What is Challenge: Definition and 942 Discussions

The Challenge (originally known as Road Rules: All Stars, followed by Real World/Road Rules Challenge and occasionally known as The Real World/Road Rules Challenge during this time), is a reality competition show on MTV that is spun off from two of the network's reality shows, The Real World and Road Rules. Originally featuring alumni from these two shows, casting for The Challenge has slowly expanded to include contestants who debuted on The Challenge itself, alumni from other MTV franchises including Are You the One?, Ex on the Beach (Brazil, UK and US), Geordie Shore and from other non-MTV shows. The contestants compete against one another in various extreme challenges to avoid elimination. The winners of the final challenge win the competition and share a large cash prize. The Challenge is currently hosted by T. J. Lavin.
The series premiered on June 1, 1998. The show was originally titled Road Rules: All Stars (in which notable Real World alumni participated in a Road Rules style road-trip). It was renamed Real World/Road Rules Challenge for the 2nd season, then later abridged to simply The Challenge by the show's 19th season.
Since the fourth season, each season has supplied the show with a unique subtitle, such as Rivals. Each season consists of a format and theme whereby the subtitle is derived. The show's most recent season, Double Agents, premiered on December 9, 2020. A new special limited-series, titled The Challenge: All Stars premiered on April 1, 2021 on the Paramount+ streaming service.

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  1. 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...
  2. lfdahl

    MHB Inequality Challenge: Prove 3x2y2+x2z2+y2z2 ≤ 3

    Prove, that \[3(x^2y^2+x^2z^2+y^2z^2)-2xyz(x+y+z) \leq 3,\: \: \: \forall x,y,z \in \left [ 0;1 \right ]\]
  3. lfdahl

    MHB Can You Solve This Definite Integral Challenge with Binomial Expansion?

    Derive an expression for the definite integral:\[I = \int_{0}^{\frac{\pi}{4}}sec^m(x)dx, \;\;\;\;m = 2,4,6,...\]
  4. 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...
  5. anemone

    MHB Can You Find the Relationship Between a and b in This Algebra Problem?

    Given that a,\,b\in\Bbb{N} such that \sqrt{a^2+2b+1}+\sqrt[3]{b^3+3a^2+3a+1} is a rational number. Find the relationship between $a$ and $b$.
  6. davenn

    Math Facebook Challenge: Multiply or End-to-End?

    hi gang this came up in one of those crazy facebook challenges and you can imagine the arguments that ensued My maths knowledge isn't brilliant ... so in the above, if there are no brackets, do you still do the multiplication first or do you just work your way through from end to end ? I...
  7. Albert1

    MHB Prove Inequality Challenge: $x,y,z,w > 0$

    $x,y,z,w>0$ prove: $(1+x)(1+y)(1+z)(1+w)\geq (\sqrt[3]{1+xyz}\,\,\,)(\sqrt[3]{1+yzw}\,\,\,)(\sqrt[3]{1+zwx}\,\,\,)(\sqrt[3]{1+wxy}\,\,\,)$
  8. anemone

    MHB Olympiad Inequality Challenge

    Let $a,\,b$ and $c$ be non-negative real numbers such that $a+b+c=1$. Prove that \sum_{cyclic}\sqrt{4a+1} \ge \sqrt{5}+2.
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. anemone

    MHB Can You Solve the Olympiad Inequality Challenge with Positive Real Numbers?

    Given that $a,\,b$ and $c$ are positive real numbers. Prove that \frac{a^3+b^3+c^3}{3abc}+\frac{8abc}{(a+b)(b+c)(c+a)}\ge 2.
  14. anemone

    MHB Prove Inequality: $x^2y\,+\,y^2z\,+\,z^2x \ge 2(x\,+\,y\,+\,z) - 3$

    Given that $x,\,y$ and $z$ are positive real numbers such that $xy + yz + zx = 3xyz.$ Prove that $x^2y + y^2z + z^2x\ge 2(x + y + z) − 3$.
  15. 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...
  16. anemone

    MHB Prove $m^5+3m^4n-5m^3n^2-15m^2n^3+4mn^4+12n^5$ ≠ 33

    Prove that $m^5+3m^4n-5m^3n^2-15m^2n^3+4mn^4+12n^5$ is never equal to 33.
  17. M

    A Challenge: splitting an angle into three equal parts

    I recently decided to take a whack at this problem. Came up with an interesting approach, thought it would make a good conversation topic. Anyone else tried to do this? What were your results?
  18. anemone

    MHB What is the ratio of sin 5x to sin x in this Trigonometric Challenge?

