What is Puzzle: Definition and 617 Discussions

A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together in a logical way, in order to arrive at the correct or fun solution of the puzzle. There are different genres of puzzles, such as crossword puzzles, word-search puzzles, number puzzles, relational puzzles, and logic puzzles.
Puzzles are often created to be a form of entertainment but they can also arise from serious mathematical or logical problems. In such cases, their solution may be a significant contribution to mathematical research.

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  1. D

    What is the Cost of a book that costs 1$ plus half of its price?

    I don't know if this already been posted but here it goes: What is the Cost of a book that costs 1$ plus half of its price?
  2. micromass

    What is the Maximum Possible Sum in the Stone Pile Puzzle?

    You have a pile of N stones. You do the following: you take a pile and separate it into two smaller piles, multiply the numbers of stones in these two piles, and write this number on the blackboard. You do that until there is N piles with only one stone in each. Then you take a sum of all...
  3. R

    Solving the Puzzle to Find a GeoCache: Can You Help?

    I'm an avid Geo Cacher (for more info on it visit www.geocaching.com) and I'm trying to solve a problem to find a geo cache. Can anyone help me with it? A Happy Buddha stops to take a rest while ascending an incline. As he rests on the incline, the coefficient of static friction (mu) is...
  4. T

    What is the mathematical approach to solving letter/digit code puzzles?

    Homework Statement I was flicking through the newspaper the other day and noticed there is a type of puzzle where words are added together to form a sum. Each letter represents one of the digits 0-9, for example: FUN +JOKE =HAHA and the aim of the puzzle is to find which...
  5. D

    My Puzzle: Does Light Travel Instantly in a Smaller Scale?

    Hi every one. Im new on this forum,and my question is my reason for joining. iv seeked this question for a long time now,and it confuses me.The answer may be very simple to a peron that already knows the answer,me on the other hand... ! hasnt got a clue...
  6. S

    Shemy's Puzzle: Calculating Yield Stress for a Metal

    Right this is the question, Determine the yield stress for a metal with an average grain diameter of 0.045mm, if the yield stress for a metal changed from 650Nmm^-2 to 720Nmm^-2 when the average grain diameter decreases from 0.054mm to 0.037mm. I cannot figure this out, I've been trying...
  7. snoopies622

    How Does Reference Frame Affect Kinetic Energy Calculations?

    I just thought of this. I think I know the answer to it now, but it took me a little bit of thinking. Maybe someone who teaches high school physics might find it useful. - - - - - I have a battery-powered toy car. I turn it on and it accelerates from speed 0 to speed 1. (I'm leaving...
  8. R

    Game Theory a problem which is a bit similar to the Impossible Puzzle

    Game Theory a problem which is a bit similar to the "Impossible Puzzle" From numbers 1 to 10, two integers X, and Y (not necessarily distinct) are chosen by a referee . The referee informs secretly to Joe the integer U where U = X + Y . The referee informs secretly to Bob the integer V where V...
  9. micromass

    A very complicated puzzle: the planet of lies

    I found this puzzle in some other forums. I found it to be very difficult. Maybe somebody would like to that a crack at it :smile: Anyway, here it is: The human race spread out to the stars, eventually terraforming and colonizing thousands of planets. On one planet, P3, they decided to...
  10. Mueiz

    Space-Time Puzzle: Why Objects Can't Be in Two Places at Once

    Why is it possible that an object can be found in the same place in different times but can not be found at the same time in different places?
  11. T

    How Many Unique Paths Through a 3x3x3 Cube Visiting All Vertices Once?

    ok, so here's the problem: given a 3 x 3 x 3 cubic system of vertices, a starting vertex, and an end vertex, how many paths that pass through all vertices ONLY ONCE and start and end at the given vertices(for example let's say the starting and end vertices are two opposite corner vertices) can...
  12. C

    Unsolvable Puzzle: Can a Puck Stop in 0.42s?

