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Subject: rec.puzzles Archive (Instructions), part 01 of 35

This article was archived around: Wed, 18 Aug 1993 06:04:18 GMT

All FAQs in Directory: puzzles/archive
All FAQs posted in: rec.puzzles
Source: Usenet Version

Archive-name: puzzles/archive/Instructions Last-modified: 17 Aug 1993 Version: 4
==> Instructions <== Instructions for Accessing rec.puzzles Archive 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 message to archive-request@questrel.com like: return_address your_name@your_site.your_domain send requested_puzzle_name For example, if your net address is "mickey@disneyland.com", to request "decision/allais.p", send the message: return_address mickey@disneyland.com send allais To request multiple puzzles, use several "send" lines in a message. Please refrain from requesting the entire archive via email. Use FTP. FTP The archive has been posted to news.answers and rec.answers, which are archived in the periodic posting archive on rtfm.mit.edu in the anonymous ftp directory /pub/usenet. Other archives are: ftp.cs.ruu.nl [] in the anonymous ftp directory /pub/NEWS.ANSWERS (also accessible via mail server requests to mail-server@cs.ruu.nl) cnam.cnam.fr [] in the anonymous ftp directory /pub/FAQ ftp.uu.net [ or] in the anonymous ftp directory /usenet ftp.win.tue.nl [] in the anonymous ftp directory /pub/usenet/news.answers grasp1.univ-lyon1.fr [] 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 rtfm.mit.edu are also accessible via Prospero and WAIS (the database name is "usenet" on port 210). CREDIT The archive is NOT the original work of the editor (just in case you were wondering :^). In keeping with the general net practice on FAQ's, I do not as a rule assign credit for solutions. There are many reasons for this: 1. The archive 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 archive 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 archive-comment@questrel.com. INDEX ==> bicycle (analysis) <== A boy, a girl and a dog go for a 10 mile walk. The boy and girl can ==> boy.girl.dog (analysis) <== A boy, a girl and a dog are standing together on a long, straight road. ==> bugs (analysis) <== Four bugs are placed at the corners of a square. Each bug walks always ==> c.infinity (analysis) <== What function is zero at zero, strictly positive elsewhere, infinitely ==> cache (analysis) <== Cache and Ferry (How far can a truck go in a desert?) ==> calculate.pi (analysis) <== How can I calculate many digits of pi? ==> cats.and.rats (analysis) <== If 6 cats can kill 6 rats in 6 minutes, how many cats does it take to ==> dog (analysis) <== A body of soldiers form a 50m-by-50m square ABCD on the parade ground. ==> e.and.pi (analysis) <== Without finding their numerical values, which is greater, e^(pi) or (pi)^e? ==> functional/distributed (analysis) <== Find all f: R -> R, f not identically zero, such that ==> functional/linear (analysis) <== Suppose f is non-decreasing with ==> integral (analysis) <== If f is integrable on (0,inf) and differentiable at 0, and a > 0, and: ==> irrational.stamp (analysis) <== You have an ink stamp which is so amazingly precise that, when inked ==> minimum.time (analysis) <== N people can walk or drive in a two-seater to go from city A to city B. What ==> particle (analysis) <== What is the longest time that a particle can take in travelling between two ==> period (analysis) <== What is the least possible integral period of the sum of functions ==> rubberband (analysis) <== A bug walks down a rubber band which is attached to a wall at one end and a car ==> sequence (analysis) <== Show that in the sequence: x, 2x, 3x, .... (n-1)x (x can be any real number) ==> snow (analysis) <== Snow starts falling before noon on a cold December day. At noon a ==> tower (analysis) <== R = N ^ (N ^ (N ^ ...)). What is the maximum N>0 that will yield a finite R? ==> 7-11 (arithmetic/part1) <== A customer at a 7-11 store selected four items to buy, and was told ==> arithmetic.progression (arithmetic/part1) <== Is there an arithmetic progression of 20 or more primes? ==> clock/day.of.week (arithmetic/part1) <== It's restful sitting in Tom's cosy den, talking quietly and sipping ==> clock/palindromic (arithmetic/part1) <== How many times per day does a digital clock display a palindromic number? ==> clock/reversible (arithmetic/part1) <== How many times per day can the hour and minute hands on an analog clock switch ==> clock/right.angle (arithmetic/part1) <== How many times per day do the hour and minute hands of a clock form a ==> clock/thirds (arithmetic/part1) <== Do the 3 hands on a clock ever divide the face of the clock into 3 ==> consecutive.composites (arithmetic/part1) <== Are there 10,000 consecutive non-prime numbers? ==> consecutive.product (arithmetic/part1) <== Prove that the product of three or more consecutive positive integers cannot ==> consecutive.sums (arithmetic/part1) <== Find all series of consecutive positive integers whose sum is exactly 10,000. ==> conway (arithmetic/part1) <== Describe the sequence a(1)=a(2)=1, a(n) = a(a(n-1)) + a(n-a(n-1)) for n>2. ==> digits/6.and.7 (arithmetic/part1) <== Does every number which is not divisible by 5 have a multiple whose ==> digits/all.ones (arithmetic/part1) <== Prove that some multiple of any integer ending in 3 contains all 1s. ==> digits/arabian (arithmetic/part1) <== What is the Arabian Nights factorial, the number x such that x! has 1001 ==> digits/circular (arithmetic/part1) <== What 6 digit number, with 6 different digits, when multiplied by all integers ==> digits/divisible (arithmetic/part1) <== Find the least number using 0-9 exactly once that is evenly divisible by each ==> digits/equations/123456789 (arithmetic/part1) <== In how many ways can "." be replaced with "+", "-", or "" (concatenate) in ==> digits/equations/1992 (arithmetic/part1) <== 1 = -1+9-9+2. Extend this list to 2 through 100 on the left side of ==> digits/equations/24 (arithmetic/part1) <== Form an expression that evaluates to 24 that contains two 3's, two 7's, ==> digits/equations/383 (arithmetic/part1) <== Make 383 out of 1,2,25,50,75,100 using +,-,*,/. ==> digits/equations/find (arithmetic/part1) <== Write