    Given that \frac{\sin 3x}{\sin x}=\frac{6}{5}, what is the ratio of \frac{\sin 5x}{\sin x}?
  19. anemone

    MHB What is the value of the floor function challenge?

    Find \left\lfloor{S}\right\rfloor if S=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\cdots+\frac{1}{\sqrt{80}}.
  20. anemone

    MHB How can we prove the inequality challenge for positive real numbers?

    Let $a,\,b$ and $c$ be positive real numbers, prove that \frac{a}{2a+b+c}+\frac{b}{a+2b+c}+\frac{c}{a+b+2c}\le \frac{3}{4}.
  21. 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...
  22. anemone

    MHB Solve Algebraic Equation: x⁴+y⁴+z⁴-xyz(x+y+z)

    Factorize $x^4+y^4+z^4-xyz(x+y+z)$.
  23. anemone

    MHB How to Prove the IMO Inequality Challenge for Positive Reals?

    For positive reals $a,\,b,\,c$, prove that \sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}\gt 2.
  24. micromass

    Challenge Micromass' big simulation challenge

    Let's do some simulations. Below are 5 simulation problems that require a computer to solve. Use any language you want. Post the answers (including graphics) and code here! Any use of outside sources is allowed, but do not look up the question directly. For example, it is ok to go check...
  25. anemone

    MHB Can You Prove this Trigonometric Inequality Challenge?

    Let the real $x\in \left(0,\,\dfrac{\pi}{2}\right)$, prove that $\dfrac{\sin^3 x}{5}+\dfrac{\cos^3 x}{12}≥ \dfrac{1}{13}$.
  26. anemone

    MHB Inequality Challenge: Prove $x^2+y^2+z^2\le xyz+2$ [0,1]

    Prove that $x^2 + y^2+ z^2\le xyz + 2$ where the reals $x,\,y,\, z\in [0,1]$.
  27. kaliprasad

    MHB Integer Challenge: Proving $2A, A+B, C$ integers for $f(x)=Ax^2+Bx+C$

    Let $f(x) = Ax^2 + Bx +C$ where A,B,C are real numbers. prove that if $f(x)$ is integer for all integers x then $2A, A + B, C$ are integers. prove the converse as well.
  28. micromass

    Challenge Micromass' big statistics challenge

    If we're having a thread about probability theory, then we must have one on statistics too! The following questions are all very open-ended and thus multiple answers may seem possible. Your goal is to find a strategy to find the answer to the questions. Furthermore, you must provide some kind of...
  29. 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...
  30. A

    Challenge problem -- rock sliding up and over a roof into an arc....

    Homework Statement One side of the roof of a house slopes up at 37.0°. A roofer kicks a round, flat rock that has been thrown onto the roof by a neighborhood child. The rock slides straight up the incline with an initial speed of 15.0 m/s. The coefficient of kinetic friction between the rock...
  31. Valerie Park

    Challenge problem: The Cable News

    Homework Statement Given the nature of the title of the problem, I need hints to guide me in the right direction. I am sort of lost. A student has a large quantity of a flexible cable. If she cuts a piece of that cable and hangs it vertically, the longest piece that does not break under its own...
  32. collinsmark

    René Heller's SETI Decrypt Challenge

    Original source: https://twitter.com/DrReneHeller/status/724935476327624704 Instructions (copied and pasted from original source): This is a call for a fun scientific challenge. Suppose a telescope on Earth receives a series of pulses from a fixed, unresolved source beyond the solar system...
  33. D