    Homework Statement A puck of mass 30g slides across rough ice, experiencing a frictional force of 0.2N. If it was moving at 10km/h when it hit the ice patch, how long did it take to stop? How long was the ice patch? Homework Equations The Attempt at a Solution I don't think this question is...
  13. M

    How are force and pressure related in a hydraulic system?

    What's going to happen?
  14. B

    How many statements are true on a sheet of paper with 100 written down?

    on a sheet of paper, you have 100 statements written down. the first says, "at most 0 of these 100 statements are true." the second says, "at most 1 of these 100 statements are true." ... the nth says, "at most (n-1) of these 100 statements are true. ... the 100th says, "at most 99 of these...
  15. F

    Cool Skyscrapers Puzzle - Cut-the-Knot

    http://www.cut-the-knot.org/Curriculum/Games/Skyscrapers.shtml I wonder of they could make it more like sudoku where there's a 9x9 latin square made out of 3x3 subsquares where only certain numbers of skyscrapers are visible in each rown & column of each subsquare. & beware the creepy eyes...
  16. T

    Solving the 65050-Digit Prime Puzzle

    Homework Statement Largest known prime is the no... P = 2216091-1 consisting of 65050 digits. Show that there exists another prime that ends in the same 65050 digits as P.Homework Equations none The Attempt at a Solution Sorry, but I have totally no ideas for this one. Comes from a Math...
  17. S

    New Dark Matter Map Solving Galactic Puzzle?

    http://blogs.nationalgeographic.com/blogs/news/breakingorbit/2010/11/new-dark-matter-map-hubble.html?source=link_tw20101112hubble" i found this article interesting , so shared here
  18. L

    Solve N Factorial Puzzle with 50 Zeros

    Homework Statement N is divisible by 4. N! has exactly 50 zeros. Find N. Homework Equations In case anyone younger doesn't know, Y!=Yx(Y-1)x(Y-2)x(Y-3)x...x3x2x1 The Attempt at a Solution No idea.
  19. AlexChandler

    Solve the Math Puzzle: A + B = 2 and |A+B| = √(2)

    Here's a little puzzle that I thought of earlier. I gave it to my roommate and he wasn't able to solve it without a pretty good hint, but I'm sure somebody here will get it. |A|+|B| = 2 |A+B| = √(2) What are A and B? (The bars are absolute value signs, and the " √(2) " is the square...
  20. K

    Lifting an Elephant with Hydraulics: A Physics Puzzle

    Homework Statement The 70kg student in the figure balances a 1200kg elephant on a hydraulic lift. A second 70kg student joins the first student. How high do they lift the elephant? diameter of the piston elephant is on = 2.0m diameter of the piston student is on = 0.48m The liquid inside...
  21. Nabeshin

    Exploring the Puzzle of Black Hole Temperature and Event Horizons

    We know the temperature of a BH is related to the area of it's event horizon. So we can imagine if we are in a very cold universe with a very nice detector measuring the temperature of a black hole and being able to infer it's radius. Great. Now, I want to explain the difference between...
  22. T

    Prisoner and Hats puzzle (variation)

    Here is a brain teaser I came across recently. Ten prisoners are arranged single file in a line. They are sorted so that the shortest prisoner (prisoner #1) is in the front, and the tallest prisoner (prisoner #10) is in the back. The are all looking forward (in the direction of #1). They...
  23. W

    Cake Division Puzzle: Max Amount for 1st Person

    Homework Statement Suppose that two people are dividing two cakes using the following rules: 1. The first person divides the first cake into two pieces in any fashion. 2. The second person then chooses which of the two cakes they will get to choose the first piece from. 3. The first person...
  24. N

    Maximizing Determinant in 3x3 Matrix with 0/1 Entries

    I was wondering what would be the largest possible value for a determinant, for a 3 by 3 matrix whose entries can only be 0 or 1. My solution is the following: 1 0 1 1 1 0 0 1 1 With a determinant of 2. Can anyone go any higher, or better yet is there an algebraic algorithm to...
  25. D

    What is the Value of the Pocket Knife?