a program for finding expressions built out of given numbers and using ==> digits/extreme.products (arithmetic/part1) <== What are the extremal products of three three-digit numbers using digits 1-9? ==> digits/labels (arithmetic/part1) <== You have an arbitrary number of model kits (which you assemble for ==> digits/least.significant/factorial (arithmetic/part1) <== What is the least significant non-zero digit in the decimal expansion of n!? ==> digits/least.significant/tower.of.power (arithmetic/part1) <== What are the least significant digits of 9^(8^(7^(6^(5^(4^(3^(2^1))))))) ? ==> digits/most.significant/googol (arithmetic/part1) <== What digits does googol! start with? ==> digits/most.significant/powers (arithmetic/part1) <== What is the probability that 2^N begins with the digits 603245? ==> digits/nine.digits (arithmetic/part1) <== Form a number using 0-9 once with its first n digits divisible by n. ==> digits/palindrome (arithmetic/part1) <== Does the series formed by adding a number to its reversal always end in ==> digits/palintiples (arithmetic/part1) <== Find all numbers that are multiples of their reversals. ==> digits/power.two (arithmetic/part1) <== Prove that for any 9-digit number (base 10) there is an integral power ==> digits/prime/101 (arithmetic/part1) <== How many primes are in the sequence 101, 10101, 1010101, ...? ==> digits/prime/all.prefix (arithmetic/part1) <== What is the longest prime whose every proper prefix is a prime? ==> digits/prime/change.one (arithmetic/part1) <== What is the smallest number that cannot be made prime by changing a single ==> digits/prime/prefix.one (arithmetic/part1) <== 2 is prime, but 12, 22, ..., 92 are not. Similarly, 5 is prime ==> digits/reverse (arithmetic/part1) <== Is there an integer that has its digits reversed after dividing it by 2? ==> digits/rotate (arithmetic/part1) <== Find integers where multiplying them by single digits rotates their digits ==> digits/sesqui (arithmetic/part1) <== Find the least number where moving the first digit to the end multiplies by 1.5. ==> digits/squares/change.leading (arithmetic/part1) <== What squares remain squares when their leading digits are incremented? ==> digits/squares/length.22 (arithmetic/part1) <== Is it possible to form two numbers A and B from 22 digits such that ==> digits/squares/length.9 (arithmetic/part1) <== Is it possible to make a number and its square, using the digits from 1 ==> digits/squares/three.digits (arithmetic/part2) <== What squares consist entirely of three digits (e.g., 1, 4, and 9)? ==> digits/squares/twin (arithmetic/part2) <== Let a twin be a number formed by writing the same number twice, ==> digits/sum.of.digits (arithmetic/part2) <== Find sod ( sod ( sod (4444 ^ 4444 ) ) ). ==> digits/zeros/million (arithmetic/part2) <== How many zeros occur in the numbers from 1 to 1,000,000? ==> digits/zeros/trailing (arithmetic/part2) <== How many trailing zeros are in the decimal expansion of n!? ==> magic.squares (arithmetic/part2) <== Are there large squares, containing only consecutive integers, all of whose ==> pell (arithmetic/part2) <== Find integer solutions to x^2 - 92y^2 = 1. ==> subset (arithmetic/part2) <== Prove that all sets of n integers contain a subset whose sum is divisible by n. ==> sum.of.cubes (arithmetic/part2) <== Find two fractions whose cubes total 6. ==> sums.of.powers (arithmetic/part2) <== Partition 1,2,3,...,16 into two equal sets, such that the sums of the ==> tests.for.divisibility/eleven (arithmetic/part2) <== What is the test to see if a number is divisible by eleven? ==> tests.for.divisibility/nine (arithmetic/part2) <== What is the test to see if a number is divisible by nine? ==> tests.for.divisibility/seven (arithmetic/part2) <== What is the test to see if a number is divisible by seven? ==> tests.for.divisibility/three (arithmetic/part2) <== What is the test to see if a number is divisible by three? ==> alphabet.blocks (combinatorics) <== What is the minimum number of dice painted with one letter on all six sides ==> coinage/combinations (combinatorics) <== Assuming you have enough coins of 1, 5, 10, 25 and 50 cents, how many ==> coinage/dimes (combinatorics) <== "Dad wants one-cent, two-cent, three-cent, five-cent, and ten-cent ==> coinage/impossible (combinatorics) <== What is the smallest number of coins that you can't make a dollar with? ==> color (combinatorics) <== An urn contains n balls of different colors. Randomly select a pair, repaint ==> full (combinatorics) <== Consider a string that contains all substrings of length n. For example, ==> gossip (combinatorics) <== n people each know a different piece of gossip. They can telephone each other ==> grid.dissection (combinatorics) <== How many (possibly overlapping) squares are in an mxn grid? Assume that all ==> permutation (combinatorics) <== Compute the nth permutation of k numbers (or objects). ==> subsets (combinatorics) <== Out of the set of integers 1,...,100 you are given ten different ==> transitions (combinatorics) <== How many n-bit binary strings (0/1) have exactly k transitions ==> contests/games.magazine (competition/part1) <== What are the best answers to various contests run by _Games_ magazine? ==> contests/national.puzzle/npc.1993 (competition/part1) <== What are the solutions to the Games magazine 1993 National Puzzle Contest? ==> games/bridge (competition/part1) <== Are there any programs for solving double-dummy Bridge? ==> games/chess/knight.control (competition/part1) <== How many knights does it take to attack or control the board? ==> games/chess/knight.most (competition/part1) <== What is the maximum number of knights that can be put on n x n chessboard ==> games/chess/knight.tour (competition/part1) <== For what size boards are knight tours possible? ==> games/chess/mutual.stalemate (competition/part1) <== What's the minimal number of pieces in a legal mutual stalemate? ==> games/chess/queen.control (competition/part1) <== How many queens does it take to attack or control the board? ==> games/chess/queen.most (competition/part1) <== How many non-mutually-attacking queens can be placed on various sized boards? ==> games/chess/queens (competition/part1) <== How