    Finding the Focal Length: A Homework Challenge

    Homework Statement Homework Equations 1/do+1/di=1/f The Attempt at a Solution I tried finding the distance of image at 27m and then at 30.5m and taking the difference but that didn't work.
  34. 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...
  35. 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...
  36. 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...
  37. anemone

    MHB Prove Acute Triangle Inequality: $\sin 2\alpha \gt \sin 2\beta \gt \sin 2\gamma$

    Let $\alpha,\,\beta$ and $\gamma$ be the interior angles of an acute triangle. Prove that if $\alpha \lt \beta \lt \gamma$, then $\sin 2\alpha \gt \sin 2\beta \gt \sin 2\gamma$.
  38. micromass

    Quantum challenge: mathematical paradoxes

    There are many apparent paradoxes in quantum mechanics. Luckily, a careful application of math reveals that all is well. But can you figure out why the following ##7## challenges are not paradoxes? Rules: Do not look at paper [1] before answering. It contains all the answers in detail. Any...
  39. strangerep

    I Can this Laplace transform integral be solved with a symbolic integrator?

    I'm up against this Laplace transform integral: $$F(s) ~:=~ \int^\infty_0 \exp\left( -sx + \frac{i\omega}{1+\lambda x} \right) \, dx $$where ##s## is complex, ##\omega## is a real constant, and ##\lambda## is a positive real constant. By inspection, I think it should converge, at least for some...
  40. jim mcnamara

    LaTeX Solving the Micromass Big Integral Challenge - Issues with Latex Rendering?

    Great thread!: https://www.physicsforums.com/threads/micromass-big-integral-challenge.867904/#post-5450007 I have a 16GB i7 windows 7 box with Firefox v45.0.2. I have NO add-ons to Firefox. Every time I open the one thread, it takes longer and longer - literally a minute the last time. No...
  41. 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...
  42. anemone

    MHB Algebra Challenge: Test Your Skills

  43. anemone

    MHB Geometry Challenge: Find $\angle BCD$ in Convex Quadrilateral

    Let $ABCD$ be a convex quadrilateral such that $AB=BC,\,AC=BD,\,\angle CBD=20^{\circ},\,\angle ABD=80^{\circ}$. Find $\angle BCD.$
  44. Greg

    MHB Is It Possible to Prove the Complex Number Challenge?

    Prove that $\arg[(a+bi)(c+di)]=\arg(a+bi)+\arg(c+di)$.
  45. anemone

    MHB Triangle Challenge: Evaluate $\cos \angle B$

    In a triangle $ABC$ with side lengths $a,\,b$ and $c$, it's given that $17a^2+b^2+9c^2=2ab+24ac$. Evaluate $\cos \angle B$.
  46. anemone

    MHB Prove Inequality w/o Knowledge of $\pi$

    Prove, with no knowledge of the decimal value of $\pi$ should be assumed or used that 1\lt \int_{3}^{5} \frac{1}{\sqrt{-x^2+8x-12}}\,dx \lt \frac{2\sqrt{3}}{3}.
  47. S

    Engineering Solving for i and v_x: A Homework Challenge

    Homework Statement Find i and v_x Given answer: 2. Homework Equations 3. The Attempt at a Solution I have attempted the problem in two different manners, and I consistently reach a different answer. I would appreciate if someone would be willing to take the time to attempt the problem and...
  48. H

    Ultimate physics challenge - fun

    Explain the physical process of the tongue action of a dog drinking water. State yr answer then watch the clip to see if you got it correct. Secret Life of Dogs: Alsatian dog drinking water …:
  49. anemone

    MHB How can you maximize a trigonometric expression?

    Maximize $\sin x \cos y+\sin y \cos z+\sin z \cos x$ for all real $x,\,y$ and $z$.
  50. anemone

    MHB Inequality Challenge: Prove $\ge 0$ for All $a,b,c$

    Prove \frac{a-\sqrt{bc}}{a+2b+2c}+\frac{b-\sqrt{ca}}{b+2c+2a}+\frac{c-\sqrt{ab}}{c+2a+2b}\ge 0 holds for all positive real $a,\,b$ and $c$.
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