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. T

    Solving the Physics Puzzle: Cycling and Driving Velocities

    Hello everyone, I am new to this forum and very much interested in physics. As a student, I find motion is my weakness in this subject. Hopefully everyone can help me out :) Homework Statement While driving North at a velocity of 28ms^-1 relative to the ground, a man notices a cyclist...
  2. K

    Product Equality and Linear Expression 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. (ABC)*(DE)=(BCD)*(BF), and: FA+DF- CE=1
  3. K

    Sum, difference and 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. GEORGE + RUGGLE + 15750 + 16220 + P = PPPPPP, and: OE - LR = LO, and: RUGGLE is divisible by 7
  4. A

    Calculating the Probability of Finding a Word in a Word Search Puzzle

    Howdy, I'm completely not sure how to go about this problem. I feel like there is more than one way to approach this problem. I just know words can go forwards, backwards, and diagonal and just get stuck there. So here it is: What is the probability that a letter in a given position...
  5. CalleighMay

    GCD in PROOF - Solving the Puzzle

    GCD in PROOF?? Hey everyone, I'm taking this course called "Number Theory" and am having a lot of difficulty with it. We're currently on "proofs" and i am having some issues. Last week was my first weeks classes. The first day my professor jumped right into the material without giving...
  6. K

    TV series and competition puzzle

    In this season's "Dancing with the Celebs" TV series, Harry and nine other famous personalities paired with professional dancers to try to claim this year's title. Each week, one of the celebrities--who are in different entertainment and media fields, with one a stand-up comic--is sent home...
  7. K

    Three Passengers and Train Station Puzzle

    Brian, Amy and Stephanie are waiting at the train station. Each of the three is waiting for a different train. When they check the station clock, they realize that Amy is going to have to wait twice as long for her train as Brian will for his, while Stephanie will have to wait twice as long...
  8. K

    Product equality and difference puzzle

    Substitute each of the capital letters by a base ten digit from 0 to 9 to satisfy this set of cryptarithmetic equations. None of the numbers can contain any leading zero. ABC*D=C*BCD, and: BC-CA-AD= 5
  9. K

    What is the sum of digits in the numbers 1 to 2010?

    Determine the sum of all the digits in the positive integers from 1 to 2010 inclusively.
  10. K

    Knight and knaves and distant planet puzzle

    A distant planet is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. Eight inhabitants of the planet: Marge, Mel, Betty, Bob, Bill, Carl, Zeke and Alice are busy at a conversation, when a visitor from a neighboring planet stops by and asks each of...
  11. K

    Infinite String and Letter Puzzle

    The string abbcccddddeeeee… continuously repeats such that after the final z, the letters abbcccddddeeeee… begin again. What will be the 3000th letter in the pattern?
  12. K

    Where is the arsenic in the Six Jars Puzzle?

    Six jars are placed (left to right: coffee, arsenic, and sugar on the top shelf; snuff, tea, and salt on the bottom shelf) and, thereafter filled up with these ingredients, making sure each jar contains something other than what the label says. It is known that: (i) The salt is located...
  13. K

    Sum of Four Squares and Digits Puzzle

    Substitute each of the small letters by a different base ten digit from 1 to 9, with a<= b<=c<=d, to satisfy this equation. a2 + b2 + c2 + d2 = e2
  14. K

    Four contestants and three statements puzzle

    Four contestants E, F, G, and H ran for a contest. When asked by a common acquaintance, three spectators A, B, C made the following statements regarding the final results. 1. A said, "Either E or H is the winner." 2. B said, "E is not the winner." 3. C said, "Neither H nor G is the...
  15. K

    Line and Letter Placement Puzzle

    Does the letter R go above or below the line? A B D O P Q __________________ C E F G H I J K L M N
  16. K

    Square Grid and Letter Assignment Puzzle

    Place the letters A, B, C, D, E, F, G, H and I into a 3x3 square grid with each square containing a different letter, using the following information: (i) I is in the same column as E which is not in the center column. (ii) D is in the row below the row which contains F. (iii) A is in...
  17. J

    Solving the Puzzle: Forces & Acceleration

    I had just asked a question about boats going across a river but that question and this question really have me stumped. Homework Statement http://img138.imageshack.us/img138/7910/68512243.png A)Find the acceleration using Newtons laws B)Find the velocity using Conservation of Total...
  18. L

    Why is diffraction most pronounced for objects on the order of the wavelength?

