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Frequently Asked Questions (FAQS);faqs.451 ==> games/connect.four.p <== Is there a winning strategy for Connect Four? ==> games/craps.p <== What are the odds in craps? ==> games/crosswords/cryptic/clues.p <== What are some clues (indicators) used in cryptics? ==> games/crosswords/cryptic/double.p <== Each clue has two solutions, one for each diagram; one of the answers to 1ac. determines which solutions are for which diagram. All solutions are in Chamber's and Webster's Third except for one solution ==> games/crosswords/cryptic/intro.p <== What are the rules for cluing cryptic crosswords? ==> games/go-moku.p <== For a game of k in a row on an n x n board, for what values of k and n is there a win? Is (the largest such) k eventually constant or does it increase with n? ==> games/hi-q.p <== What is the quickest solution of the game Hi-Q (also called Solitair)? For those of you who aren't sure what the game looks like: ==> games/jeopardy.p <== What are the highest, lowest, and most different scores contestants can achieve during a single game of Jeopardy? ==> games/knight.tour.p <== For what board sizes is a knight's tour possible? ==> games/nim.p <== Place 10 piles of 10 $1 bills in a row. A valid move is to reduce the last i>0 piles by the same amount j>0 for some i and j; a pile reduced to nothing is considered to have been removed. The loser is the player who picks up the last dollar, and they must forfeit ==> games/othello.p <== How good are computers at Othello? ==> games/risk.p <== What are the odds when tossing dice in Risk? ==> games/rubiks.clock.p <== How do you quickly solve Rubik's clock? ==> games/rubiks.cube.p <== What is known about bounds on solving Rubik's cube? ==> games/rubiks.magic.p <== How do you solve Rubik's Magic? ==> games/scrabble.p <== What are some exceptional scrabble games? ==> games/square-1.p <== Does anyone have any hints on how to solve the Square-1 puzzle? ==> games/think.and.jump.p <== THINK & JUMP: FIRST THINK, THEN JUMP UNTIL YOU ARE LEFT WITH ONE PEG! O - O O - O / \ / \ / \ / \ O---O---O---O---O ==> games/tictactoe.p <== In random tic-tac-toe, what is the probability that the first mover wins? ==> geometry/K3,3.p <== Can three houses be connected to three utilities without the pipes crossing? _______ _______ _______ | oil | |water| | gas | ==> geometry/bear.p <== If a hunter goes out his front door, goes 50 miles south, then goes 50 miles west, shoots a bear, goes 50 miles north and ends up in front of his house. What color was the bear? ==> geometry/bisector.p <== If two angle bisectors of a triangle are equal, then the triangle is isosceles (more specifically, the sides opposite to the two angles being bisected are equal). ==> geometry/calendar.p <== Build a calendar from two sets of cubes. On the first set, spell the months with a letter on each face of three cubes. Use lowercase three-letter abbreviations for the names of all twelve months (e.g., "jan", "feb", "mar"). On the second set, ==> geometry/circles.and.triangles.p <== Find the radius of the inscribed and circumscribed circles for a triangle. ==> geometry/coloring/cheese.cube.p <== A cube of cheese is divided into 27 subcubes. A mouse starts at one corner and eats through every subcube. Can it finish in the middle? ==> geometry/coloring/dominoes.p <== There is a chess board (of course with 64 squares). You are given 21 dominoes of size 3-by-1 (the size of an individual square on a chess board is 1-by-1). Which square on the chess board can you cut out so that the 21 dominoes exactly cover the remaining ==> geometry/construction/4.triangles.6.lines.p <== Can you construct 4 equilateral triangles with 6 toothpicks? ==> geometry/construction/5.lines.with.4.points.p <== Arrange 10 points so that they form 5 rows of 4 each. ==> geometry/construction/square.with.compass.p <== Construct a square with only a compass and a straight edge. ==> geometry/cover.earth.p <== A thin membrane covers the surface of the earth. One square meter is added to the area of this membrane. How much is added to the radius and volume of this membrane? ==> geometry/dissections/circle.p <== Can a circle be cut into similar pieces without point symmetry about the midpoint? Can it be done with a finite number of pieces? ==> geometry/dissections/hexagon.p <== Divide the hexagon into: 1) 3 indentical rhombuses. 2) 6 indentical kites(?). 