Instructions for Accessing the rec.puzzles Archive (27. Nov 1997) INTRODUCTION The rec.puzzles Archive 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 "geometry/duck.and.fox.p", send the message: return_address mickey@disneyland.com send duck.and.fox To request the index, use: send index To request multiple puzzles, use several "send" lines in a message. Please refrain from requesting the entire archive via email. Use FTP. FTP The entire archive is also accessible via anonymous FTP, from any site which maintains archives of the newsgroups news.answers or rec.answers. The file part01 contains the index. The remaining files contain alternating problem text and solution text for all the puzzles. Some FTP sites are: North America: ftp://rtfm.mit.edu/pub/usenet/news.answers/puzzles/archive ftp://ftp.uu.net/usenet/news.answers/puzzles/archive ftp://mirrors.aol.com/pub/rtfm/usenet/news.answers/puzzles/archive ftp://ftp.cis.ksu.edu/pub/mirrors/news.answers/puzzles/archive Europe: ftp://ftp.cs.ruu.nl/pub/NEWS.ANSWERS/puzzles/archive ftp://src.doc.ic.ac.uk/usenet/news-faqs/news.answers/puzzles/archive ftp://ftp.uni-paderborn.de/doc/FAQ/rec/puzzles Asia: ftp://ftp.hk.super.net/mirror/faqs/puzzles/archive GOPHER >From the global home page, the menu choices to access the archives at "cs.ttu.edu" are: North America/USA/Texas/Texas Tech University, Computer Sciences /Entertainment/Games/Puzzles To access "uni-hohenheim.de" your menu choices are: Europe/Germany/University of Hohenheim/Lots of Interesting Stuff /FAQ Frequently Asked Questions/rec/puzzles/archive WAIS wais://xraysgi.ims.uconn.edu:8000/rpa WEB http://xraysgi.ims.uconn.edu/searchform.html By keyword as well as subject. http://einstein.et.tudelft.nl/~arlet/puzzles/index.html Partially HTMLized. http://www.nova.edu/Inter-Links/puzzles.html http://xraysgi.ims.uconn.edu/others.html A list of other sites (maintained by David Moews) THE rec.puzzles ORACLE This is a group of rec.puzzles regulars, who are familiar with the rec.puzzles archive, and who will find your answer there if it exists, or maybe compose an original answer if they are interested enough! At any rate, they promise to respond to your question within two days, and perhaps save you the embarrassment of posting a well-worn question. They will respond within two days even if they do not know the answer to your question. To query the rec.puzzles oracle, send email containing your question to the following address: puzzle-oracle@questrel.com 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 ==> analysis/bicycle.p <== A boy, a girl and a dog go for a 10 mile walk. The boy and girl can walk at 2 mph and the dog can trot at 4 mph. They also have a bicycle ==> analysis/boy.girl.dog.p <== A boy, a girl and a dog are standing together on a long, straight road. Simultaneously, they all start walking in the same direction: ==> analysis/bugs.p <== Four bugs are placed at the corners of a square. Each bug walks always directly toward the next bug in the clockwise direction. How far do ==> analysis/c.infinity.p <== What function is zero at zero, strictly positive elsewhere, infinitely differentiable at zero and has all zero derivatives at zero? ==> analysis/cache.p <== Cache and Ferry (How far can a truck go in a desert?) A pick-up truck in the desert gets 10 miles per gallon of gas and starts ==> analysis/calculate.pi.p <== How can I calculate many digits of pi? ==> 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/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 ==> analysis/e.and.pi.p <== Without finding their numerical values, 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. ==> analysis/goat.p <== A goat grazes on a circular meadow, its tail is tacked to a stake of the fence - What's the length of the goat to feed half of the pasture? ==> analysis/integral.p <== If f is integrable on (0,inf) and differentiable at 0, and a > 0, and: ==> analysis/irrational.stamp.p <== You have an ink stamp which is so amazingly precise that, when inked and pressed down on the plane, it makes every circle of irrational ==> analysis/minimum.time.p <== N people can walk or drive in a two-seater to go from city A to city B. What is the minimum time required to do so? ==> analysis/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 ==> 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 rubber band 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 ==> analysis/sequence.p <== Show that in the sequence: 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 snow plow starts plowing a street. It travels 1 mile in the first hour, ==> analysis/tower.p <== R = N ^ (N ^ (N ^ ...)). What is the maximum N>0 that will yield a finite R? ==> 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 ==> arithmetic/arithmetic.progression.p <== Is there an arithmetic progression of 20 or more primes? ==> arithmetic/clock/day.of.week.p <== It's restful sitting in Tom's cosy den, talking quietly and sipping a glass of his Madeira. ==> arithmetic/clock/palindromic.p <== How many times per day does a digital clock display a palindromic number? ==> arithmetic/clock/reversible.p <== How many times per day can the hour and minute hands on an analog clock switch roles and still signify a valid time, ignoring the second hand? ==> arithmetic/clock/right.angle.p <== How many times per day do the hour and minute hands of a clock form a right angle? ==> 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.composites.p <== Are there 10,000 consecutive non-prime numbers? ==> arithmetic/consecutive.product.p <== Prove that the product of three or more consecutive positive integers cannot be a perfect square. ==> arithmetic/consecutive.sums.p <== Find all series of consecutive positive integers whose sum is exactly 10,000. ==> arithmetic/conway.p <== Describe the sequence a(1)=a(2)=1, a(n) = a(a(n-1)) + a(n-a(n-1)) for n>2. ==> arithmetic/digits/6.and.7.p <== Does every number which is not divisible by 5 have a multiple whose only digits are 6 and 7? ==> 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 ==> 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: ==> arithmetic/digits/cryptarithm.p <== How do I solve letter