    Hello! Recently, I'm always thinking about why diffraction effects are generally most pronounced for the size of the diffracting objectsis that is on the order of the wavelength. How about a relatively bigger object? I try to find it everywhere I can but failed. So anyone can help? Thanks!
  19. A

    Solving the 9-Piece Animal Puzzle

    Hello all, Recently while on a 'schoolies' vacation a few friends presented a puzzle of 9 squares pieces that can be arranged into a larger 3x3 square. Each small piece had half an animal on each edge (either the head or tail, of say, a goat for a seahorse). The aim was to rotate each piece...
  20. K

    Bus ticket and sum of digits puzzle

    Yesterday Professor Q rode on a bus with his friend. As soon as he got the tickets for himself and his friend, which were consecutively numbered with each of the tickets bearing a 5-digit number with no leading zero, he added the digits on them and told his friend that the sum of all ten digits...
  21. K

    Solving Don's Birthday Gift Puzzle

    Albert, Bob and Cal each gave a birthday gift to their friend Don, who was so impressed by the presents, that he exclaimed: "Good thing your parents gave you credit cards!" Bob explained that those cards had already been confiscated by the parents of each, and that they had to spend cold...
  22. K

    Two friends and age puzzle

    Two friends Andy and Cal form a team together. Andy is as old as Cal will be when Andy is twice as old as Cal was when Andy was half as old as the sum of their current ages. Cal is as old as Andy was when Cal was half as old as he will become in ten years. Determine the respective current...
  23. Y

    (A puzzle) The largest size cliques in n-grouping graphs

    (I apologize in advance for the abuse of the word "group" in this problem. It does not mean a group in the mathematical sense). Imagine you have n^2 objects that need to be grouped in n groups of size n each. Let's call one such arrangement an "n-grouping." You can create n-groupings in...
  24. K

    Analog Clock and Minute Marks Puzzle

    The minute hand of a 12 hour analog clock is situated precisely on a minute mark, while the hour hand is situated exactly 2 minute marks behind the minute hand. What time is it? Note: For purposes of the problem, each hour mark is deemed as a valid minute mark.
  25. K

    Even Perfect and Prime Puzzle

    Determine all possible even perfect number(s) C such that each of C-1 and C+1 is a prime number.
  26. Helios

    Number Puzzle: Solve 34 in 11 Lines Using 1-17

    Using the numbers 1 - 17, place the numbers in the circles so that the sum of the numbers on every line equals 34. There are 11 lines. I have one solution. I think this is a very challenging puzzle that few can solve.
  27. S

    Solving a Math Puzzle: What Went Wrong?

    Homework Statement http://img121.imageshack.us/img121/8907/graphr.jpg Homework Equations The Attempt at a Solution i can't believe i got this wrong.. i even checked the textbook for that and still got it wrong :/ B,C,D,E are 100% correct. the other 2 i logically matched them...
  28. T

    Solve Math Puzzle: Proving Nonemptiness of Intersection

    Here's a math problem that's giving me a head ache (though to some of you it might seem to be quite trivial) r,s\in N^\ast , r+1\leq s ; |A_i|=r, \forall i\in \{1,2,...,s\} the intersection of any r+1 of sets A_i is nonempty [1] prove that \bigcap_{i=1,s} A_i \neq \emptyset [C]...
  29. C

    Physics Puzzle: Magnetic Field Generated by Approximation of a Flower

    Here's an attachment. A poor artist might approximate a flower as a series of straight lines and arcs such as that shown below. We could caracterize the flower by specifying the inner and outer radii, and the inner and outer angles (shown). If a current I flows around along the lines and...
  30. J

    A Tough Logical Puzzle- Requires Utilization of Mathematical Algorithms

    A 6x6 grid features two different types of pieces: x's and o's. You are given three separate views of the same grid in a step by step progression. The number of pieces gradually decreases with each step and also change in location. This is the layout of the grid progression...
  31. I

    Solving the Puzzle: Ball Thrown Upward

    Homework Statement A ball is thrown straight up with an initial speed of 40 m/s. (Neglect air resistance.) How high does it go? how long does it stay i the air Homework Equations i know the second part is 8 because its basically saying 40m every second divide by acc.(gravity)...
  32. B

    Time for Car 1 and Car 2 Collision: Solving the Puzzle

    Homework Statement I am trying to find the time a collision occurs of car 1 that is traveling 31m/s and can accelerate at -1.8m/s and car 2 that is traveling at a constant velocity of 6m/s. Homework Equations v(final)^2=v(initial)+ 2a(x(final) - x(initial)) v(final) = v(initial) + at...
  33. G

    Hexagon Book puzzle that doesnt work

    Hi guys, I was given a puzzle book resently (Brain Training Puzzles; Difficult Book 1; Carlton) and rather excited cause I really want to get into logic/maths puzzles. So I have only got a few pages in and saw two grid of hexagons either blue or red and the questions goes: "The colour of each...
  34. J

    Determine if a Sudoku puzzle is easy, medium, hard, or evil

    I can't find a solution to these questions. Can someone help? 1. An algorithm to determine if a Sudoku puzzle is easy, medium, hard, or evil. 2. For every valid Sudoku puzzle, there exist at least one valid solution. True or false? Proof?
  35. B