3) 4 indentical trapezoids. ==> geometry/dissections/square.70.p <== Since 1^2 + 2^2 + 3^2 + ... + 24^2 = 70^2, can a 70x70 sqaure be dissected into 24 squares of size 1x1, 2x2, 3x3, etc.? ==> geometry/dissections/square.five.p <== Can you dissect a square into 5 parts of equal area with just a straight edge? ==> geometry/duck.and.fox.p <== A duck is swimming about in a circular pond. A ravenous fox (who cannot swim) is roaming the edges of the pond, waiting for the duck to come close. The fox can run faster than the duck can swim. In order to escape, the duck must swim to the edge of the pond before flying away. Assume that ==> geometry/earth.band.p <== How much will a band around the equator rise above the surface if it is made one meter longer? ==> geometry/ham.sandwich.p <== Consider a ham sandwich, consisting of two pieces of bread and one of ham. Suppose the sandwich was dropped into a machine and spindled, torn and mutiliated. Is it still possible to divide the ham sandwich with a straight knife cut such that both the ham and the bread are ==> geometry/hike.p <== You are hiking in a half-planar woods, exactly 1 mile from the edge, when you suddenly trip and lose your sense of direction. What's the shortest path that's guaranteed to take you out of the woods? Assume that you can navigate perfectly relative to your current location and ==> geometry/hole.in.sphere.p <== Old Boniface he took his cheer, Then he bored a hole through a solid sphere, Clear through the center, straight and strong, And the hole was just six inches long. ==> geometry/ladders.p <== Two ladders form a rough X in an alley. The ladders are 11 and 13 meters long and they cross 4 meters off the ground. How wide is the alley? ==> geometry/lattice/area.p <== Prove that the area of a triangle formed by three lattice points is integer/2. ==> geometry/lattice/equilateral.p <== Can an equlateral triangle have vertices at integer lattice points? ==> geometry/rotation.p <== What is the smallest rotation that returns an object to its original state? ==> geometry/smuggler.p <== Somewhere on the high sees smuggler S is attempting, without much luck, to outspeed coast guard G, whose boat can go faster than S's. G is one mile east of S when a heavy fog descends. It's so heavy that nobody can see or hear anything further than a few feet. Immediately ==> geometry/table.in.corner.p <== Put a round table into a (perpendicular) corner so that the table top touches both walls and the feet are firmly on the ground. If there is a point on the perimeter of the table, in the quarter circle between the two points of contact, which is 10 cm from one wall and 5 cm from ==> geometry/tesseract.p <== If you suspend a cube by one corner and slice it in half with a horizontal plane through its centre of gravity, the section face is a hexagon. Now suspend a tesseract (a four dimensional hypercube) by one corner and slice it in half with a hyper-horizontal hyperplane through ==> geometry/tetrahedron.p <== Suppose you have a sphere of radius R and you have four planes that are all tangent to the sphere such that they form an arbitrary tetrahedron (it can be irregular). What is the ratio of the surface area of the tetrahedron to its volume? ==> geometry/tiling/rational.sides.p <== A rectangular region R is divided into rectangular areas. Show that if each of the rectangles in the region has at least one side with rational length then the same can be said of R. ==> geometry/tiling/rectangles.with.squares.p <== Given two sorts of squares, (axa) and (bxb), what rectangles can be tiled? ==> geometry/tiling/scaling.p <== A given rectangle can be entirely covered (i.e. concealed) by an appropriate arrangement of 25 disks of unit radius. Can the same rectangle be covered by 100 disks of 1/2 unit radius? ==> geometry/tiling/seven.cubes.p <== Consider 7 cubes of equal size arranged as follows. Place 5 cubes so that they form a Swiss cross or a + (plus). ( 4 cubes on the sides and 1 in the middle). Now place one cube on top of the middle cube and the seventh below the middle cube, to effectively form a 3-dimensional ==> group/group.01.p <== AEFHIKLMNTVWXYZ BCDGJOPQRSU ==> group/group.01a.p <== 147 0235689 ==> group/group.02.p <== ABEHIKMNOPTXZ CDFGJLQRSUVWY ==> group/group.03.p <== BEJQXYZ DFGHLPRU KSTV CO AIW MN ==> group/group.04.p <== BDO P ACGJLMNQRSUVWZ EFTY HIKX ==> group/group.05.p <== CEFGHIJKLMNSTUVWXYZ ADOPQR B ==> group/group.06.p <== BCEGKMQSW DFHIJLNOPRTUVXYZ ==> induction/hanoi.p <== Is there an algorithom for solving the hanoi tower puzzle for any number of towers? Is there an equation for determining the minimum number of moves required to solve it, given a variable number of disks and towers? ==> induction/n-sphere.p <== With what odds do three random points on an