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  1. QuantumQuest

    Challenge Math Challenge - February 2019

    Time for our new winter challenge! This time our challenge has also two Computer Science related questions and a separate section with five High School math problems. Enjoy! Rules: a) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be...
  2. fresh_42

    Challenge Math Challenge - January 2019

    Merry Christmas to all who celebrate it today! Rules: a) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. Solutions will be posted around 15th of the following month. b) It is fine to use nontrivial results without proof as long...
  3. fresh_42

    Challenge Intermediate Math Challenge - July 2018

    Summer is coming and brings a new intermediate math challenge! Enjoy! If you find the problems difficult to solve don't be disappointed! Just check our other basic level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no...
  4. fresh_42

    Challenge Basic Math Challenge - July 2018

    Summer is coming and brings a new basic math challenge! Enjoy! For more advanced problems you can check our other intermediate level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. Solutions will...
  5. QuantumQuest

    Challenge Basic Math Challenge - May 2018

    It's time for a basic math challenge! For more advanced problems you can check our other intermediate level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results...
  6. fresh_42

    Revival of the Challenges

    We, a small group of currently four members, want to try a new version of the math-challenges-threads once a month. It turned out to be not as easy as we thought, to find good problems. So what we've gathered are ten questions on "B" level and ten on "I" level for May, and plan to do the same...
  7. Greg Bernhardt

    Challenge Math Challenge by QuantumQuest #4

    Submitted by: @QuantumQuest Challenge Level: High School RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common...
  8. Greg Bernhardt

    Challenge Math Challenge by QuantumQuest #3

    Submitted and judged by: @QuantumQuest Solution credit awarded to: @ddddd28 RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as...
  9. Chestermiller

    Challenge Thermochemistry Challenge Problem - Chet's Paradox

    I have a reversible chemical reaction described by the balanced equation: ##aA+bB=cC+dD##. I devise a reversible process to take a closed system containing these species (and its surroundings) from thermodynamic equilibrium state 1 to thermodynamic equilibrium state 2: State 1: a moles of...
  10. Greg Bernhardt

    Challenge Math Challenge by QuantumQuest #2

    Submitted and judged by: @QuantumQuest Solution credit: @MAGNIBORO RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is...
  11. Greg Bernhardt

    Challenge Physics Challenge by QuantumQuest #1

    Submitted and Judged by @QuantumQuest Solution credited to: @TSny RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is...
  12. Greg Bernhardt

    Challenge Math Challenge by Erland #2

    Submitted and judged by: @Erland Solution Credit: @SSequence for 2a, 2B, C, D RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long...
  13. Greg Bernhardt

    Challenge Math Challenge by Erland #1

    Submitted by @Erland Solution Credit: @mfb RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common knowledge to all...
  14. Alex_C

    I Need Difficult Questions!

    Hey all, I have a unit test tomorrow on Gravitational and Electric Fields. If you have any good practice questions for Grade 12 University level please leave them below! :) In my class we've learned gravitational force, gravitational field strength and orbits (omit geosynchronous) as well as...
  15. micromass

    I Micromass' big October challenge!

    Time for the october challenge! This time a lot of people sent me suggestions for challenges. I wish to thank them a lot! If you think of a good challenge that could be included here, don't hesitate to send me! Ranking [and previous challenges] here...
  16. micromass

    Challenge Micromass' big September challenge!

    September, schools restart, summer ends, but a new challenge is here: Ranking here: https://www.physicsforums.com/threads/micromass-big-challenge-ranking.879070/ RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It...
  17. micromass

    Challenge Micromass' big August challenge!

    August is already well underway, so time for some nice challenges! This thread contains both challenges for high schoolers and college freshmen, and for more advanced people. Also some previously unsolved challenges are omitted. Ranking here...
  18. D

    Designing a 5L Football for the MFL

    Homework Statement You have been employed but(sic) the Mathematics Football League (MFL) to design a football. Using the volume of revolution technique, your football design must have a capacity of 5L ± 100mL. You must present a statement considering the brief below. Just a quick side note, I...
  19. micromass

    Challenge Micromass' big high school challenge thread

    Here is a thread of challenges made especially for high school students and first year university students. All the following problems can be solved with algebra, trigonometry, analytic geometry, precalculus and single-variable calculus. That does not mean that the question are all easy. For...
  20. micromass

    Challenge Micromass' big summer challenge

    Summer, July, hot weather: every reason is good enough for some new challenge questions. NEW: ranking can be found here: https://www.physicsforums.com/threads/micromass-big-challenge-ranking.879070/ For high school and first year university students, there is a special challenge thread for you...
  21. micromass

    Challenge Micromass' math challenges and ranking

    List of challenges: Integral Challenge: https://www.physicsforums.com/threads/micromass-big-integral-challenge.867904/ Counterexample Challenge: https://www.physicsforums.com/threads/micromass-big-counterexample-challenge.869194/ Counterexample Challenge 2...
  22. micromass

    Challenge Micromass' big July Challenge

    In this thread, I present a few challenging problems from all kinds of mathematical disciplines. RULES: In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. It is fine to use nontrivial results without proof as long as you cite...
  23. micromass

    Challenge Micromass' big series challenge

    We had integrals, so we have to have series as well. Here are 10 easy to difficult series and infinite products. Up to you to find out the exact sum. Rules: The answer must be a finite expression. The only expressions allowed are integers written in base 10, the elementary arithmetic...
  24. micromass

    Challenge Micromass' big probability challenge

    Probability theory is very nice. It contains many questions which are very easy to state, but not so easily solved. Let's see if you can solve these questions. For an answer to count, not only the answer must be given but also a detailed explanation. Any use of outside sources is allowed, but...
  25. micromass

    Challenge Aren't you tired of counterexamples already?

    And we continue our parade of counterexamples! Most of them are again in the field of real analysis, but I put some other stuff in there as well. This time the format is a bit different. We present 10 statements that are all of the nature ##P## if and only if ##Q##. As it turns out, only one of...
  26. micromass

    Challenge Yet another counterexample challenge!

    Well, the last thread of counterexamples was pretty fun. So why not do it again! Again, I present you a list with 10 mathematical statements. The only rub now is that only ##9## are false, thus one of the statements is true. Provide a counterexample to the false statements and a proof for the...
  27. micromass

    Challenge Micromass' big counterexample challenge

    I adore counterexamples. They're one of the most beautiful things about math: a clevery found ugly counterexample to a plausible claim. Below I have listed 10 statements about basic analysis which are all false. Your job is to find the correct counterexample. Some are easy, some are not so easy...
  28. micromass

    Challenge Micromass' big integral challenge

    Integrals are pretty interesting, and there are a lot of different methods to solve them. In this thread, I will give as a challenge 10 integrals. Here are the rules: For a solution to count, the answer must not only be correct, but a detailed solution must also be given. A correct answer...
  29. I

    Physics Challenge Question: Stability on a Cylinder

    Homework Statement A solid cube of side ##l = r*pi/2## and of uniform density is placed on the highest point of a cylinder of radius ##r## as shown in the attached figure. If the cylinder is sufficiently rough that no sliding occurs, calculate the full range of the angle through which the block...
  30. K

    Very hard problems about work

    Do you have very hard problems about work? I referred to my algebra book and googled in vain. Not talking about the product of the force magnitude and the displacement magnitude. This is what I’m talking about – Jennifer takes 4 hours to do a job. John takes 6 hours to do the same job. Working...
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