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. anemone

    MHB Trigonometry Challenge (Find x)

    Solve $\large 3^{3\cos x(1+\sin^2 x)}-3^{\cos x(4-\sin^2 x)}=6\cos 3x$.
  2. K

    Solving Work Problems: Algebra Techniques for Jennifer and John

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  3. S

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  4. anemone

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  5. kostoglotov

    Multiple Integral Challenge Question, I just need a hint

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  6. kostoglotov

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  7. anemone

    MHB Prove Existence of $n$ for Integer $\sqrt{n^3+xn^2+yn+z}$

    Prove that for any integers $x,\,y,\,z$, there exists a positive integers $n$ such that $\sqrt{n^3+xn^2+yn+z}$ is not an integer.
  8. I

    MHB Prove $x=-y$: A Math Challenge

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  9. anemone

    MHB Algebra Challenge: Express $(x^3-y^3)(y^3-z^3)(z^3-x^3)$ in Terms of a & b

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  10. anemone

    MHB Can you prove the trigonometry challenge with angles of a triangle?

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  11. Dethrone

    MHB What is the basis for $F$ in linear algebra?

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  12. Boccadoro

    The challenge of transmitting radio frequencies underwater.

    If both a transmitter and receiver antennae were submerged, and within a defined range and depth, what range might be available to a civilian operator? Are two divers able to communicate by radio? B
  13. anemone

    MHB Value of $\dfrac{2k^2}{k-1}$: Solving the Equation

    Determine the value of $\dfrac{2k^2}{k-1}$ given $\dfrac{k^2}{k-1}=k^2-8$.
  14. L

    What is the biggest challenge to improve white LEDs?

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  15. anemone

    MHB Prove Inequality for $0<x<\dfrac{\pi}{2}$: Math Challenge

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  16. anemone

    MHB Prove $|P(a)-P(b)|<\dfrac{1}{2}$ for Algebra Challenge Function $P$

    Let $P$ be a function defined on $[0, 1]$ such that $P(0)=P(1)=1$ and $|P(a)-P(b)|<|a-b|$, for all $a\ne b$ in the interval $[0, 1]$. Prove that $|P(a)-P(b)|<\dfrac{1}{2}$.
  17. anemone

    MHB Prove: $\sin P+\sin Q> \cos P+\cos Q +\cos R$ | Trig Challenge

    Let $P,\,Q,\,R$ be the angles of an acute-angled triangle. Prove that $\sin P+\sin Q> \cos P+\cos Q +\cos R$.
  18. anemone

    MHB Prove Geometry Challenge: Cyclic Quadrilateral PQRS

    Given a cyclic quadrilateral $PQRS$ where $PQ=p,\,QR=q,\,RS=r$, $\angle PQR=120^{\circ}$ and $\angle PQS=30^{\circ}$. Prove that $|\sqrt{r+p}-\sqrt{r+q}|=\sqrt{r-p-q}$
  19. Spock

    Turning Around in Space: The Challenge of No Gravity

    Can a person suspended in space with nothing to push off of, turn themselves around?
  20. anemone

    MHB Solve Trigonometry Challenge: $\cos^k x-\sin^k x=1$

    Solve the equation $\cos^k x-\sin^k x=1$, where $k$ is a given positive integer.
  21. D

    Identifying Hydrocarbon X: A Homework Challenge

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  22. T

    MHB Biggest Loser prize distribution challenge.

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  23. anemone

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  24. jacobi1

    MHB Probability of Reaching Room Q in n Seconds

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  25. anemone

    MHB Can $k>1$ Prove This Inequality?

    Prove that for all integers $k>1$: $\left(\dfrac{1+(k+1)^{k+1}}{k+2}\right)^{k-1}>\left(\dfrac{1+k^k}{k+1}\right)^{k}$
  26. Dethrone

    MHB How can the integration limit be determined for a continuous function?