many ways can eight queens be placed so that they control the board? ==> games/chess/rook.paths (competition/part1) <== How many non-overlapping paths can a rook take from one corner to the opposite ==> games/chess/size.of.game.tree (competition/part1) <== How many different positions are there in the game tree of chess? ==> games/cigarettes (competition/part1) <== The game of cigarettes is played as follows: ==> games/connect.four (competition/part1) <== Is there a winning strategy for Connect Four? ==> games/craps (competition/part1) <== What are the odds in craps? ==> games/crosswords (competition/part1) <== Are there programs to make crosswords? What are the rules for cluing cryptic ==> games/cube (competition/part2) <== What are some games involving cubes? ==> games/go-moku (competition/part2) <== For a game of k in a row on an n x n board, for what values of k and n is ==> games/hi-q (competition/part2) <== What is the quickest solution of the game Hi-Q (also called Solitaire)? ==> games/jeopardy (competition/part2) <== What are the highest, lowest, and most different scores contestants ==> games/nim (competition/part2) <== Place 10 piles of 10 $1 bills in a row. A valid move is to reduce ==> games/online/online.scrabble (competition/part2) <== How can I play Scrabble online on the Internet? ==> games/online/unlimited.adventures (competition/part2) <== Where can I find information about unlimited adventures? ==> games/othello (competition/part2) <== How good are computers at Othello? ==> games/pc/best (competition/part2) <== What are the best PC games? ==> games/pc/reviews (competition/part2) <== Are reviews of PC games available online? ==> games/pc/solutions (competition/part2) <== What are the solutions to various popular PC games? ==> games/poker.face.up (competition/part2) <== In Face-Up Poker, two players each select five cards from a face-up deck, ==> games/risk (competition/part2) <== What are the odds when tossing dice in Risk? ==> games/rubiks/rubiks.clock (competition/part2) <== How do you quickly solve Rubik's clock? ==> games/rubiks/rubiks.cube (competition/part3) <== What is known about bounds on solving Rubik's cube? ==> games/rubiks/rubiks.magic (competition/part3) <== How do you solve Rubik's Magic? ==> games/scrabble (competition/part3) <== What are some exceptional Scrabble Brand Crossword Game (TM) games? ==> games/set (competition/part3) <== What is the size of the largest collection of cards from which NO "set" ==> games/soma (competition/part3) <== What is the solution to Soma Cubes? ==> games/square-1 (competition/part3) <== Does anyone have any hints on how to solve the Square-1 puzzle? ==> games/think.and.jump (competition/part3) <== THINK & JUMP: FIRST THINK, THEN JUMP UNTIL YOU ==> games/tictactoe (competition/part3) <== In random tic-tac-toe, what is the probability that the first mover wins? ==> tests/analogies/long (competition/part3) <== 1. Host : Guest :: Cynophobia : ? ==> tests/analogies/pomfrit (competition/part3) <== 1. NATURAL: ARTIFICIAL :: ANKYLOSIS: ? ==> tests/analogies/quest (competition/part3) <== 1. Mother: Maternal :: Stepmother: ? ==> tests/math/putnam/putnam.1967 (competition/part3) <== ==> tests/math/putnam/putnam.1987 (competition/part4) <== WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION ==> tests/math/putnam/putnam.1988 (competition/part4) <== Problem A-1: Let R be the region consisting of the points (x,y) of the ==> tests/math/putnam/putnam.1990 (competition/part4) <== Problem A-1 ==> tests/math/putnam/putnam.1992 (competition/part5) <== Problem A1 ==> Beale (cryptology) <== What are the Beale ciphers? ==> Feynman (cryptology) <== What are the Feynman ciphers? ==> Voynich (cryptology) <== What are the Voynich ciphers? ==> swiss.colony (cryptology) <== What are the 1987 Swiss Colony ciphers? ==> vcrplus (cryptology) <== What is the code used by VCR+? ==> allais (decision) <== The Allais Paradox involves the choice between two alternatives: ==> division (decision) <== N-Person Fair Division ==> dowry (decision) <== Sultan's Dowry ==> envelope (decision) <== Someone has prepared two envelopes containing money. One contains twice as ==> exchange (decision) <== At one time, the Canadian and US dollars were discounted by 10 cents on ==> high.or.low (decision) <== I pick two numbers, randomly, and tell you one of them. You are supposed ==> monty.hall (decision) <== You are a participant on "Let's Make a Deal." Monty Hall shows you ==> newcomb (decision) <== Newcomb's Problem ==> prisoners (decision) <== Three prisoners on death row are told that one of them has been chosen ==> red (decision) <== I show you a shuffled deck of standard playing cards, one card at a ==> rotating.table (decision) <== Four glasses are placed upside down in the four corners of a square ==> stpetersburg (decision) <== What should you be willing to pay to play a game in which the payoff is ==> truel (decision) <== A, B, and C are to fight a three-cornered pistol duel. All know that ==> K3,3 (geometry/part1) <== Can three houses be connected to three utilities without the pipes crossing? ==> bear (geometry/part1) <== If a hunter goes out his front door, goes 50 miles south, then goes 50 ==> bisector (geometry/part1) <== Prove if two angle bisectors of a triangle are equal, then the triangle is ==> calendar (geometry/part1) <== Build a calendar from two sets of cubes. On the first set, spell the ==> circles.and.triangles (geometry/part1) <== Find the radius of the inscribed and circumscribed circles for a triangle. ==> coloring/cheese.cube (geometry/part1) <== A cube of cheese is divided into 27 subcubes. A mouse starts at one ==> coloring/triominoes (geometry/part1) <== There is a chess board (of course with 64 squares). You are given 21 ==> construction/4.triangles.6.lines (geometry/part1) <== Can you construct 4 equilateral triangles with 6 toothpicks? ==> construction/5.lines.with.4.points (geometry/part1) <== Arrange 10 points so that they form 5 rows of 4 each. ==> construction/square.with.compass (geometry/part1) <== Construct a square with only a compass and a straight edge. ==> corner (geometry/part1) <== A hallway of width A turns through 90 degrees into a hallway of width ==> cover.earth (geometry/part1) <== A thin membrane covers the surface of the (spherical) earth. One ==> cycle.polynomial (geometry/part1) <== What are the cycle polynomials for the Platonic solids? ==> dissections/disk (geometry/part1) <== Can a disk be cut into similar pieces without point symmetry about the ==> dissections/hexagon (geometry/part1) <== Divide the hexagon into: ==> dissections/largest.circle (geometry/part1) <== What is the largest circle that can be assembled from two semicircles cut from ==> dissections/square.70 (geometry/part1) <== Since 1^2 + 2^2 + 3^2 + ... + 24^2 = 70^2, can a 70x70 square be dissected into ==> dissections/square.five (geometry/part1) <== Can you dissect a square into 5 parts of equal area with just a straight edge? ==> dissections/tesseract (geometry/part1) <== If you suspend a cube by one corner and slice it in half with a ==> duck.and.fox (geometry/part1) <== A duck is swimming about in a circular pond. A ravenous fox (who cannot ==> earth.band (geometry/part1) <== How much will a band around the equator rise above the surface if it is ==> fence (geometry/part1) <== A farmer wishes to enclose the maximum possible area with 100 meters of fence. ==> ham.sandwich (geometry/part1) <== Consider a ham sandwich, consisting of two pieces of bread and one of ==> hike (geometry/part1) <== You are hiking in a half-planar woods, exactly 1 mile from the edge, ==> hole.in.sphere (geometry/part1) <== Old Boniface he took his cheer, ==> hypercube (geometry/part1) <== How many vertices, edges, faces, etc. does a hypercube have? ==> kissing.number (geometry/part1) <== How many n-dimensional unit spheres can be packed around one unit sphere? ==> konigsberg (geometry/part1) <== Can you draw a line through each edge on the diagram below without crossing ==> ladders (geometry/part1) <== Two ladders form a rough X in an alley. The ladders are 11 and 13 meters ==> lattice/area (geometry/part1) <== Prove that the area of a triangle formed by three lattice points is integer/2. ==> lattice/equilateral (geometry/part1) <== Can an equlateral triangle have vertices at integer lattice points? ==> manhole.cover (geometry/part1) <== Why is a manhole cover round? ==> pentomino (geometry/part1) <== Arrange pentominos in 3x20, 4x15, 5x12, 6x10, 2x3x10, 2x5x6 and 3x4x5 forms. ==> points.in.sphere (geometry/part1) <== What is the expected distance between two random points inside a sphere? ==> points.on.sphere (geometry/part1) <== What are the odds that n random points on a sphere lie in the same hemisphere? ==> revolutions (geometry/part1) <== A circle with radius 1 rolls without slipping once around a circle with radius ==> rotation (geometry/part1) <== What is the smallest rotation that returns an object to its original state? ==> shephard.piano (geometry/part1) <== What's the maximum area shape that will fit around a right-angle corner? ==> smuggler (geometry/part1) <== Somewhere on the high sees smuggler S is attempting, without much ==> spiral (geometry/part1) <== How far must one travel to reach the North Pole if one starts from the ==> table.in.corner (geometry/part1) <== Put a round table into a (perpendicular) corner so that the table top ==> tetrahedron (geometry/part1) <== Suppose you have a sphere of radius R and you have four planes that are ==> tiling/count.1x2 (geometry/part1) <== Count the ways to tile an MxN rectangle with 1x2 dominos. ==> tiling/rational.sides (geometry/part1) <== A rectangular region R is divided into rectangular areas. Show that if ==> tiling/rectangles.with.squares (geometry/part2) <== Given two sorts of squares, (axa) and (bxb), what rectangles can be tiled? ==> tiling/scaling (geometry/part2) <== A given rectangle can be entirely covered (i.e. concealed) by an ==> tiling/seven.cubes (geometry/part2) <== Consider 7 cubes of equal size arranged as follows. Place 5 cubes so ==> topology/fixed.point (geometry/part2) <== A man hikes up a mountain, and starts hiking at 2:00 in the afternoon ==> touching.blocks (geometry/part2) <== Can six 1x2x4 blocks be arranged so that each block touches n others, for all n? ==> trigonometry/euclidean.numbers (geometry/part2) <== For what numbers x is sin(x) expressible using only integers, +, -, *, / and ==> trigonometry/inequality (geometry/part2) <== Show that (sin x)^(sin x) < (cos x)^(cos x) when 0 < x < pi/4. ==> group.01 (group) <== AEFHIKLMNTVWXYZ BCDGJOPQRSU ==> group.01a (group) <== 147 0235689 ==> group.02 (group) <== ABEHIKMNOTXZ CDFGJLPQRSUVWY ==> group.03 (group) <== BEJQXYZ DFGHLPRU KSTV CO AIW MN ==> group.04 (group) <== BDO P ACGIJLMNQRSUVWZ EFTY HKX ==> group.05 (group) <== CEFGHIJKLMNSTUVWXYZ ADOPQR B ==> group.06 (group) <== BCEGKMQSW DFHIJLNOPRTUVXYZ ==> group.07 (group) <== CDEFLOPTZ ABGHIJKMNQRSUVWXY ==> group.08 (group) <== COS ABDEFGHIJKLMNPQRTUVWXYZ ==> group.09 (group) <== CDILMVX ABEFGHJKNOPQRSTUWYZ ==> group.10 (group) <== AHIMOTUVWXY BCDEFGJKLNPQRSZ ==> group.11 (group) <== BCDIJLMNOPQRSUVWZ AEFGHKTXY ==> group.12 (group) <== COPSUVWXZ ABDEFGHIJKLMNQRTY ==> group.13 (group) <== BCDEHIKOX AFGJLMNPQRSTUVWYZ ==> group.14 (group) <== EHIS MOT ABCDFGJKLNPQRUVWXYZ ==> group.15 (group) <== HIOX ABCDEFGJKLMNPQRSTUVWYZ ==> group.16 (group) <== IJ ABCDEFGHKLMNOPQRSTUVWXYZ ==> group.17 (group) <== J BDFHIKLT GPQY ACEMNORSUVWXZ ==> handshake (induction) <== A married couple organizes a party. They only invite other married ==> hanoi (induction) <== Is there an algorithm for solving the Hanoi tower puzzle for any number ==> n-sphere (induction) <== With what odds do three random points on an n-sphere form an acute triangle? ==> paradox (induction) <== Is there a non-trivial property that holds for the first 10,000 positive ==> party (induction) <== You're at a party. Any two (different) people at the party have exactly one ==> roll (induction) <== An ordinary die is thrown until the running total of the throws first ==> takeover (induction) <== After graduating from college, you have taken an important managing position ==> close.antonyms (language/part1) <== What words are similar to their antonyms in other langauges? ==> dutch/dutch.record (language/part1) <== What are some Dutch words with unusual properties? ==> english/equations (language/part1) <== 1 = E. on a C. ==> english/etymology/acronym (language/part1) <== What acronyms have become common words or are otherwise interesting? ==> english/etymology/fossil (language/part1) <== What are some examples of idioms that include obsolete words? ==> english/etymology/portmanteau (language/part1) <== What are some words formed by combining together parts of other words? ==> english/frequency (language/part1) <== In the English language, what are the most frequently appearing: ==> english/idioms (language/part1) <== List some idioms that say the opposite of what they mean. ==> english/less.ness (language/part1) <== Find a word that forms two other words, unrelated in meaning, when "less" ==> english/letter.rebus (language/part1) <== Define the letters of the alphabet using self-referential common phrases (e.g., ==> english/malaprop (language/part1) <== List some phrases with the same meaning that differ by one sound. ==> english/piglatin (language/part1) <== What words in pig latin also are words? ==> english/pleonasm (language/part1) <== What are some redundant terms that occur frequently (like "ABM missile")? ==> english/plurals/collision (language/part1) <== Two words, spelled and pronounced differently, have plurals spelled ==> english/plurals/doubtful.number (language/part1) <== A little word of doubtful number, ==> english/plurals/drop.terminal (language/part1) <== What words have their plurals formed by dropping the final letter? ==> english/plurals/endings (language/part1) <== List a plural ending with each letter of the alphabet. ==> english/plurals/man (language/part1) <== Words ending with "man" make their plurals by adding "s". ==> english/plurals/switch.first (language/part1) <== What plural is formed by switching the first two letters? ==> english/potable.color (language/part1) <== Find words that are both beverages and colors. ==> english/pronunciation/autonym (language/part1) <== What is the longest word whose phonetic and normal spellings are the same? ==> english/pronunciation/homograph/different.pronunciation (language/part1) <== What sequence of letters has the most different pronunciations? ==> english/pronunciation/homograph/homographs (language/part1) <== List some homographs (words spelled the same but pronounced differently) ==> english/pronunciation/homophone/homophones.alphabet (language/part1) <== Homophones can be confusing when used to exemplify a letter. For example, ==> english/pronunciation/homophone/homophones.letter (language/part1) <== For each letter, list homophones that differ by that letter. ==> english/pronunciation/homophone/homophones.most (language/part1) <== What words have four or more spellings that sound alike? ==> english/pronunciation/homophone/trivial (language/part2) <== Consider the free non-abelian group on the twenty-six letters of the ==> english/pronunciation/oronym (language/part2) <== List some oronyms (phrases or sentences that can be read in two ways ==> english/pronunciation/phonetic.letters (language/part2) <== What does "FUNEX" mean? ==> english/pronunciation/rhyme (language/part2) <== What English words are hard to rhyme? ==> english/pronunciation/silent.letter (language/part2) <== For each letter, what word contains that letter silent? ==> english/pronunciation/silent.most (language/part2) <== What word has the most silent letters in a row? ==> english/pronunciation/syllable (language/part2) <== What words have an exceptional number of letters per syllable? ==> english/pronunciation/telegrams (language/part2) <== Since telegrams cost by the word, phonetically similar messages can be cheaper. ==> english/puns (language/part2) <== Where can I find a collection of puns? ==> english/rare.trigraphs (language/part2) <== What trigraphs (three-letter combinations) occur in only one word? ==> english/self.ref/self.ref.letters (language/part2) <== Construct a true sentence of the form: "This sentence contains _ a's, _ b's, ==> english/self.ref/self.ref.numbers (language/part2) <== What true sentence has the form: "There are _ 0's, _ 1's, _ 2's, ..., ==> english/self.ref/self.ref.words (language/part2) <== What sentence describes its own word, syllable and letter count? ==> english/sentences/behead (language/part2) <== Is there a sentence that remains a sentence when all its words are beheaded? ==> english/sentences/charades (language/part2) <== A ....... surgeon was ....... to operate because he had ....... ==> english/sentences/emphasis (language/part2) <== List some sentences that change meaning when the emphasis is moved. ==> english/sentences/pangram (language/part2) <== A "pangram" is a sentence containing all 26 letters. ==> english/sentences/repeated.words (language/part2) <== What is a sentence with the same word several times repeated? Do not use ==> english/sentences/sentence (language/part2) <== Find a sentence with words beginning with the letters of the alphabet, in order. ==> english/sentences/snowball (language/part2) <== Construct the longest coherent sentence you can such that the nth word ==> english/sentences/weird (language/part2) <== Make a sentence containing only words that violate the "i before e" rule. ==> english/sentences/word.boundaries (language/part2) <== List some sentences that can be radically altered by changing word boundaries ==> english/spelling/gry (language/part2) <== Find three completely different words ending in "gry." ==> english/spelling/j.ending (language/part2) <== What words and names end in j? ==> english/spelling/lipograms (language/part2) <== What books have been written without specific letters, vowels, etc.? ==> english/spelling/longest (language/part2) <== What is the longest word in the English language? ==> english/spelling/most (language/part2) <== What word has the most variant spellings? ==> english/spelling/near.palindrome (language/part2) <== What are some long near palindromes, i.e., words that except for one ==> english/spelling/operations.on.words/deletion (language/part2) <== What exceptional words turn into other words by deletion of letters? ==> english/spelling/operations.on.words/insertion.and.deletion (language/part2) <== What exceptional words turn into other words