    Math puzzle involving the game Connect 4

    I was playing Connect 4 the other day, and I started to wonder how you could fill the board entirely without connecting 4. I haven't tackled the problem so I don't know if it's of general interest at all, or if it yields any interesting results...but I thought I'd share it with you all...
  36. K

    Power and value assignment puzzle

    Substitute each capital letter in bold by a different digit from 0 to 9, such that (TAU).BETA when rounded off to the nearest integer is equal to PI, and the absolute difference of (TAU).BETA and PI is the minimum. Each of T, B and P is nonzero.
  37. N

    Java Manipulating a String: Solving the 6G2N42B Puzzle

    Hi guys, I was wondering if anyone could explain to me/point me in the right direction on how to manipulate a String read in from the user in a particular way. I'm trying to read in a String, and then I want to sort of split the string up into ints and chars and associate them to variables...
  38. K

    Row total and column total puzzle

    Arrange the nine cells of a 3x3 square with digits from 1 to 9, with each digit occurring exactly once, such that: ## The respective totals of the first column, second column and the third column are 15, 19 and 11, and: ## The respective totals of the first row, second row and the...
  39. K

    Solve the Repaid-Diaper-RA-RE Puzzle

    Substitute each of the letters by a different digit from 0 to 9 to satisfy this equation. None of the four numbers can contain any leading zero. (REPAID)/(DIAPER) = (RA)/(RE) Note: Each of the four numbers represent the concatenation of the digits, and does not denote the product of the...
  40. K

    3x3 square and common sum puzzle

    Substitute each of the capital letters by a different digit from 0 to 9, such that each of the columns, each of the rows and each of the two main diagonals of this 3x3 square have the common sum LRK. It is known that L is nonzero and, each of the numbers in the nine cells contains non leading...
  41. K

    Squares, subsquares and arrangement puzzle

    Substitute each of the capital letters in this 3x3 square by a different digit from 1 to 9 such that the sum of digits in each of the four 2x2 subsquares is equal to 6*E. A B C D E F G H I What will be the arrangement(s), if keeping all the other conditions unaltered, the...
  42. K

    MEER, EMMA, EMIR, RARE Puzzle Value

    Determine the value of each of the four perfect squares MEER, EMMA, EMIR and RARE, where each of the capital letters denotes a different digit from 0 to 9. None of the four numbers contains any leading zero.
  43. K

    Twelve Sum and Digit Substitution Puzzle

    Substitute each of the capital letters in the figure given below by a different digit from 0 to 7 such that: A+B+C = A+D+F = C+E+H = F+G+H = 12. A B C D E F G H Note: The rotations and reflections of a valid arrangement are deemed as the same solution.
  44. K

    Hundred Sum and Prime Puzzle

    Substitute each of the capital letters by a different digit from 1 to 9 to satisfy this cryptarithmetic equation: (P*Q)/R + (S*T*U)/V + W*X = 100, where the 2-digit number WR is prime.
  45. K

    Train station, speed and time puzzle

    George took a train at station X with the intention of going to Station Y (which is located 8 kilometers from station X). At the precise instant that the train started leaving station X, the minute hand of his 12 hour analog wristwatch was located precisely on a minute mark. George looked at...
  46. Y

    Explaining a Bath Time Reflection Puzzle

    This is a picture of me in my bath. (dont worry, it is purely diagramatic!). I face a wall to the front of the bath. There is also a wall to the left hand side of me. Both with shiny tiles. Their is a light above me and slightly behind to my right. While relaxing, I took note of the light bulb...
  47. P

    Shifting Centre of Mass Puzzle?

    Homework Statement A child crouches on a swing. She is held AT REST, at 30 degrees to the vertical. The distance from her centre of mass (CM) while crouching to the suspension point is 3 m. The swing is released. When she reaches the lowest point, she SUDDENLY stands up. Her CM is now 2.6m...
  48. W

    My twin galaxy puzzle Please help

    Help on my thought experiment. We know the further galaxy, the faster it runs apart from us. Let's say there is a galaxy (assuming the laws of physics are the same there) running away from us at 99% of the speed of light. Let's say at the SAME time, the people in that galaxy doing the same...
  49. Chewy0087

    Solving the Liquid Density Puzzle

    [Solved] Liquid Density Puzzle Homework Statement The Attempt at a Solution I think there's an assumption here that I'm missing, firstly I worked out how big each cube was by setting up simple simultaneous equations which gave me; Green = 0.21m Red = 0.14m & Blue = 0.28m And...
  50. N

    Help Solve Unique Digit Puzzle - Thank You!

    Hi guys, Can you help me with this problem, please? :confused: ...H ...______ EJS)HWNR ...CFJL ...______ ...CHW where each letter is unique digit from 0 to 9 thank you!
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