/priest.p <== A priest takes confession of all the inhabitants in a small town. He discovers that in N married pairs in the town, one of the pair has committed adultery. Assume that the spouse of each adulterer does not know about the infidelity of his or her spouse, but that, since it is ==> logic/smullyan/stamps.p <== The moderator takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician so that each logician can see all the other stamps except those 2 in the moderator's pocket and the two on her own head. He asks them in turn ==> logic/timezone.p <== Two people are talking long distance on the phone; one is in an East- Coast state, the other is in a West-Coast state. The first asks the other "What time is it?", hears the answer, and says, "That's funny. It's the same time here!" ==> logic/unexpected.p <== Swedish civil defense authorities announced that a civil defense drill would be held one day the following week, but the actual day would be a surprise. However, we can prove by induction that the drill cannot be held. Clearly, they cannot wait until Friday, since everyone will know it will be held that ==> logic/verger.p <== A very bright and sunny Day The Priest didst to the Verger say: "Last Monday met I strangers three None of which were known to Thee. ==> logic/weighing/balance.p <== You are given N balls and a balance scale and told that one ball is slightly heavier or lighter than the other identical ones. The scale lets you put the same number of balls on each side and observe which side (if either) is heavier. ==> logic/weighing/box.p <== You have ten boxes; each contains nine balls. The balls in one box weigh 0.9 kg; the rest weigh 1.0 kg. You have one weighing on a scale to find the box containing the light balls. How do you do it? ==> logic/weighing/gummy.bears.p <== Real gummy drop bears have a mass of 10 grams, while imitation gummy drop bears have a mass of 9 grams. Spike has 7 cartons of gummy drop bears, 4 of which contain real gummy drop bears, the others imitation. Using a scale only once and the minimum number of gummy drop bears, how ==> logic/weighing/weighings.p <== Some of the supervisors of Scandalvania's n mints are producing bogus coins. It would be easy to determine which mints are producing bogus coins but, alas, the only scale in the known world is located in Nastyville, which isn't on very friendly terms with Scandalville. In fact, Nastyville's ==> logic/zoo.p <== I took some nephews and nieces to the Zoo, and we halted at a cage marked Tovus Slithius, male and female. Beregovus Mimsius, male and female. ==> physics/balloon.p <== A helium-filled balloon is tied to the floor of a car that makes a sharp right turn. Does the balloon tilt while the turn is made? If so, which way? The windows are closed so there is no connection with the outside air. ==> physics/bicycle.p <== A boy, a girl and a dog go for a 10 mile walk. The boy and girl can walk 2 mph and the dog can trot at 4 mph. They also have bicycle which only one of them can use at a time. When riding, the boy and girl can travel at 12 mph while the dog can peddle at 16 mph. ==> physics/boy.girl.dog.p <== A boy, a girl and a dog are standing together on a long, straight road. Simulataneously, they all start walking in the same direction: The boy at 4 mph, the girl at 3 mph, and the dog trots back and forth between them at 10 mph. Assume all reversals of direction instantaneous. ==> physics/brick.p <== What is the maximum overhang you can create with an infinite supply of bricks? ==> physics/cannonball.p <== A person in a boat drops a cannonball overboard; does the water level change? ==> physics/dog.p <== A body of soldiers form a 50m-by-50m square ABCD on the parade ground. In a unit of time, they march forward 50m in formation to take up the position DCEF. The army's mascot, a small dog, is standing next to its handler at location A. When the ==> physics/magnets.p <== You have two bars of iron. One is magnetic, the other is not. Without using any other instrument (thread, filings, other magnets, etc.), find out which is which. ==> physics/milk.and.coffee.p <== You are just served a hot cup of coffee and want it to be as hot as possible when you drink it some number of minutes later. Do you add milk when you get the cup or just before you drink it? ==> physics/mirror.p <== Why does a mirror appear to invert the left-right directions, but not up-down? ==> physics/monkey.p <== Hanging over a pulley, there is a rope, with a weight at one end. At the other end hangs a monkey of equal weight. The rope weighs 4 ounces per