by both insertion and ==> english/spelling/operations.on.words/insertion (language/part2) <== What exceptional words turn into other words by insertion of letters? ==> english/spelling/operations.on.words/movement (language/part2) <== What exceptional words turn into other words by movement of letters? ==> english/spelling/operations.on.words/substitution (language/part2) <== What exceptional words turn into other words by substitution of letters? ==> english/spelling/operations.on.words/transposition (language/part3) <== What exceptional words turn into other words by transposition of letters? ==> english/spelling/operations.on.words/words.within.words (language/part3) <== What exceptional words contain other words? ==> english/spelling/palindromes (language/part3) <== What are some long palindromes? ==> english/spelling/sets.of.words/ladder (language/part3) <== Find the shortest word ladders stretching between the following pairs: ==> english/spelling/sets.of.words/nots.and.crosses (language/part3) <== What is the most number of letters that can be fit into a three by three grid ==> english/spelling/sets.of.words/perfect.ladder (language/part3) <== A "perfect" ladder comprises five-letter words where every letter is ==> english/spelling/sets.of.words/squares (language/part3) <== What are some exceptional word squares (square crosswords with no blanks)? ==> english/spelling/sets.of.words/variogram (language/part3) <== What is the largest known variogram (word square where repeated letters count ==> english/spelling/sets.of.words/word.torture (language/part3) <== What is the longest word all of whose contiguous subsequences are words? ==> english/spelling/single.words (language/part3) <== What words have exceptional lengths, patterns, etc.? ==> english/spoonerisms (language/part3) <== List some exceptional spoonerisms. ==> english/synonyms/ambiguous (language/part3) <== What word in the English language is the most ambiguous? ==> english/synonyms/antonym (language/part3) <== What words, when a single letter is added, reverse their meanings? ==> english/synonyms/contradictory.proverbs (language/part3) <== What are some proverbs that contradict one another? ==> english/synonyms/contranym (language/part3) <== What words are their own antonym? ==> english/synonyms/double.synonyms (language/part3) <== What words have two different synonymous meanings? ==> finnish/finnish.plural (language/part3) <== What Finnish word is the anagram of its plural? ==> finnish/finnish.record (language/part4) <== What are some Finnish words with unusual properties? ==> french/french.palindromes (language/part4) <== List some French palindromes. ==> french/french.record (language/part4) <== What are some French words with unusual properties? ==> german/german.palindromes (language/part4) <== List some German palindromes. ==> german/german.record (language/part4) <== What are some German words with unusual properties? ==> italian/italian.record (language/part5) <== What are some Italian words with unusual properties? ==> multi.palindromes (language/part5) <== List some multi-lingual palindromes. ==> norwegian/norwegian.record (language/part5) <== What are some Norwegian words with unusual properties? ==> repeated.word (language/part5) <== In any language, construct a sentence by repeating one word four times. ==> swedish/swedish.record (language/part5) <== What are some Swedish words with unusual properties? ==> synonymous.reversals (language/part5) <== What words are synonymous with their reversals in other langauges? ==> vowels.repeated (language/part5) <== In any language, what word contains the same vowel repeated four times in a row? ==> 29 (logic/part1) <== Three people check into a hotel. They pay $30 to the manager and go ==> ages (logic/part1) <== 1) Ten years from now Tim will be twice as old as Jane was when Mary was ==> attribute (logic/part1) <== All the items in the first list share a particular attribute. The second ==> bookworm (logic/part1) <== A bookworm eats from the first page of an encyclopedia to the last ==> boxes (logic/part1) <== Which Box Contains the Gold? ==> camel (logic/part1) <== An Arab sheikh tells his two sons to race their camels to a distant ==> centrifuge (logic/part1) <== You are a biochemist, working with a 12-slot centrifuge. This is a gadget ==> chain (logic/part1) <== What is the least number of links you can cut in a chain of 21 links to be able ==> children (logic/part1) <== A man walks into a bar, orders a drink, and starts chatting with the ==> condoms (logic/part1) <== How can a man have mutually safe sex with three women with only two condoms? ==> dell (logic/part1) <== How can I solve logic puzzles (e.g., as published by Dell) automatically? ==> elimination (logic/part1) <== 97 baseball teams participate in an annual state tournament. ==> flip (logic/part1) <== How can a toss be called over the phone (without requiring trust)? ==> flowers (logic/part1) <== How many flowers do I have if all of them are roses except two, all of ==> friends (logic/part1) <== Any group of 6 or more contains either 3 mutual friends or 3 mutual strangers. ==> hofstadter (logic/part1) <== In first-order logic, find a predicate P(x) which means "x is a power of 10." ==> hundred (logic/part1) <== A sheet of paper has statements numbered from 1 to 100. Statement n says ==> inverter (logic/part1) <== Can a digital logic circuit with two inverters invert N independent inputs? ==> josephine (logic/part1) <== The recent expedition to the lost city of Atlantis discovered scrolls ==> locks.and.boxes (logic/part1) <== You want to send a valuable object to a friend. You have a box which ==> min.max (logic/part1) <== In a rectangular array of people, which will be taller, the tallest of the ==> mixing (logic/part1) <== Start with a half cup of tea and a half cup of coffee. Take one tablespoon ==> monty.52 (logic/part1) <== Monty and Waldo play a game with N closed boxes. Monty hides a ==> number (logic/part1) <== Mr. S. and Mr. P. are both perfect logicians, being able to correctly deduce ==> riddle (logic/part2) <== Who makes it, has no need of it. Who buys it, has no use for it. Who ==> river.crossing (logic/part2) <== Three