    Homework Statement Two farmers have no more than 15 cows. They get as many dollars for each cow as they have cows. For example, if they have 3 cows then they get 3 dollars per cow so a total of 9 dollars. After taking this money they bought as many sheep as possible at $10 a sheep. The...
  26. S

    Force, Mass, & Acceleration: Solving the Puzzle

    1. A force acts on a 2 kg mass and gives it an acceleration of 3 m/s^2. What acceleration is produced by the same force when acting on a mass of (a) 1 kg? (b) 4 kg? (c) How large is the force? Answers: (a) 6 m/s^2 (b) 1.5 m/s^2 (c) 6 N 2. - 3. I can't figure out what formula to...
  27. T

    Force Exerted by Shot-Putter: Solving the Puzzle

    1. What is the average force exerted by a shot-putter on a 7.0 kilogram shot if the shot is moved through a distance of 2.8 meters and is released with a speed of 13 m/s? 2. F=ma, x = vo t + 1/2 at^2, v=vo at 3. I think you get time by using D = vt, but when I use this time and...
  28. C

    Two Thermally Insulated Tanks: Solving the Puzzle

    The drawing shows two thermally insulated tanks. drawing: http://www.webassign.net/CJ/14_26.gif They are connected by a valve that is initially closed. Each tank contains neon gas at the pressure, temperature, and volume indicated in the drawing. When the valve is opened, the contents of the...
  29. F

    Where Does the Missing Energy Go in a Capacitor Circuit?

    I got this from Brainteaser Physics. [PLAIN]http://img820.imageshack.us/img820/4614/lostenergy.jpg
  30. R

    Roll 6 Dice: Solve Probability Puzzle!

    On average, how many times do you need to roll six dice together to see all six different numbers turn up within a single such group roll?
  31. P

    Unraveling Ince's Wronskian Puzzle: Linear Dependence of Minors

    I'm reading Ince on ODEs, and I'm in the section (in Chapter 5) where he talks about the Wronskian. There are quite a few things here that I don't quite understand or follow. I'm not going to get into all the details, but briefly, suppose we have the Wronskian of k functions: W =...
  32. A

    A learn's puzzle on transformation equation

    Hi, I'm a new learner of CM and I was stuck at the very beginning. TT The transformation equation is ri=ri(q1,q2,...,qn,t) I wonder why t should be in the bracket. Aren't r determined by these independent coordinates？ Isn't t already contained in them?
  33. K

    Pipe C - More Water Pressure: Solve Puzzle

    Look at the attached 2 pictures. Tell me in which structure Pipe C will have more water pressure and I can get more water from pipe C. Some info :– Pipe A – Bigger in size, Pipe B – 1” pipe (1 inch), Pipe B – 3/4” pipe (3/4 inch)
  34. M

    Statistics: SSE, MSE, R^2, and C-statistic | Fill in the blank puzzle

    Hello, I'm studying for a final exam and I'm having trouble with this particular question. I attached the data required to solve the problem. I am required to fill in the missing information in the data. I've defined the acronyms below: SSE = Sum of Square Errors MSE = Mean Square of...
  35. 1

    Solving the Puzzle: 2 tan2A+sin2A-1

    Homework Statement If A is an acute angle and sinA = cosA Find the value of 2 tan2 A+ sin2 A-1 Homework Equations The Attempt at a Solution I well tried this way >> 2 (sin 2 A/cos 2A) +sin 2 A-1 = 1+ cos 2 A But I am unable to get the 'value' the answer given in the book...
  36. B

    Solving the Friction Force Puzzle: Range of Acceleration for Slab

    I just realized I don't even have to do this problem, but I've thought too much about it, and at times like this I tend to be a bit OCD. If someone could just get me started on the right track of thought that would be great! Q: In figure...
  37. T

    Solve Ali's Solid Volume Puzzle: 9 Faces, 27 cm^3 Cubes

    Homework Statement Ali is making solids out of cubes . Each cube has a volume of 27 cm^3. The diagram shows one solid Ali made . It has 10 faces and a volume of 108 cm^3. Ali made a solid out of the cubes that has 9 faces.What is the smallest volume in cm^3 the solid could have? Homework...
  38. U