foot. The combined ages of the monkey and it's mother is 4 years. The weight of the monkey is as many pounds as the mother ==> physics/particle.p <== What is the longest time that a particle can take in travelling between two points if it never increases its acceleration along the way and reaches the second point with speed V? ==> physics/pole.in.barn.p <== Accelerate a pole of length l to a constant speed of 90% of the speed of light (.9c). Move this pole towards an open barn of length .9l (90% the length of the pole). Then, as soon as the pole is fully inside the barn, close the door. What do you see and what actually happens? ==> physics/resistors.p <== What are the resistances between lattices of resistors in the shape of a: 1. Cube ==> physics/sail.p <== A sailor is in a sailboat on a river. The water (current) is flowing downriver at a velocity of 3 knots with respect to the land. The wind (air velocity) is zero, with respect to the land. The sailor wants to proceed downriver as quickly as possible, maximizing his downstream ==> physics/skid.p <== What is the fastest way to make a 90 degree turn on a slippery road? ==> physics/spheres.p <== Two spheres are the same size and weight, but one is hollow. They are made of uniform material, though of course not the same material. Without a minimum of apparatus, how can I tell which is hollow? ==> physics/wind.p <== Is a round-trip by airplane longer or shorter if there is wind blowing? ==> probability/amoeba.p <== A jar begins with one amoeba. Every minute, every amoeba turns into 0, 1, 2, or 3 amoebae with probability 25% for each case ( dies, does nothing, splits into 2, or splits into 3). What is the probability that the amoeba population ==> probability/apriori.p <== An urn contains one hundred white and black balls. You sample one hundred balls with replacement and they are all white. What is the probability that all the balls are white? ==> probability/cab.p <== A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. Here is some data: a) Although the two companies are equal in size, 85% of cab ==> probability/coincidence.p <== Name some amazing coincidences. ==> probability/coupon.p <== There is a free gift in my breakfast cereal. The manufacturers say that the gift comes in four different colours, and encourage one to collect all four (& so eat lots of their cereal). Assuming there is an equal chance of getting any one of the colours, what is the ==> probability/darts.p <== Peter throws two darts at a dartboard, aiming for the center. The second dart lands farther from the center than the first. If Peter now throws another dart at the board, aiming for the center, what is the probability that this third throw is also worse (i.e., farther from ==> probability/flips.p <== Consider a run of coin tosses: HHTHTTHTTTHTTTTHHHTHHHHHTHTTHT Define a success as a run of one H or T (as in THT or HTH). Use two different methods of sampling. The first method would consist of ==> probability/flush.p <== Which set contains more flushes than the set of all possible hands? (1) Hands whose first card is an ace (2) Hands whose first card is the ace of spades (3) Hands with at least one ace ==> probability/hospital.p <== A town has two hospitals, one big and one small. Every day the big hospital delivers 1000 babies and the small hospital delivers 100 babies. There's a 50/50 chance of male or female on each birth. Which hospital has a better chance of having the same number of boys ==> probability/icos.p <== The "house" rolls two 20-sided dice and the "player" rolls one 20-sided die. If the player rolls a number on his die between the two numbers the house rolled, then the player wins. Otherwise, the house wins (including ties). What are the probabilities of the player ==> probability/intervals.p <== Given two random points x and y on the interval 0..1, what is the average size of the smallest of the three resulting intervals? ==> probability/lights.p <== Waldo and Basil are exactly m blocks west and n blocks north from Central Park, and always go with the green light until they run out of options. Assuming that the probability of the light being green is 1/2 in each direction and that if the light is green in one direction it is red in the other, find the ==> probability/lottery.p <== There n tickets in the lottery, k winners and m allowing you to pick another ticket. The problem is to determine the probability of winning the lottery when you start by picking 1 (one) ticket. ==> probability/particle.in.box.p <== A particle is bouncing randomly in a two-dimensional box. How