n-sphere form an acute triangle? ==> induction/paradox.p <== What simple property holds for the first 10,000 integers, then fails? ==> induction/party.p <== You're at a party. Any two (different) people at the party have exactly one friend in common (the friend is also at the party). Prove that there is at least one person at the party who is a friend of everyone else. Assume that the friendship relation is symmetric and not reflexive. ==> induction/roll.p <== An ordinary die is thrown until the running total of the throws first exceeds 12. What is the most likely final total that will be obtained? ==> induction/takeover.p <== After graduating from college, you have taken an important managing position in the prestigious financial firm of "Mary and Lee". You are responsable for all the decisions concerning take-over bids. Your immediate concern is whether to take over "Financial Data". ==> logic/29.p <== Three people check into a hotel. They pay $30 to the manager and go to their room. The manager finds out that the room rate is $25 and gives $5 to the bellboy to return. On the way to the room the bellboy reasons that $5 would be difficult to share among three people so ==> logic/ages.p <== 1) Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim. 2) Eight years ago, Mary was half as old as Jane will be when Jane is one year ==> logic/bookworm.p <== A bookworm eats from the first page of an encyclopedia to the last page. The bookworm eats in a straight line. The encyclopedia consists of ten 1000-page volumes. Not counting covers, title pages, etc., how many pages does the bookworm eat through? ==> logic/boxes.p <== Which Box Contains the Gold? Two boxes are labeled "A" and "B". A sign on box A says "The sign on box B is true and the gold is in box A". A sign on box B says ==> logic/calibans.will.p <== ---------------------------------------------- | Caliban's Will by M.H. Newman | ---------------------------------------------- ==> logic/camel.p <== An Arab sheikh tells his two sons that are to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days, ask a wiseman for advise. After hearing the advice they jump on the ==> logic/centrifuge.p <== You are a biochemist, working with a 12-slot centrifuge. This is a gadget that has 12 equally spaced slots around a central axis, in which you can place chemical samples you want centrifuged. When the machine is turned on, the samples whirl around the central axis and do their thing. ==> logic/children.p <== A man walks into a bar, orders a drink, and starts chatting with the bartender. After a while, he learns that the bartender has three children. "How old are your children?" he asks. "Well," replies the bartender, "the product of their ages is 72." The man thinks for a ==> logic/condoms.p <== How can you have mutually safe sex with three women with only two condoms? ==> logic/dell.p <== How can I solve logic puzzles (e.g., as published by Dell) automatically? ==> logic/elimination.p <== 97 baseball teams participate in an annual state tournament. The way the champion is chosen for this tournament is by the same old elimination schedule. That is, the 97 teams are to be divided into pairs, and the two teams of each pair play against each other. ==> logic/family.p <== Suppose that it is equally likely for a pregnancy to deliver a baby boy as it is to deliver a baby girl. Suppose that for a large society of people, every family continues to have children until they have a boy, then they stop having children. ==> logic/flip.p <== How can a toss be called over the phone (without requiring trust)? ==> logic/friends.p <== Any group of 6 or more contains either 3 mutual friends or 3 mutual strangers. Prove it. ==> logic/hundred.p <== A sheet of paper has statements numbered from 1 to 100. Statement n says "exactly n of the statements on this sheet are false." Which statements are true and which are false? What if we replace "exactly" by "at least"? ==> logic/inverter.p <== Can a digital logic circuit with two inverters invert N independent inputs? The circuit may contain any number of AND or OR gates. ==> logic/josephine.p <== The recent expedition to the lost city of Atlantis discovered scrolls attributted to the great poet, scholar, philosopher Josephine. They number eight in all, and here is the first. ==> logic/locks.and.boxes.p <== You want to send a valuable object to a friend. You have a box which is more than large enough to contain the object. You have several locks with keys. The box has a locking ring which is more than large enough to have a lock attached. But your friend does not have the