    Solving the Spring Launcher Puzzle: Making it Work at Different Heights

    I have designed a spring launcher for my class and it works really well using the range equation...x=sqrt(Rmg/KSin2(Theta)). So I have made a contraption that displaces the spring by x metres. I even have re-arranged and have it working using angles of launch and determining the range (R)...
  39. E

    Max Nozzle Size to Reach 35m: Solving the Fire-Hose Puzzle

    Homework Statement A fire-hose must be able to shoot water to the top of a building 35.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m³.s¯¹ and shoots out of a round nozzle. (a) What is the maximum diameter that this nozzle can have? (b) If the only...
  40. K

    Product equality and sum of squares equality puzzle

    Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero. ABCD*EF=GHJB*KE, and: (EH)2 + (KC)2 = (KH)2
  41. S

    Explain Paradox of Light Moving at c in All Frames

    My friend is moving in my inertial frame and receives light in the two directions parallel to her movement: from behind and from ahead. The photons that reach her travel at c in my frame, so I presume they will approach my friend at different speeds (as I view it): faster from ahead and slower...
  42. S

    Solving the "Black Box" Puzzle with Math Lovers

    Hello, my name is Eugene, i am glad i found a forum for people who love math. I was reading a book on mathematical puzzles recently, and there was one which i couldn't solve, mostly because i am not a very clever guy. Perhaps you will have some ideas? The area of the puzzle is non...
  43. K

    Two successive digits and divisibility puzzle

    Determine all possible value(s) of a 8-digit base 10 positive integer having the form ABCDEFGH, where each of the capital letters denotes a different digit from 1 to 9, that satisfy each of the following conditions: (I) AB is divisible by 2, and: (II) BC is divisible by 6, and: (III) CD...
  44. N

    Solving the Curved Space Puzzle: e or c?

    If you think of a bow (as in bow and arrow) placed in space in the proximity of a massive object. This bow for arguments sake is 100 km from tip to tip. Now replace the bow (wooden part and string) with what might be considered waypoints. The curved wooden part represents a straight line in...
  45. A

    Smallest Area Poster Dimensions: Solve the Puzzle!

    the top and bottom margins of a poster are 2cm and the side margins are each 4cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area. so the area l*w = 382 and the perimiter = 2(l-4)+2(w-8) but if i...
  46. S

    What Causes the Rapid Changes in Sea Level?

    There is in the past significant very rapid rises and falls of sea level. As there is no mechanism to rapidly melt and reform ice sheets to explain the sea level rise and fall based on mass balance (more or less water in the ocean) specifically what is causing the rapid changes in sea level is...
  47. N

    Solving the Summation Puzzle: Analyzing Convergence and Calculating the Sum

    \sum^k_{n=1}e^{-n\sum^k_{n=2}...e^{-n\sum^k_{n=k-1}e^{-n}}} Can anyone help me find out if this converges and if so how to calculate the sum? I don't have an idea on how to even start. This is not homework
  48. M

    Solving the F16 Jet Fighter Turning Circle Puzzle

    Question 1. Homework Statement The question shows a circle labeled as follows -A at the uppermost point -B at the most-right point -C at the lowest point -D at the most-left point so, the length along the circle from A to B (and B to C, C to D, D to A) is one quarter of the...
  49. G

    Revisiting the Value of (2+5)2: 9 or 49?

    Is the value of this expression 49? The andwers in my book say that it should be 9! (2 + 5)2
  50. S

    Einstein Puzzle: Can You Solve It & What's Your IQ?

    Hola..Pardon my intrusion for this question! I m 18..I heard about einstein puzzle nd solved it correctly in like 40 -45 minutes..Then after i googled about it,i read that it is beleived that only 2%people in world can solve it..I was a little happy..lol..Anyways..I want to ask what should be my...
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