substitutions (cryptarithms) like SEND + MORE = MONEY? ==> 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 through 100 on the left side of the equals sign. ==> arithmetic/digits/equations/24.p <== Form an expression that evaluates to 24 that contains two 3's, two 7's, and zero or more of the operators +, -, *, and /, and parentheses. What ==> arithmetic/digits/equations/383.p <== Make 383 out of 1,2,25,50,75,100 using +,-,*,/. ==> arithmetic/digits/equations/find.p <== Write a program for finding expressions built out of given numbers and using given operators that evaluate to a given value, or listing all possible values. ==> arithmetic/digits/extreme.products.p <== What are the extremal products of three three-digit numbers using digits 1-9? ==> 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 ==> arithmetic/digits/least.significant/factorial.p <== What is the least significant non-zero digit in the decimal expansion of n!? ==> arithmetic/digits/least.significant/tower.of.power.p <== What are the least significant digits of 9^(8^(7^(6^(5^(4^(3^(2^1))))))) ? ==> arithmetic/digits/most.significant/googol.p <== What digits does googol! start with? ==> arithmetic/digits/most.significant/powers.p <== What is the probability that 2^N begins with the digits 603245? ==> 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 ==> 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 one position, so that the last digit become the first digit. ==> arithmetic/digits/sesqui.p <== Find the least number where moving the first digit to the end multiplies by 1.5. ==> arithmetic/digits/squares/change.leading.p <== What squares remain squares when their leading digits are incremented? ==> 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/million.p <== How many zeros occur in the numbers from 1 to 1,000,000? ==> arithmetic/digits/zeros/trailing.p <== How many trailing zeros are in the decimal expansion of n!? ==> 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/subset.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/sums.of.powers.p <== Partition 1,2,3,...,16 into two equal sets, such that the sums of the numbers in each set are equal, as are the sums of their squares and cubes. ==> 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 seven? ==> arithmetic/tests.for.divisibility/three.p <== What is the test to see if a number is divisible by three? ==> combinatorics/alphabet.blocks.p <== What is the minimum number of dice painted with one letter on all six sides such that all permutations without repetitions of n letters can be formed ==> combinatorics/bus.p <== Putting 33 students in each bus, the teacher has one student left over. Putting more in each bus, but always the same number in each bus, the ==> combinatorics/coinage/combinations.p <== Assuming you have enough coins of 1, 5, 10, 25 and 50 cents, how many ways are there to make change for a dollar? ==> 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 ==> 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? ==> 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 ==> 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 ==> 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 ==> combinatorics/grid.dissection.p <== How many (possibly overlapping) squares are in an mxn grid? Assume that all the squares have their edges parallel to the edges of the grid. ==> combinatorics/paths.through.grid.p <== How many distict paths exist from one corner of a rectangular grid to the opposite corner, traveling along edges without reusing an edge? ==> combinatorics/permutation.p <== Compute the nth permutation of k numbers (or objects). ==> 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 ==> combinatorics/transitions.p <== How many n-bit binary strings (0/1) have exactly k transitions (an adjacent pair of dissimilar bits, i.e., a 01 or a 10)? ==> competition/contests/games.magazine.p <== What are the best answers to various contests run by _Games_ magazine? ==> competition/contests/national.puzzle/npc.1993.p <== What are the solutions to the Games magazine 1993 National Puzzle Contest? ==> competition/games/alcatraz.p <== What is the solution to Alcatraz? ==> competition/games/bridge.p <== Are there any programs for solving double-dummy Bridge? ==> competition/games/chess/knight.control.p <== How many knights does it take to attack or control the board? ==> competition/games/chess/knight.most.p <== What is the maximum number of knights that can be put on n x n chessboard without threatening each other? ==> competition/games/chess/knight.tour.p <== For what size boards are knight tours possible? ==> competition/games/chess/mutual.stalemate.p <== What's the minimal number of pieces in a legal mutual stalemate? ==> competition/games/chess/queen.control.p <== How many queens does it take to attack or control the board? ==> competition/games/chess/queen.most.p <== How many non-mutually-attacking queens can be placed on various sized boards? ==> competition/games/chess/queens.p <== How many ways can eight queens be placed so that they control the board? ==> competition/games/chess/rook.paths.p <== How many non-overlapping paths can a rook take from one corner to the opposite on an MxN chess board? ==> competition/games/chess/size.of.game.tree.p <== How many different positions are there in the game tree of chess? ==> competition/games/cigarettes.p <== The game of cigarettes is played as follows: Two players take turns placing a cigarette on a circular table. The cigarettes ==> competition/games/connect.four.p <== Is there a winning strategy for Connect Four? ==> competition/games/craps.p <== What are the odds in craps? ==> competition/games/crosswords.p <== Are there programs to make crosswords? What are the rules for cluing cryptic crosswords? Is there an on-line competition for cryptic cluers? ==> competition/games/cube.p <== What are some games involving cubes? ==> competition/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 ==> competition/games/hi-q.p <== What is the quickest solution of the game Hi-Q (also called Solitaire)? ==> competition/games/jeopardy.p <== What are the highest, lowest, and most different scores contestants