key to any ==> logic/mixing.p <== Start with a half cup of tea and a half cup of coffee. Take one tablespoon of the tea and mix it in with the coffee. Take one tablespoon of this mixture and mix it back in with the tea. Which of the two cups contains more of its original contents? ==> logic/number.p <== Mr. S. and Mr. P. are both perfect logicians, being able to correctly deduce any truth from any set of axioms. Two integers (not necessarily unique) are somehow chosen such that each is within some specified range. Mr. S. is given the sum of these two integers; Mr. P. is given the product of these ==> logic/riddle.p <== Who makes it, has no need of it. Who buys it, has no use for it. Who uses it can neither see nor feel it. Tell me what a dozen rubber trees with thirty boughs on each might be? ==> logic/river.crossing.p <== Three humans, one big monkey and two small monkeys are to cross a river: a) Only humans and the big monkey can row the boat. b) At all times, the number of human on either side of the river must be GREATER OR EQUAL to the number of monkeys ==> logic/ropes.p <== Two fifty foot ropes are suspended from a forty foot ceiling, about twenty feet apart. Armed with only a knife, how much of the rope can you steal? ==> logic/same.street.p <== Sally and Sue have a strong desire to date Sam. They all live on the same street yet neither Sally or Sue know where Sam lives. The houses on this street are numbered 1 to 99. ==> logic/self.ref.p <== Find a number ABCDEFGHIJ such that A is the count of how many 0's are in the number, B is the number of 1's, and so on. ==> logic/situation.puzzles.outtakes.p <== The following puzzles have been removed from my situation puzzles list, or never made it onto the list in the first place. There are a wide variety of reasons for the non-inclusion: some I think are obvious, some don't have enough of a story, some involve gimmicks that annoy me, ==> logic/situation.puzzles.p <== Jed's List of Situation Puzzles History: original compilation 11/28/87 ==> logic/smullyan/black.hat.p <== Three logicians, A, B, and C, are wearing hats, which they know are either black or white but not all white. A can see the hats of B and C; B can see the hats of A and C; C is blind. Each is asked in turn if they know the color of their own hat. The answers are: ==> logic/smullyan/fork.three.men.p <== Three men stand at a fork in the road. One fork leads to Someplaceorother; the other fork leads to Nowheresville. One of these people always answers the truth to any yes/no question which is asked of him. The other always lies when asked any yes/no question. The third person randomly lies and ==> logic/smullyan/fork.two.men.p <== Two men stand at a fork in the road. One fork leads to Someplaceorother; the other fork leads to Nowheresville. One of these people always answers the truth to any yes/no question which is asked of him. The other always lies when asked any yes/no question. By asking one yes/no question, can you ==> logic/smullyan/integers.p <== Two logicians place cards on their foreheads so that what is written on the card is visible only to the other logician. Consecutive positive integers have been written on the cards. The following conversation ensues: A: "I don't know my number." ==> logic/smullyan/liars.et.al.p <== Of a group of n men, some always lie, some never lie, and the rest sometimes lie. They each know which is which. You must determine the identity of each man by asking the least number of yes-or-no questions. ==> logic/smullyan/painted.heads.p <== While three logicians were sleeping under a tree, a malicious child painted their heads red. Upon waking, each logician spies the child's handiwork as it applied to the heads of the other two. Naturally they start laughing. Suddenly one falls silent. Why? ==> logic/smullyan/priest.p <== A priest takes confession of all the inhabitants in a small town. He discovers that in N married pairs in the town, one of the pair has committed adultery. Assume that the spouse of each adulterer does not know about the infidelity of his or her spouse, but that, since it is ==> logic/smullyan/stamps.p <== The moderator takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician so that each logician can see all the other stamps except those 2 in the moderator's pocket and the two on her own head. He asks them in turn ==> logic/timezone.p <== Two people are talking long distance on the phone; one is in an East- Coast state, the other is in a West-Coast state. The first asks the other "What time is it?", hears the answer, and says, "That's funny. It's the same time