humans, one big monkey and two small monkeys are to cross a river: ==> ropes (logic/part2) <== Two fifty foot ropes are suspended from a forty foot ceiling, about ==> same.street (logic/part2) <== Sally and Sue have a strong desire to date Sam. They all live on the ==> self.ref (logic/part2) <== Find a number ABCDEFGHIJ such that A is the count of how many 0's are in the ==> situation.puzzles (logic/part3) <== Jed's List of Situation Puzzles ==> smullyan/black.hat (logic/part4) <== Three logicians, A, B, and C, are wearing hats, which they know are either ==> smullyan/fork.three.men (logic/part4) <== Three men stand at a fork in the road. One fork leads to Someplaceorother; ==> smullyan/fork.two.men (logic/part4) <== Two men stand at a fork in the road. One fork leads to Someplaceorother; the ==> smullyan/integers (logic/part4) <== Two logicians place cards on their foreheads so that what is written on the ==> smullyan/painted.heads (logic/part4) <== While three logicians were sleeping under a tree, a malicious child painted ==> smullyan/priest (logic/part5) <== In a small town there are N married couples in which one of the pair ==> smullyan/stamps (logic/part5) <== The moderator takes a set of 8 stamps, 4 red and 4 green, known to the ==> supertasks (logic/part5) <== You have an empty urn, and an infinite number of labeled balls. Each ==> timezone (logic/part5) <== Two people are talking long distance on the phone; one is in an East- ==> unexpected (logic/part5) <== Swedish civil defense authorities announced that a civil defense drill would ==> verger (logic/part5) <== A very bright and sunny Day ==> weighing/balance (logic/part5) <== You are given 12 identical-looking coins, one of which is counterfeit ==> weighing/box (logic/part5) <== You have ten boxes; each contains nine balls. The balls in one box ==> weighing/find.median (logic/part5) <== What is the least number of pairwise comparisons needed to find the median of ==> weighing/gummy.bears (logic/part5) <== Real gummy drop bears have a mass of 10 grams, while imitation gummy ==> weighing/optimal.weights (logic/part5) <== What is the smallest set of weights that allow you to weigh on a ==> weighing/weighings (logic/part5) <== Some of the supervisors of Scandalvania's n mints are producing bogus coins. ==> zoo (logic/part5) <== I took some nephews and nieces to the Zoo, and we halted at a cage marked ==> balloon (physics) <== A helium-filled balloon is tied to the floor of a car that makes a ==> brick (physics) <== What is the maximum overhang you can create with an infinite supply of bricks? ==> bubbles (physics) <== In a universe with the same physical laws, but which is mostly water ==> cannonball (physics) <== A person in a boat drops a cannonball overboard; does the water level change? ==> magnets (physics) <== You have two bars of iron. One is magnetized along its length, the ==> milk.and.coffee (physics) <== You are just served a hot cup of coffee and want it to be as hot as ==> mirror (physics) <== Why does a mirror appear to invert the left-right directions, but not up-down? ==> monkey (physics) <== Hanging over a pulley there is a rope, with a weight at one end. ==> pole.in.barn (physics) <== Accelerate a pole of length l to a constant speed of 90% of the speed of ==> resistors (physics) <== What is the resistance between various pairs of vertices on a lattice ==> sail (physics) <== A sailor is in a sailboat on a river. The current is 3 knots with respect ==> shoot.sun (physics) <== If you are standing at the equator at sunrise, where must you point a laser ==> skid (physics) <== What is the fastest way to make a 90 degree turn on a slippery road? ==> spheres (physics) <== Two spheres are the same size and weight, but one is hollow. They are ==> wind (physics) <== Is a round-trip by airplane longer or shorter if there is wind blowing? ==> pickover.01 (pickover/part1) <== Title: Cliff Puzzle 1: Can you beat the numbers game? ==> pickover.02 (pickover/part1) <== Title: Cliff Puzzle 2: Grid of the Gods ==> pickover.03 (pickover/part1) <== Title: Cliff Puzzle 3: Too many 3's ==> pickover.04 (pickover/part1) <== Title: Cliff Puzzle 4: Time in a Bottle ==> pickover.05 (pickover/part1) <== Title: Cliff Puzzle 5: Mystery Sequence ==> pickover.06 (pickover/part1) <== Title: Cliff Puzzle 6: Star Chambers ==> pickover.07 (pickover/part2) <== Title: Cliff Puzzle 7: 3x3 Recursion ==> pickover.08 (pickover/part2) <== Title: Cliff Puzzle 8: Squares and Squares and Squares .... ==> pickover.09 (pickover/part2) <== Title: Cliff Puzzle 9: 3-Atoms and Growth ==> pickover.10 (pickover/part2) <== Title: Cliff Puzzle 10: The Ark Series ==> pickover.11 (pickover/part2) <== Title: Cliff Puzzle 11: The Leviathan Number ==> pickover.12 (pickover/part3) <== Title: Cliff Puzzle 12: Slides in Hell ==> pickover.13 (pickover/part3) <== Title: Cliff Puzzle 13: Ladders to Heaven ==> pickover.14 (pickover/part3) <== Title: Cliff Puzzle 14: Geography Genuflection ==> pickover.15 (pickover/part3) <== Title: Cliff Puzzle 15: Cherries in Wine Glasses ==> pickover.16 (pickover/part3) <== Title: Cliff Puzzle 16: Undulating Squares ==> pickover.17 (pickover/part3) <== Title: Cliff Puzzle 17: Weird Recursive Sequence ==> pickover.18 (pickover/part3) <== Title: Cliff Puzzle 18: Difficult Nested Roots ==> amoeba (probability) <== A jar begins with one amoeba. Every minute, every amoeba ==> apriori (probability) <== An urn contains one hundred white and black balls. You sample one hundred ==> bayes (probability) <== One urn contains black marbles, and the other contains white or black ==> birthday/line (probability) <== At a movie theater, the manager announces that they will give a free ticket ==> birthday/same.day (probability) <== How many people must be at a party before you have even odds or better ==> cab (probability) <== A cab was involved in a hit and run accident at night. Two cab companies, ==> coupon (probability) <== There is a free gift in my breakfast cereal. The manufacturers say that ==> darts (probability) <== Peter throws two darts at a dartboard, aiming for the center. The ==> derangement (probability) <== 12 men leave their hats with the hat check. If the hats are randomly ==> family (probability) <== Suppose that it is equally likely for a pregnancy to deliver ==> flips/once.in.run (probability) <== What are the odds that a run of one H or T (i.e., THT or HTH) will occur ==> flips/twice.in.run (probability) <== What is the probability in n flips of a fair coin that there will be two ==> flips/unfair (probability) <== Generate even odds from an unfair coin. For example, if you ==> flips/waiting.time (probability) <== Compute the expected waiting time for a sequence of coin flips, or the ==> flush (probability) <== Which set contains proportionately more flushes than the set of all ==> hospital (probability) <== A town has two hospitals, one big and one small. Every day the big ==> icos (probability) <== The "house" rolls two 20-sided dice and the "player" rolls one ==> intervals (probability) <== Given two random points x and y on the interval 0..1, what is the average ==> killers.and.pacifists (probability) <== You enter a town that has K killers and P pacifists. When a ==> leading.digit (probability) <== What is the probability that the ratio of two random reals starts with a 1? ==> lights (probability) <== Waldo and Basil are exactly m blocks west and n blocks north from ==> lottery (probability) <== There n tickets in the lottery, k winners and m allowing you to pick another ==> oldest.girl (probability) <== You meet a stranger on the street, and ask how many children he has. He ==> particle.in.box (probability) <== A particle is bouncing randomly in a two-dimensional box. How far does it ==> pi (probability) <== Are the digits of pi random (i.e., can you make money betting on them)? ==> random.walk (probability) <== Waldo has lost his car keys! He's not using a very efficient search; ==> reactor (probability) <== There is a reactor in which a reaction is to take place. This reaction ==> roulette (probability) <== You are in a game of Russian roulette, but this time the gun (a 6 ==> transitivity (probability) <== Can you number dice so that die A beats die B beats die C beats die A? ==> icecubes (real-life) <== You have an old-fashioned refrigerator with a small freezer compartment ==> microwave (real-life) <== Every morning when I warm my milk for breakfast, I put one cup of milk ==> books/bloopers (references) <== What are some errors made in puzzle books? ==> books/masquerade (references) <== What is the solution to _Masquerade_ by Kit Williams? ==> books/maze (references) <== What is the solution to _Maze_ by Christopher Manson? ==> books/treasure (references) <== What is the solution to _Treasure_ by Dr. Crypton? ==> books/unnamed (references) <== What is the solution to the unnamed book by Kit Williams? ==> faq (references) <== Where should I look if I can't find the answer here? ==> magazines (references) <== What magazines and journals contain puzzles? ==> organizations (references) <== What organizations exist for puzzle lovers? ==> series.00 (series) <== Are "complete this series" problems well defined? ==> series.01 (series) <== M, N, B, D, P ? ==> series.02 (series) <== H, H, L, B, B, C, N, O, F ? ==> series.03 (series) <== W, A, J, M, M, A, J? ==> series.03a (series) <== G, J, T, J, J, J, A, M, W, J, J, Z, M, F, J, ? ==> series.03b (series) <== A, J, B, C, G, T, C, V, J, T, D, F, K, B, H, ? ==> series.03c (series) <== M, A, M, D, E, L, R, H, ? ==> series.04 (series) <== A, E, H, I, K, L, ? ==> series.05 (series) <== A B C D E F G H? ==> series.06 (series) <== Z, O, T, T, F, F, S, S, E, N? ==> series.06a (series) <== F, S, T, F, F, S, ? ==> series.07 (series) <== 1, 1 1, 2 1, 1 2 1 1, ... ==> series.08a (series) <== G, L, M, B, C, L, M, C, F, S, ? ==> series.08b (series) <== A, V, R, R, C, C, L, L, L, E, ? ==> series.09a (series) <== S, M, S, S, S, C, P, P, P, ? ==> series.09b (series) <== M, S, C, P, P, P, S, S, S, ? ==> series.10 (series) <== D, P, N, G, C, M, M, S, ? ==> series.11 (series) <== R O Y G B ? ==> series.12 (series) <== A, T, G, C, L, ? ==> series.13 (series) <== M, V, E, M, J, S, ? ==> series.14 (series) <== A, B, D, O, P, ? ==> series.14a (series) <== A, B, D, E, G, O, P, ? ==> series.15 (series) <== A, E, F, H, I, ? ==> series.16 (series) <== 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.17 (series) <== T, P, O, F, O, F, N, T, S, F, T, F, E, N, S, N? ==> series.18 (series) <== 10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, ___ , 100, 121, 10000 ==> series.19 (series) <== 0 01 01011 0101101011011 0101101011011010110101101101011011 etc. ==> series.20 (series) <== 1 2 5 16 64 312 1812 12288 ==> series.21 (series) <== 5, 6, 5, 6, 5, 5, 7, 5, ? ==> series.22 (series) <== 3 1 1 0 3 7 5 5 2 ? ==> series.23 (series) <== 22 22 30 13 13 16 16 28 28 11 ? ==> series.24 (series) <== What is the next letter in the sequence: W, I, T, N, L, I, T? ==> series.25 (series) <== 1 3 4 9 10 12 13 27 28 30 31 36 37 39 40 ? ==> series.26 (series) <== 1 3 2 6 7 5 4 12 13 15 14 10 11 9 8 24 25 27 26 ? ==> series.27 (series) <== 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.28 (series) <== 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.29 (series) <== 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.30 (series) <== I I T Y W I M W Y B M A D ==> series.31 (series) <== 6 2 5 5 4 5 6 3 7 ==> series.32 (series) <== 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 ==> series.33 (series) <== 2 12 360 75600 ==> series.34 (series) <== 3 5 4 4 3 5 5 4 3 ==> series.35 (series) <== 1 2 3 2 1 2 3 4 2 1 2 3 4 2 2 3 ==> series.36 (series) <== ETIANMSURWDKGO ==> series.37 (series) <== 10^3 10^9 10^27 10^2 0 4 8 3 ==> area.codes (trivia) <== When looking at a map of the distribution of telephone area codes for ==> body.parts (trivia) <== Name ten body parts that are spelled with three letters. No slang words. ==> coincidence (trivia) <== Name some amazing coincidences. ==> eskimo.snow (trivia) <== How many words do the Eskimo have for snow? ==> federal.reserve (trivia) <== What is the pattern to this list: ==> jokes.self-referential (trivia) <== What are some self-referential jokes? ==> memory.tricks (trivia) <== When asked to name a color, many people answer "red." What are some other ==> quotations (trivia) <== Where can I find the source for a quotation?