can achieve during a single game of Jeopardy? ==> competition/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 ==> competition/games/online/online.scrabble.p <== How can I play Scrabble online on the Internet? ==> competition/games/online/unlimited.adventures.p <== Where can I find information about unlimited adventures? ==> competition/games/othello.p <== How good are computers at Othello? ==> competition/games/pc/The7thGuest.p <== What are solutions to some of the puzzles in The 7th Guest? ==> competition/games/pc/best.p <== What are the best PC games? ==> competition/games/pc/reviews.p <== Are reviews of PC games available online? ==> competition/games/pc/solutions.p <== What are the solutions to various popular PC games? ==> competition/games/poker.face.up.p <== In Face-Up Poker, two players each select five cards from a face-up deck, bet, discard and draw. Is there a winning strategy for this game? What if ==> competition/games/risk.p <== What are the odds when tossing dice in Risk? ==> competition/games/rubiks/rubiks.clock.p <== How do you quickly solve Rubik's clock? ==> competition/games/rubiks/rubiks.cube.p <== What is known about bounds on solving Rubik's cube? ==> competition/games/rubiks/rubiks.magic.p <== How do you solve Rubik's Magic? ==> competition/games/rubiks/rubiks.tangle.p <== What is the solution to Rubik's Tangle? ==> competition/games/scrabble.p <== What are some exceptional Scrabble Brand Crossword Game (TM) games? ==> competition/games/set.p <== What is the size of the largest collection of cards from which NO "set" can be selected ? ==> competition/games/soma.p <== What is the solution to Soma Cubes? ==> competition/games/square-1.p <== Does anyone have any hints on how to solve the Square-1 puzzle? ==> competition/games/think.and.jump.p <== THINK & JUMP: FIRST THINK, THEN JUMP UNTIL YOU ARE LEFT WITH ONE PEG! O - O O - O ==> competition/games/tictactoe.p <== In random tic-tac-toe, what is the probability that the first mover wins? ==> competition/tests/analogies/long.p <== 1. Host : Guest :: Cynophobia : ? 2. Mountain : Plain :: Acrocephalic : ? ==> competition/tests/analogies/pomfrit.p <== 1. NATURAL: ARTIFICIAL :: ANKYLOSIS: ? 2. RESCUE FROM CHOKING ON FOOD, etc.: HEIMLICH :: ADJUSTING MIDDLE EAR PRESSURE: ? ==> competition/tests/analogies/quest.p <== 1. Mother: Maternal :: Stepmother: ? 2. Club: Axe :: Claviform: ? ==> competition/tests/math/putnam/putnam.1967.p <== In article <5840002@hpesoc1.HP.COM>, nicholso@hpesoc1.HP.COM (Ron Nicholson) writes: ==> competition/tests/math/putnam/putnam.1987.p <== WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION ==> competition/tests/math/putnam/putnam.1988.p <== Problem A-1: Let R be the region consisting of the points (x,y) of the cartesian plane satisfying both |x| - |y| <= 1 and |y| <= 1. Sketch ==> competition/tests/math/putnam/putnam.1990.p <== Problem A-1 How many primes among the positive integers, written as usual in base ==> competition/tests/math/putnam/putnam.1992.p <== Problem A1 ==> 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? ==> cryptology/vcrplus.p <== What is the code used by VCR+? ==> decision/allais.p <== The Allais Paradox involves the choice between two alternatives: ==> decision/crossing/bridge.crossing.p <== Four people need to get across a bridge that can only support two at a time. It is night and one of the two must carry a flashlight. There ==> decision/crossing/river.crossing.p <== How can various combinations of people, animals, and things get across a river when there are restrictions on how many can be in the boat, or ==> decision/division.p <== N-Person Fair Division ==> decision/dowry.p <== Sultan's Dowry ==> 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 ==> decision/exchange.p <== At one time, the Canadian and US dollars were discounted by 10 cents on each side of the border (i.e., a Canadian dollar was worth 90 US cents ==> decision/high.or.low.p <== I pick two numbers, randomly, and tell you one of them. You are supposed to guess whether this is the lower or higher one of the two numbers I ==> decision/monty.hall.p <== You are a participant on "Let's Make a Deal." Monty Hall shows you three closed doors. He tells you that two of the closed doors have a ==> decision/newcomb.p <== Newcomb's Problem ==> 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 ==> 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!". ==> decision/rotating.table.p <== Four glasses are placed in the four corners of a square rotating table (like a lazy susan). You wish to turn them all in the same direction, ==> 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 it comes up heads on the ==> 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. ==> geometry/K3,3.p <== Can three houses be connected to three utilities without the pipes crossing? ==> 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 ==> geometry/bisector.p <== Prove if two angle bisectors of a triangle are equal, then the triangle is isosceles (more specifically, the sides opposite to the two angles ==> 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 ==> 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 each subcube, one at a time. Can it finish in the middle? ==> geometry/coloring/triominoes.p <== There is a chess board (of course with 64 squares). You are given 21 "triominoes" of size 3-by-1 (the size of an individual square on a ==> 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/corner.p <== A hallway of width A turns through 90 degrees into a hallway of width B. A ladder is to be passed around the corner. If the movement is ==> geometry/cover.earth.p <== A thin membrane covers the surface of the (spherical) earth. One square meter is added to the area of this membrane to form a larger ==> geometry/cycle.polynomial.p <== What are the cycle polynomials for the Platonic solids? ==> geometry/dissections/disk.p <== Can a disk 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 identical rhombuses. ==> geometry/dissections/largest.circle.p <== What is the largest circle that can be assembled from two semicircles cut from a rectangle with edges a and b? ==> geometry/dissections/square.70.p <== Since 1^2 + 2^2 + 3^2 + ... + 24^2 = 70^2, can a 70x70 square 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/dissections/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 ==> 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 ==> geometry/earth.band.p <== How much will a band around the equator rise above the surface if it is made one meter longer? Assume the equator is a circle. ==> geometry/fence.p <== A farmer wishes to enclose the maximum possible area with 100 meters of fence. The pasture is bordered by a straight cliff, which may be used as part of the ==> 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, ==> 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 ==> geometry/hole.in.sphere.p <== Old Boniface he took his cheer, Then he bored a hole through a solid sphere, ==> geometry/hypercube.p <== How many vertices, edges, faces, etc. does a hypercube have? ==> geometry/intersection.free.p <== 1,000,000 black points and 1,000,000 white points exist on a planar disk. No three points are colinear. Can each black point be connected ==> geometry/kissing.number.p <== How many n-dimensional unit spheres can be packed around one unit sphere? ==> geometry/konigsberg.p <== Can you draw a line through each edge on the diagram below without crossing any edge twice and without lifting your pencil from the paper? ==> geometry/ladder.and.box.p <== A 3' * 3' packing case is placed against a wall. A 15' ladder is placed such that it touches the floor, the edge of the packing case and ==> 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/manhole.cover.p <== Why is a manhole cover round? ==> geometry/pentomino.p <== Arrange pentominos in 3x20, 4x15, 5x12, 6x10, 2x3x10, 2x5x6 and 3x4x5 forms. ==> geometry/points.in.sphere.p <== What is the expected distance between two random points inside a sphere? Assume the points are uniformly and independently distributed. ==> geometry/points.on.sphere.p <== What are the odds that n random points on a sphere lie in the same hemisphere? ==> geometry/puzzle.ring.p <== How can I put together my puzzle rings (where four bands become one)? ==> geometry/revolutions.p <== A circle with radius 1 rolls without slipping once around a circle with radius 3. How many revolutions does the smaller circle make? ==> geometry/rotation.p <== What is the smallest rotation that returns an object to its original state? ==> geometry/shephard.piano.p <== What's the maximum area shape that will fit around a right-angle corner? ==> 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 ==> geometry/spiral.p <== How far must one travel to reach the North Pole if one starts from the equator and always heads northwest? ==> 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 ==> 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 ==> geometry/tiling/count.1x2.p <== Count the ways to tile an MxN rectangle with 1x2 dominos. ==> 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 ==> 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. ==> 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 ==> geometry/topology/fixed.point.p <== A man hikes up a mountain, and starts hiking at 2:00 in the afternoon on a Friday. He does not hike at the same speed (a constant rate), and ==> geometry/touching.blocks.p <== Can six 1x2x4 blocks be arranged so that each block touches n others, for all n? ==> geometry/triangle.20.degrees.p <== In isoceles triangle ABC angle A=20, B=80, C=80. Draw a line from C to side AB. ==> geometry/trigonometry/euclidean.numbers.p <== For what numbers x is sin(x) expressible using only integers, +, -, *, / and square root? ==> geometry/trigonometry/inequality.p <== Show that (sin x)^(sin x) < (cos x)^(cos x) when 0 < x < pi/4. ==> group/group.01.p <== AEFHIKLMNTVWXYZ BCDGJOPQRSU ==> group/group.01a.p <== 147 0235689 ==> group/group.02.p <== ABEHIKMNOTXZ CDFGJLPQRSUVWY ==> group/group.02a.p <== ABEIKMNOTZ CDFGHJLPQRSUVWXY ==> group/group.02b.p <== ABEHIKMNOPTXYZ CDFGJLQRSUVW ==> group/group.03.p <== BEJQXYZ DFGHLPRU KSTV CO AIW MN ==> group/group.04.p <== BDO P ACGIJLMNQRSUVWZ EFTY HKX ==> group/group.05.p <== CEFGHIJKLMNSTUVWXYZ ADOPQR B ==> group/group.06.p <== BCEGKMQSW DFHIJLNOPRTUVXYZ ==> group/group.07.p <== CDEFLOPTZ ABGHIJKMNQRSUVWXY ==> group/group.08.p <== COS ABDEFGHIJKLMNPQRTUVWXYZ ==> group/group.09.p <== CDILMVX ABEFGHJKNOPQRSTUWYZ ==> group/group.10.p <== AHIMOTUVWXY BCDEFGJKLNPQRSZ ==> group/group.11.p <== BCDIJLMNOPQRSUVWZ AEFGHKTXY ==> group/group.12.p <== COPSUVWXZ ABDEFGHIJKLMNQRTY ==> group/group.13.p <== BCDEHIKOX AFGJLMNPQRSTUVWYZ ==> group/group.14.p <== EHIS MOT ABCDFGJKLNPQRUVWXYZ ==> group/group.15.p <== HIOX ABCDEFGJKLMNPQRSTUVWYZ ==> group/group.16.p <== IJ ABCDEFGHKLMNOPQRSTUVWXYZ ==> group/group.17.p <== J BDFHIKLT GPQY ACEMNORSUVWXZ ==> induction/handshake.p <== At a party people shake hands with all the people they do not know. A married couple organizes the party; they only invite other married ==> induction/hanoi.p <== Is there an algorithm for solving the Hanoi tower puzzle for any number of towers? Is there an equation for determining the minimum number of ==> induction/n-sphere.p <== With what odds do three random points on an n-sphere form an acute triangle? ==> induction/paradox.p <== Is there a non-trivial property that holds for the first 10,000 positive 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 ==> 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". ==> language/close.antonyms.p <== What words are similar to their antonyms in other langauges? ==> language/dutch/dutch.record.p <== What are some Dutch words with unusual properties? ==> language/english/contradictory.proverbs.p <== What are some proverbs that contradict one another? ==> language/english/equations.p <== What are the solutions to various letter equations like: 1 = W. on a U. ==> language/english/etymology/acronym.p <== What acronyms have become common words or are otherwise interesting? ==> language/english/etymology/fossil.p <== What are some examples of idioms that include obsolete words? ==> language/english/etymology/portmanteau.p <== What are some words formed by combining together parts of other words? ==> language/english/frequency.p <== In the English language, what are the most frequently appearing: 1) letters overall? ==> language/english/idioms.p <== List some idioms that say the opposite of what they mean. ==> language/english/less.ness.p <== Find a word that forms two other words, unrelated in meaning, when "less" and "ness" are added. ==> language/english/letter.rebus.p <== Define the letters of the alphabet using self-referential common phrases (e.g., "first of all" defines "a"). ==> language/english/malaprop.p <== List some homophonic or near homophonic idioms. ==> language/english/piglatin.p <== What words in pig latin also are words? ==> language/english/pleonasm.p <== What are some redundant terms that occur frequently (like "ABM missile")? ==> language/english/plurals/collision.p <== Two words, spelled and pronounced differently, have plurals spelled the same but pronounced differently. ==> language/english/plurals/doubtful.number.p <== A little word of doubtful number, a foe to rest and peaceful slumber. ==> language/english/plurals/drop.terminal.p <== What words have their plurals formed by dropping the final letter? ==> language/english/plurals/endings.p <== List a plural ending with each letter of the alphabet. ==> language/english/plurals/man.p <== Words ending with "man" make their plurals by adding "s". ==> language/english/plurals/switch.first.p <== What plural is formed by switching the first two letters? ==> language/english/potable.color.p <== Find words that are both beverages and colors. ==> language/english/pronunciation/autonym.p <== What is the longest word whose phonetic and normal spellings are the same? ==> language/english/pronunciation/ghost.p <== What words sound like they contain letters that they do not? ==> language/english/pronunciation/gramogram.p <== "XS" is pronounced like "excess." For each starting letter, what is the longest such sequence? ==> language/english/pronunciation/homograph/different.pronunciation.p <== What sequence of letters has the most different pronunciations? ==> language/english/pronunciation/homograph/homographs.p <== List some homographs (words spelled the same but pronounced differently). ==> language/english/pronunciation/homophone/homophone.longest.p <== What are long homophones (words spelled differently but pronounced alike)? ==> language/english/pronunciation/homophone/homophones.alphabet.p <== Homophones can be confusing when used to exemplify a letter. For example, "g as in gnu" or "k as in knot." Give one for each letter. ==> language/english/pronunciation/homophone/homophones.disjoint.p <== What words sound alike but have no letters in common? ==> language/english/pronunciation/homophone/homophones.letter.p <== For each letter, list homophones that differ by that letter. ==> language/english/pronunciation/homophone/homophones.most.p <== What words have four or more spellings that sound alike? ==> language/english/pronunciation/homophone/trivial.p <== Consider the free non-abelian group on the twenty-six letters of the alphabet with all relations of the form = , where ==> language/english/pronunciation/oronym.p <== List some oronyms (phrases or sentences that can be read in two ways with the same sound). ==> language/english/pronunciation/phonetic.letters.p <== What does "FUNEX" mean? ==> language/english/pronunciation/rhyme.p <== What English words are hard to rhyme? ==> language/english/pronunciation/silent.letter.p <== For each letter, what word contains that letter silent? ==> language/english/pronunciation/silent.most.p <== What word has the most silent letters in a row? ==> language/english/pronunciation/syllable.p <== What words have an exceptional number of letters per syllable? ==> language/english/pronunciation/telegrams.p <== Since telegrams cost by the word, phonetically similar messages can be cheaper. See if you can decipher these extreme cases: ==> language/english/puns.p <== Where can I find a collection of puns? ==> language/english/sentences/behead.p <== Is there a sentence that remains a sentence when all its words are beheaded? ==> language/english/sentences/charades.p <== A ....... surgeon was ....... to operate because he had ....... ==> language/english/sentences/emphasis.p <== List some sentences that change meaning when the emphasis is moved. ==> language/english/sentences/palindromes.p <== What are some long palindromes? ==> language/english/sentences/pangram.p <== A "pangram" is a sentence containing all 26 letters. What is the shortest pangram (measured by number of letters or words)? ==> language/english/sentences/repeated.words.p <== What is a sentence with the same word several times repeated? Do not use quotation marks, proper names, a language other than English, or anything ==> language/english/sentences/self.ref/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. ==> language/english/sentences/self.ref/self.ref.numbers.p <== What true sentence has the form: "There are _ 0's, _ 1's, _ 2's, ..., in this sentence"? The "'s" can be dropped if there is only one of any ==> language/english/sentences/self.ref/self.ref.words.p <== What sentence describes its own word, syllable and letter count? ==> language/english/sentences/sentence.p <== Find a sentence with words beginning with the letters of the alphabet, in order. ==> language/english/sentences/snowball.p <== Construct the longest coherent sentence you can such that the nth word is n letters long. ==> language/english/sentences/weird.p <== Make a sentence containing only words that violate the "i before e" rule. ==> language/english/sentences/word.boundaries.p <== List some sentences that can be radically altered by changing word boundaries and punctuation. ==> language/english/spelling/gry.p <== Find three completely different words ending in "gry." ==> language/english/spelling/j.ending.p <== What words and names end in j? ==> language/english/spelling/lipograms.p <== What books have been written without specific letters, vowels, etc.? ==> language/english/spelling/longest.p <== What is the longest word in the English language? ==> language/english/spelling/most.p <== What word has the most variant spellings? ==> language/english/spelling/near.palindrome.p <== What are some long near palindromes, i.e., words that except for one letter would be palindromes? ==> language/english/spelling/nym.p <== List some words ending in -nym. ==> language/english/spelling/operations.on.words/deletion.p <== What exceptional words turn into other words by deletion of letters? ==> language/english/spelling/operations.on.words/insertion.and.deletion.p <== What exceptional words turn into other words by both insertion and deletion of letters? ==> language/english/spelling/operations.on.words/insertion.p <== What exceptional words turn into other words by insertion of letters? ==> language/english/spelling/operations.on.words/movement.p <== What exceptional words turn into other words by movement of letters? ==> language/english/spelling/operations.on.words/substitution.and.transposition.p <== What exceptional words turn into other words by substitution and transposition of letters? ==> language/english/spelling/operations.on.words/substitution.p <== What exceptional words turn into other words by substitution of letters? ==> language/english/spelling/operations.on.words/transposition.p <== What exceptional words turn into other words by transposition of letters? ==> language/english/spelling/operations.on.words/words.within.words.p <== What exceptional words contain other words? ==> language/english/spelling/rare.trigraphs.p <== What trigraphs (three-letter combinations) occur in only one word? ==> language/english/spelling/sets.of.words/ladder.p <== Find the shortest word ladders stretching between the following pairs: hit - ace ==> language/english/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? ==> language/english/spelling/sets.of.words/perfect.ladder.p <== A "perfect" ladder comprises five-letter words where every letter is the new letter once, no position is changed twice in a row, and fifth ==> language/english/spelling/sets.of.words/squares.p <== What are some exceptional word squares (square crosswords with no blanks)? ==> language/english/spelling/sets.of.words/threepeaters.p <== Form the shortest list of six-letter words in which each word in the list has as its second, fourth, and sixth letters the first, third, and ==> language/english/spelling/sets.of.words/variogram.p <== What is the largest known variogram (word square where repeated letters count as one square)? ==> language/english/spelling/sets.of.words/word.torture.p <== What is the longest word all of whose contiguous subsequences are words? ==> language/english/spelling/single.words.p <== What words have exceptional lengths, patterns, etc.? ==> language/english/spoonerisms.p <== List some exceptional spoonerisms. ==> language/english/synonyms/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 ==> language/english/synonyms/antonym.p <== What words, when a single letter is added, reverse their meanings? ==> language/english/synonyms/contranym.p <== What words are their own antonym? ==> language/english/synonyms/double.synonyms.p <== What words have two different synonymous meanings? ==> language/english/synonyms/pseudantonym.p <== List some (near) synonyms that, in form, appear to be antonyms. ==> language/english/synonyms/transposals.p <== What synonyms are transposals of one another? ==> language/finnish/finnish.record.p <== What are some Finnish words with unusual properties? ==> language/french/french.palindromes.p <== List some French palindromes. ==> language/french/french.record.p <== What are some French words with unusual properties? ==> language/german/german.palindromes.p <== List some German palindromes. ==> language/german/german.record.p <== What are some German words with unusual properties? ==> language/italian/italian.record.p <== What are some Italian words with unusual properties? ==> language/multi.palindromes.p <== List some multi-lingual palindromes. ==> language/norwegian/norwegian.record.p <== What are some Norwegian words with unusual properties? ==> language/repeated.word.p <== In any language, construct a sentence by repeating one word four times. ==> language/swedish/swedish.record.p <== What are some Swedish words with unusual properties? ==> language/synonymous.reversals.p <== What words are synonymous with their reversals in other languages? ==> language/vowels.repeated.p <== In any language, what word contains the same vowel repeated four times in a row? ==> 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 ==> 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. ==> logic/attribute.p <== All the items in the first list share a particular attribute. The second list is of some items lacking the attribute. ==> 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 ==> logic/boxes.p <== 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 "The ==> logic/calibans.will.p <== When Caliban's will was opened it was found to contain the following clause: ==> logic/camel.p <== An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is ==> 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 ==> logic/chain.p <== What is the least number of links you can cut in a chain of 21 links to be able to give someone all possible number of links up to 21? ==> 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 ==> logic/condoms.p <== In each case, show how the parties involved can have mutually safe sex 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 ==> logic/flip.p <== How can a toss be called over the phone (without requiring trust)? ==> logic/flowers.p <== How many flowers do I have if all of them are roses except two, all of them are tulips except two, and all of them are daisies except two? ==> logic/friends.p <== Any group of 6 or more contains either 3 mutual friends or 3 mutual strangers. Prove it. ==> logic/hofstadter.p <== In first-order logic, find a predicate P(x) which means "x is a power of 10." ==> logic/hundred.p <== There is a piece of paper with 100 sentences written on: " 1. At least one sentence on this page is false. ==> 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 ==> logic/lateral.p <== What are some classic lateral thinking puzzles, and where can I find more? ==> 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 ==> logic/min.max.p <== In a rectangular array of people, which will be taller, the tallest of the shortest people in each column, or the shortest of the tallest people in each row? ==> 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 ==> logic/monty.52.p <== Monty and Waldo play a game with N closed boxes. Monty hides a dollar in one box; the others are empty. Monty opens the empty boxes ==> 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 ==> 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. ==> 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 ==> 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 ==> 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.p <== Jed's List of Situation Puzzles ==> 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 ==> 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 ==> 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 ==> 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 ==> 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 ==> logic/smullyan/priest.p <== In a small town there are N married couples in which one of the pair has committed adultery. Each adulterer has succeeded in keeping their ==> 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 ==> logic/supertasks.p <== You have an empty urn, and an infinite number of labeled balls. Each has a number written on it corresponding to when it will go in. At a ==> logic/timezone.p <== Two people are talking long distance on the phone; one is in an East- Coast state of the US, the other is in a West-Coast state of the US. ==> 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. ==> logic/verger.p <== A very bright and sunny Day The Priest did to the Verger say: ==> logic/weighing/balance.p <== You are given 12 identical-looking coins, one of which is counterfeit and weighs slightly more or less (you don't know which) than the ==> 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 an ==> logic/weighing/find.median.p <== What is the least number of pairwise comparisons needed to find the median of 2n+1 distinct real numbers? ==> 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, ==> logic/weighing/optimal.weights.p <== What is the smallest set of weights that allow you to weigh on a balance scale every integer number of kilograms up to some number N? ==> 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, ==> logic/wrong.labels.p <== Three candle boxes are labeled "white", "red", and "white and red." All three labels are incorrect. How many candles do I have to pull out to ==> logic/zoo.p <== I took some nephews and nieces to the Zoo, and we halted at a cage marked ==> 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? ==> physics/brick.p <== What is the maximum overhang you can create with an infinite supply of bricks? ==> physics/bubbles.p <== In a universe with the same physical laws, but which is mostly water with little bubbles in it, do the bubbles attract, repel, or what? ==> physics/cannonball.p <== A person in a boat drops a cannonball overboard; does the water level change? ==> physics/magnets.p <== You have two bars of iron. One is magnetized along its length, the other is not. Without using any other instrument (thread, filings, ==> physics/milk.and.coffee.p <== You are just served a hot cup of coffee and want it to be as hot as possible later. If you like milk in your coffee, should you add 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. What happens if ==> 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% ==> physics/resistors.p <== What is the resistance between various pairs of vertices on a lattice of unit resistors in the shape of a ==> physics/sail.p <== A sailor is in a sailboat on a river. The current is 3 knots with respect to the land. The wind (air velocity) is zero, with respect to the ==> physics/shoot.sun.p <== If you are standing at the equator at sunrise, where must you point a laser cannon to hit the Sun dead center? Assume that the Sun is stationary and ==> 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 each made of uniform material, though of course not the same material. ==> physics/wind.p <== Is a round-trip by airplane longer or shorter if there is wind blowing? ==> pickover/pickover.01.p <== Title: Cliff Puzzle 1: Can you beat the numbers game? From: cliff@watson.ibm.com ==> pickover/pickover.02.p <== Title: Cliff Puzzle 2: Grid of the Gods From: cliff@watson.ibm.com ==> pickover/pickover.03.p <== Title: Cliff Puzzle 3: Too many 3's From: cliff@watson.ibm.com ==> pickover/pickover.04.p <== Title: Cliff Puzzle 4: Time in a Bottle From: cliff@watson.ibm.com ==> pickover/pickover.05.p <== Title: Cliff Puzzle 5: Mystery Sequence From: cliff@watson.ibm.com ==> pickover/pickover.06.p <== Title: Cliff Puzzle 6: Star Chambers From: cliff@watson.ibm.com ==> pickover/pickover.07.p <== Title: Cliff Puzzle 7: 3x3 Recursion From: cliff@watson.ibm.com ==> pickover/pickover.08.p <== Title: Cliff Puzzle 8: Squares and Squares and Squares .... From: cliff@watson.ibm.com ==> pickover/pickover.09.p <== Title: Cliff Puzzle 9: 3-Atoms and Growth From: cliff@watson.ibm.com ==> pickover/pickover.10.p <== Title: Cliff Puzzle 10: The Ark Series From: cliff@watson.ibm.com ==> pickover/pickover.11.p <== Title: Cliff Puzzle 11: The Leviathan Number From: cliff@watson.ibm.com ==> pickover/pickover.12.p <== Title: Cliff Puzzle 12: Slides in Hell From: cliff@watson.ibm.com ==> pickover/pickover.13.p <== Title: Cliff Puzzle 13: Ladders to Heaven From: cliff@watson.ibm.com ==> pickover/pickover.14.p <== Title: Cliff Puzzle 14: Geography Genuflection From: cliff@watson.ibm.com ==> pickover/pickover.15.p <== Title: Cliff Puzzle 15: Cherries in Wine Glasses From: cliff@watson.ibm.com ==> pickover/pickover.16.p <== Title: Cliff Puzzle 16: Undulating Squares From: cliff@watson.ibm.com ==> pickover/pickover.17.p <== Title: Cliff Puzzle 17: Weird Recursive Sequence From: cliff@watson.ibm.com ==> pickover/pickover.18.p <== Title: Cliff Puzzle 18: Difficult Nested Roots From: cliff@watson.ibm.com ==> probability/amoeba.p <== A jar begins with one amoeba. Every minute, every amoeba turns into 0, 1, 2, or 3 amoebae with probability 25% ==> 