    Suppose $f$ is a continuous function on $(-\infty,\infty)$. Calculating the following in terms of $f$. $$\lim_{{x}\to{0}}f\left(\int_{0}^{\int_{0}^{x}f(y) \,dy} f(t)\,dt\right)$$
  27. 8008jsmith

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  28. anemone

    MHB Triangle Challenge: Prove 2.5<PQ/QR<3

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  29. Dethrone

    MHB Calculate w/ Defective Calculator: Multiply w/ Add, Subtract, & Reciprocal

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  30. anemone

    MHB Geometry Challenge: Prove $PT+PU\ge 2\sqrt{2}p$

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  31. Dethrone

    MHB Differential Equation Challenge

    Find $y(x)$ to satisfy y(x)=y'(x)+\int e^{2x}y(x) \, dx+\lim_{{x}\to{-\infty}}y(x) given \lim_{{x}\to{0}}y(x)=0 and \lim_{{x}\to{\ln\left({\pi/2}\right)}}y(x)=1.
  32. anemone

    MHB Polynomial Challenge: Show $f(5y^2)=P(y)Q(y)$

    Given that $f(x)=x^4+x^3+x^2+x+1$. Show that there exist polynomials $P(y)$ and $Q(y)$ of positive degrees, with integer coefficients, such that $f(5y^2)=P(y)\cdot Q(y)$ for all $y$.
  33. anemone

    MHB Challenge for Polynomial with Complex Coefficients

    Let $ax^2+bx+c$ be a quadratic polynomial with complex coefficients such that $a$ and $b$ are non-zero. Prove that the roots of this quadratic polynomial lie in the region $|x|\le\left|\dfrac{b}{a}\right|+\left|\dfrac{c}{b}\right|$.
  34. anemone

    MHB Inequality: $\dfrac{\ln x}{x^3-1}<\dfrac{x+1}{3(x^3+x)}$ for $x>0,\,x\ne 1$

    Prove that $\dfrac{\ln x}{x^3-1}<\dfrac{x+1}{3(x^3+x)}$ for $x>0,\,x\ne 1$.
  35. Greg Bernhardt

    Challenge 25: Finite Abelian Groups

    What is the smallest positive integer n such that there are exactly 3 nonisomorphic Abelian group of order n
  36. anemone

    MHB Prove Divisibility of $a^3+b^3+c^3$ Using $(a-b)^2+(b-c)^2+(c-a)^2=abc$

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  37. anemone

    MHB Evaluating $a^2+ab+b^2=0$: A 2015 Challenge

    If $a,\,b$ are non-zero numbers with $a^2+ab+b^2=0$. Evaluate $\left(\dfrac{a}{a+b}\right)^{2015}+\left(\dfrac{b}{a+b}\right)^{2015}$.
  38. anemone

    MHB Is There an Inequality Challenge with Real Numbers?

    Let $a,\,b,\,c,\,d$ be real numbers such that $abcd=1$ and $a+b+c+d>\dfrac{a}{b}+\dfrac{b}{c}+\dfrac{c}{d}+\dfrac{d}{a}$. Prove that $a+b+c+d<\dfrac{b}{a}+\dfrac{c}{b}+\dfrac{d}{c}+\dfrac{a}{d}$.
  39. anemone

    MHB Trig Challenge: Proving $\cos^3 y+\sin^3 y=\cos x+\sin x$

    Show that if $\dfrac{\cos x}{\cos y}+\dfrac{\sin x}{\sin y}=-1$, then $\dfrac{\cos^3 y}{\cos x}+\dfrac{\sin^3 y}{\sin x}=1$.
  40. S

    MHB How Far Does a Bookworm Travel Through a 3-Volume Set?

    There is a 3-volume set of books $\quad$on a bookshelf in the usual manner. Each volume has two covers, each $\frac{1}{4}$ inch thick, $\quad$and the printed portion is $1$ inch thick. A bookworm starts at the first page of Volume 1 $\quad$and eats his way to the last page of Volume 3. How...
  41. Greg Bernhardt

    How many 7-digit numbers are divisible by 7 and composed of digits 1-7?

    Submitted by @PeroK Consider all 7-digit numbers which are a permutation of the digits 1-7. How many of these are divisible by 7? Can you prove the answer algebraically, rather than simply counting them? Please make use of the spoiler tag
  42. Greg Bernhardt

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  43. TheDemx27

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  44. C

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    Homework Statement Here it is: Let Ω be a convex region in R2 and let L be a line segment of length ι that connects points on the boundary of Ω. As we move one end of L around the boundary, the other end will also move about this boundary, and the midpoint of L will trace out a curve within Ω...
  45. Greg Bernhardt

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  46. Greg Bernhardt

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  47. M

    MHB Sequence Challenge: Find $a_{2015}$

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  48. kaliprasad

    MHB Inequality: Prove $a^4+b^4+c^4 \ge abc(a+b+c)$

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  49. Greg Bernhardt

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  50. Y

    Design a Winning Egg Capsule Challenge

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