here!" ==> logic/unexpected.p <== Swedish civil defense authorities announced that a civil defense drill would be held one day the following week, but the actual day would be a surprise. However, we can prove by induction that the drill cannot be held. Clearly, they cannot wait until Friday, since everyone will know it will be held that ==> logic/verger.p <== A very bright and sunny Day The Priest didst to the Verger say: "Last Monday met I strangers three None of which were known to Thee. ==> logic/weighing/balance.p <== You are given N balls and a balance scale and told that one ball is slightly heavier or lighter than the other identical ones. The scale lets you put the same number of balls on each side and observe which side (if either) is heavier. ==> logic/weighing/box.p <== You have ten boxes; each contains nine balls. The balls in one box weigh 0.9 kg; the rest weigh 1.0 kg. You have one weighing on a scale to find the box containing the light balls. How do you do it? ==> logic/weighing/gummy.bears.p <== Real gummy drop bears have a mass of 10 grams, while imitation gummy drop bears have a mass of 9 grams. Spike has 7 cartons of gummy drop bears, 4 of which contain real gummy drop bears, the others imitation. Using a scale only once and the minimum number of gummy drop bears, how ==> logic/weighing/weighings.p <== Some of the supervisors of Scandalvania's n mints are producing bogus coins. It would be easy to determine which mints are producing bogus coins but, alas, the only scale in the known world is located in Nastyville, which isn't on very friendly terms with Scandalville. In fact, Nastyville's ==> logic/zoo.p <== I took some nephews and nieces to the Zoo, and we halted at a cage marked Tovus Slithius, male and female. Beregovus Mimsius, male and female. ==> physics/balloon.p <== A helium-filled balloon is tied to the floor of a car that makes a sharp right turn. Does the balloon tilt while the turn is made? If so, which way? The windows are closed so there is no connection with the outside air. ==> physics/bicycle.p <== A boy, a girl and a dog go for a 10 mile walk. The boy and girl can walk 2 mph and the dog can trot at 4 mph. They also have bicycle which only one of them can use at a time. When riding, the boy and girl can travel at 12 mph while the dog can peddle at 16 mph. ==> physics/boy.girl.dog.p <== A boy, a girl and a dog are standing together on a long, straight road. Simulataneously, they all start walking in the same direction: The boy at 4 mph, the girl at 3 mph, and the dog trots back and forth between them at 10 mph. Assume all reversals of direction instantaneous. ==> physics/brick.p <== What is the maximum overhang you can create with an infinite supply of bricks? ==> physics/cannonball.p <== A person in a boat drops a cannonball overboard; does the water level change? ==> physics/dog.p <== A body of soldiers form a 50m-by-50m square ABCD on the parade ground. In a unit of time, they march forward 50m in formation to take up the position DCEF. The army's mascot, a small dog, is standing next to its handler at location A. When the ==> physics/magnets.p <== You have two bars of iron. One is magnetic, the other is not. Without using any other instrument (thread, filings, other magnets, etc.), find out which is which. ==> physics/milk.and.coffee.p <== You are just served a hot cup of coffee and want it to be as hot as possible when you drink it some number of minutes later. Do you add milk when you get the cup or just before you drink it? ==> physics/mirror.p <== Why does a mirror appear to invert the left-right directions, but not up-down? ==> physics/monkey.p <== Hanging over a pulley, there is a rope, with a weight at one end. At the other end hangs a monkey of equal weight. The rope weighs 4 ounces per foot. The combined ages of the monkey and it's mother is 4 years. The weight of the monkey is as many pounds as the mother ==> physics/particle.p <== What is the longest time that a particle can take in travelling between two points if it never increases its acceleration along the way and reaches the second point with speed V? ==> physics/pole.in.barn.p <== Accelerate a pole of length l to a constant speed of 90% of the speed of light (.9c). Move this pole towards an open barn of length .9l (90% the length of the pole). Then, as soon as the pole is fully inside the barn, close the door. What do you see and what actually happens? ==> physics/resistors.p <== What are the resistances between lattices of resistors in the shape of a: 1. Cube ==> physics/sail.p <== A sailor is in a sailboat on a river. The water (current) is flowing downriver at a velocity of 3 knots with respect to the land. The wind (air velocity) is zero, with respect to the land. The sailor wants to proceed downriver as quickly as possible, maximizing his downstream ==> physics/skid.p <== What is the fastest way to make a 90 degree turn on a slippery road? ==> physics/spheres.p <== Two spheres are the same size and weight, but one is hollow. They are made of uniform material, though of course not the same material. Without a minimum of apparatus, how can I tell which is hollow? ==> physics/wind.p <== Is a round-trip by airplane longer or shorter if there is wind blowing? ==> probability/amoeba.p <== A jar begins with one amoeba. Every minute, every amoeba turns into 0, 1, 2, or 3 amoebae with probability 25% for each case ( dies, does nothing, splits into 2, or splits into 3). What is the probability that the amoeba population ==> probability/apriori.p <== An urn contains one hundred white and black balls. You sample one hundred balls with replacement and they are all white. What is the probability that all the balls are white? ==> probability/cab.p <== A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. Here is some data: a) Although the two companies are equal in size, 85% of cab ==> probability/coincidence.p <== Name some amazing coincidences. ==> probability/coupon.p <== There is a free gift in my breakfast cereal. The manufacturers say that the gift comes in four different colours, and encourage one to collect all four (& so eat lots of their cereal). Assuming there is an equal chance of getting any one of the colours, what is the ==> probability/darts.p <== Peter throws two darts at a dartboard, aiming for the center. The second dart lands farther from the center than the first. If Peter now throws another dart at the board, aiming for the center, what is the probability that this third throw is also worse (i.e., farther from ==> probability/flips.p <== Consider a run of coin tosses: HHTHTTHTTTHTTTTHHHTHHHHHTHTTHT Define a success as a run of one H or T (as in THT or HTH). Use two different methods of sampling. The first method would consist of ==> probability/flush.p <== Which set contains more flushes than the set of all possible hands? (1) Hands whose first card is an ace (2) Hands whose first card is the ace of spades (3) Hands with at least one ace ==> probability/hospital.p <== A town has two hospitals, one big and one small. Every day the big hospital delivers 1000 babies and the small hospital delivers 100 babies. There's a 50/50 chance of male or female on each birth. Which hospital has a better chance of having the same number of boys ==> probability/icos.p <== The "house" rolls two 20-sided dice and the "player" rolls one 20-sided die. If the player rolls a number on his die between the two numbers the house rolled, then the player wins. Otherwise, the house wins (including ties). What are the probabilities of the player ==> probability/intervals.p <== Given two random points x and y on the interval 0..1, what is the average size of the smallest of the three resulting intervals? ==> probability/lights.p <== Waldo and Basil are exactly m blocks west and n blocks north from Central Park, and always go with the green light until they run out of options. Assuming that the probability of the light being green is 1/2 in each direction and that if the light is green in one direction it is red in the other, find the ==> probability/lottery.p <== There n tickets in the lottery, k winners and m allowing you to pick another ticket. The problem is to determine the probability of winning the lottery when you start by picking 1 (one) ticket. ==> probability/particle.in.box.p <== A particle is bouncing randomly in a two-dimensional box. How far does it travel between bounces, on avergae? Suppose the particle is initially at some random position in the box and is ==> probability/pi.p <== Are the digits of pi random (i.e., can you make money betting on them)? ==> probability/random.walk.p <== Waldo has lost his car keys! He's not using a very efficient search; in fact, he's doing a random walk. He starts at 0, and moves 1 unit to the left or right, with equal probability. On the next step, he moves 2 units to the left or right, again with equal probability. For ==> probability/reactor.p <== There is a reactor in which a reaction is to take place. This reaction stops if an electron is present in the reactor. The reaction is started with 18 positrons; the idea being that one of these positrons would combine with any incoming electron (thus destroying both). Every second,