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 ==> probability/bayes.p <== One urn contains black marbles, and the other contains white or black marbles with even odds. You pick a marble from an urn; it is black; ==> probability/birthday/line.p <== At a movie theater, the manager announces that they will give a free ticket to the first person in line whose birthday is the same as someone who has ==> probability/birthday/same.day.p <== How many people must be at a party before you have even odds or better of two having the same bithday (not necessarily the same year, of course)? ==> 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: ==> probability/coupon.p <== There is a free gift in my breakfast cereal. The manufacturers say that the gift comes in four different colors, and encourage one to collect ==> 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 ==> probability/derangement.p <== 12 men leave their hats with the hat check. If the hats are randomly returned, what is the probability that nobody gets the correct hat? ==> probability/fair.russian.roulette.p <== How can you play Russian Roulette with each person having a 50/50 chance of losing? Assume you only have one bullet and you may not take ==> probability/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 ==> probability/flips/once.in.run.p <== What are the odds that a run of one H or T (i.e., THT or HTH) will occur in n flips of a fair coin? ==> probability/flips/twice.in.run.p <== What is the probability in n flips of a fair coin that there will be two heads in a row? ==> probability/flips/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 ==> probability/flips/waiting.time.p <== Compute the expected waiting time for a sequence of coin flips, or the probabilty that one sequence of coin flips will occur before another. ==> probability/flush.p <== Which set contains proportionately more flushes than the set of all possible poker hands? ==> 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 ==> 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 ==> 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/killers.and.pacifists.p <== You enter a town that has K killers and P pacifists. When a pacifist meets a pacifist, nothing happens. When a pacifist meets a ==> probability/leading.digit.p <== What is the probability that the ratio of two random reals starts with a 1? What about 9? ==> 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 ==> probability/lottery.p <== There are n tickets in the lottery, k winners and m allowing you to pick another ticket. The problem is to determine the probability of ==> probability/martingale.p <== In roulette, if you begin by betting one dollar on red, then double your bet if you lose, and double again if you lose again...but return ==> probability/oldest.girl.p <== You meet a stranger on the street, and ask how many children he has. He truthfully says two. You ask "Is the older one a girl?" He truthfully ==> probability/particle.in.box.p <== A particle is bouncing randomly in a two-dimensional box. How far does it travel between bounces, on average? ==> 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 ==> 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 ==> 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 ==> probability/transitivity.p <== Can you number dice so that on average die A beats die B beats die C beats A? What is the largest probability p with which each event can occur? ==> real-life/icecubes.p <== You have an old-fashioned refrigerator with a small freezer compartment which could hold seven ice cube trays stacked vertically, but there are ==> real-life/lost.nuts.p <== While changing a flat tire, all five of the tire lugs roll into a storm drain, out of reach. How can the car proceed to town to get some new lugs? ==> real-life/microwave.p <== Every morning when I warm my milk for breakfast, I put one cup of milk in the microwave (which is in working order) for exactly 84 seconds. Why? ==> real-life/three.switches.p <== A lightbulb is turned on by one of three switches, but you cannot see the bulb from the switches. How can you determine which switch turns ==> real-life/truck.under.bridge.p <== A truck doesn't quite fit under a bridge and becomes stuck. How can it get out? ==> references/books/bloopers.p <== What are some errors made in puzzle books? ==> references/books/masquerade.p <== What is the solution to _Masquerade_ by Kit Williams? ==> references/books/maze.p <== What is the solution to _Maze_ by Christopher Manson? ==> references/books/treasure.biblio.p <== ==> references/books/treasure.p <== What is the solution to _Treasure_ by Dr. Crypton? ==> references/books/unnamed.p <== What is the solution to the unnamed book by Kit Williams? ==> references/faq.p <== Where should I look if I can't find the answer here? ==> references/magazines.p <== What magazines and journals contain puzzles? ==> references/organizations.p <== What organizations exist for puzzle lovers? ==> references/quotations.p <== Where can I find the source for a quotation? ==> series/series.00.p <== Are "complete this series" problems well defined? ==> 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, ... ==> 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 <== 0 01 01011 0101101011011 0101101011011010110101101101011011 etc. ==> series/series.20.p <== 1 2 5 16 64 312 1812 12288 ==> series/series.21.p <== 5, 6, 5, 6, 5, 5, 7, 6, ? ==> 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 ==> series/series.36.p <== ETIANMSURWDKGO ==> series/series.37.p <== 10^3 10^9 10^27 10^2 0 4 8 3 ==> series/series.38.p <== ?, ?, ?, T, W, H, R, F, U, I, ?, ?, ... ==> series/series.39.p <== M, E, P, B, P, ? ==> 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 ==> trivia/body.parts.p <== Name ten body parts that are spelled with three letters. No slang words. ==> trivia/coincidence.p <== Name some amazing coincidences. ==> 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 ==> trivia/jokes.self-referential.p <== What are some self-referential jokes? ==> trivia/memory.tricks.p <== What's 3 + 7? What's 4 + 6? What's 8 + 2? Name a vegetable. ==> trivia/smiley.p <== What are some ways to make a smliey?