far does it travel between bounces, on avergae? Suppose the particle is initially at some random position in the box and is ==> probability/pi.p <== Are the digits of pi random (i.e., can you make money betting on them)? ==> probability/random.walk.p <== Waldo has lost his car keys! He's not using a very efficient search; in fact, he's doing a random walk. He starts at 0, and moves 1 unit to the left or right, with equal probability. On the next step, he moves 2 units to the left or right, again with equal probability. For ==> probability/reactor.p <== There is a reactor in which a reaction is to take place. This reaction stops if an electron is present in the reactor. The reaction is started with 18 positrons; the idea being that one of these positrons would combine with any incoming electron (thus destroying both). Every second, ==> probability/roulette.p <== You are in a game of Russian roulette, but this time the gun (a 6 shooter revolver) has three bullets _in_a_row_ in three of the chambers. The barrel is spun only once. Each player then points the gun at his (her) head and pulls the trigger. If he (she) is still ==> probability/unfair.p <== Generate even odds from an unfair coin. For example, if you thought a coin was biased toward heads, how could you get the equivalent of a fair coin with several tosses of the unfair coin? ==> series/series.01.p <== M, N, B, D, P ? ==> series/series.02.p <== H, H, L, B, B, C, N, O, F ? ==> series/series.03.p <== W, A, J, M, M, A, J? ==> series/series.03a.p <== G, J, T, J, J, J, A, M, W, J, J, Z, M, F, J, ? ==> series/series.03b.p <== A, J, B, C, G, T, C, V, J, T, D, F, K, B, H, ? ==> series/series.03c.p <== M, A, M, D, E, L, R, H, ? ==> series/series.04.p <== A, E, H, I, K, L, ? ==> series/series.05.p <== A B C D E F G H? ==> series/series.06.p <== Z, O, T, T, F, F, S, S, E, N? ==> series/series.06a.p <== F, S, T, F, F, S, ? ==> series/series.07.p <== 1, 1 1, 2 1, 1 2 1 1, ... What is the pattern and asymptotics of this series? ==> series/series.08a.p <== G, L, M, B, C, L, M, C, F, S, ? ==> series/series.08b.p <== A, V, R, R, C, C, L, L, L, E, ? ==> series/series.09a.p <== S, M, S, S, S, C, P, P, P, ? ==> series/series.09b.p <== M, S, C, P, P, P, S, S, S, ? ==> series/series.10.p <== D, P, N, G, C, M, M, S, ? ==> series/series.11.p <== R O Y G B ? ==> series/series.12.p <== A, T, G, C, L, ? ==> series/series.13.p <== M, V, E, M, J, S, ? ==> series/series.14.p <== A, B, D, O, P, ? ==> series/series.14a.p <== A, B, D, E, G, O, P, ? ==> series/series.15.p <== A, E, F, H, I, ? ==> series/series.16.p <== A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, X, Y? ==> series/series.17.p <== T, P, O, F, O, F, N, T, S, F, T, F, E, N, S, N? ==> series/series.18.p <== 10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, ___ , 100, 121, 10000 ==> series/series.19.p <== 1 01 01011 0101101011011 0101101011011010110101101101011011 etc. Each string is formed from the previous string by substituting '01' for '1' and '011' for '0' simultaneously at each occurance. ==> series/series.20.p <== 1 2 5 16 64 312 1812 12288 ==> series/series.21.p <== 5, 6, 5, 6, 5, 5, 7, 5, ? ==> series/series.22.p <== 3 1 1 0 3 7 5 5 2 ? ==> series/series.23.p <== 22 22 30 13 13 16 16 28 28 11 ? ==> series/series.24.p <== What is the next letter in the sequence: W, I, T, N, L, I, T? ==> series/series.25.p <== 1 3 4 9 10 12 13 27 28 30 31 36 37 39 40 ? ==> series/series.26.p <== 1 3 2 6 7 5 4 12 13 15 14 10 11 9 8 24 25 27 26 ? ==> series/series.27.p <== 0 1 1 2 1 2 1 3 2 2 1 3 1 2 2 4 1 3 1 3 2 2 1 4 2 ? ==> series/series.28.p <== 0 2 3 4 5 5 7 6 6 7 11 7 13 9 8 8 17 8 19 9 10 13 23 9 10 ? ==> series/series.29.p <== 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 4 3 4 ? ==> series/series.30.p <== I I T Y W I M W Y B M A D ==> series/series.31.p <== 6 2 5 5 4 5 6 3 7 ==> series/series.32.p <== 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 ==> series/series.33.p <== 2 12 360 75600 ==> series/series.34.p <== 3 5 4 4 3 5 5 4 3 ==> series/series.35.p <== 1 2 3 2 1 2 3 4 2 1 2 3 4 2 2 3 ==> trivia/area.codes.p <== When looking at a map of the distribution of telephone area codes for North America, it appears that they are randomly distributed. I am doubtful that this is the case, however. Does anyone know how the area codes were/are chosen? ==> trivia/eskimo.snow.p <== How many words do the Eskimo have for snow? ==> trivia/federal.reserve.p <== What is the pattern to this list: Boston, MA New York, NY Philadelphia, PA ==> trivia/jokes.self-referential.p <== What are some self-referential jokes?