Challenge Definition and 942 Threads

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. RonL

    Boeing GoFly Prize: A Challenge to Make People Fly

    I'm a little surprised this has not been posted already, also because of constraints of the rules I'm putting it in mechanical engineering (mods are welcome to change it as they see fit) :smile: https://herox.com/GoFly/guidelines VISION Remember when you were a child and wanted to fly? We...
  2. I like Serena

    MHB TikZ Challenge 3 - Vector Diagram

    Who can make the most impressive, interesting, or pretty TikZ picture? This third challenge is to create a vector diagram. Such as used in geometric figures, or in physical diagrams with forces and velocities, or in state diagrams. For more impressive arrows, we might use the arrows tikz...
  3. lfdahl

    MHB Counting Squares Challenge: Proving Formula and Evaluating Sum

    We have an $n \times n$ square grid of dots ($n \ge 2$). Let $s_n$ denote the number of squares that can be constructed from the grid points. (a). Show, that $$s_n = \frac{n^4-n^2}{12}.$$ Note, that squares with "diagonal sides" also count. (b). Evaluate the sum: \[S = \sum_{k = 2}^{\infty...
  4. lfdahl

    MHB How Do You Solve This Complex Double Integral with Given Curves?

    Evaluate the double integral: \[I = \int \int _R\frac{1}{(1+x^2)y}dxdy\] - where $R$ is the region in the upper half plane between the two curves: $2x^4+y^4+ y = 2$ and $x^4 + 8y^4+y = 1$.
  5. andrewkirk

    Challenge Origami Puzzle Challenge

    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 mathematicians". Whether the latter is...
  6. I like Serena

    MHB TikZ Challenge 2 - Function Graph

    Who can make the most impressive, interesting, or pretty TikZ picture? This second challenge is to create a function graph. We can use vanilla TikZ, or the pgfplots package, or... well... that's up to you! If it's not immediately obvious, please mention what makes your picture special. Please...
  7. I like Serena

    MHB TikZ Challenge 1 - Geometrical Diagram - Votes

    Hey all, 2 weeks ago I created a challenge to create a geometrical diagram, like a triangle, that is somehow interesting or impressive. Now the moment of truth is here. Please everyone, give your vote! Voting will close in 2 weeks time. Let me recap the submissions.I like Serena...
  8. I like Serena

    MHB TikZ Challenge 1 - Geometrical Diagram

    Who can make the most impressive, interesting, or pretty TikZ picture? This first challenge is to create a geometrical diagram, like a triangle, that is somehow interesting or impressive. We might make it a very complicated figure, or an 'impossible' figure, or use pretty TikZ embellishments...
  9. lfdahl

    MHB Find $a_{2017}$: Sequence Challenge

    Find $a_{2017}$, if $a_1 = 1$, and $$\frac{a_n}{n+1}=\frac{\sum_{i=1}^{n-1}a_i}{n-1}.$$
  10. lfdahl

    MHB Definite integral challenge ∫cos2017xsin2017xdx

    Calculate the following definite trigonometric integral: \[\int_{0}^{\frac{\pi}{2}} \cos^{2017}x \sin^{2017}x dx\].
  11. P

    MHB Challenge: Is cos(pi/60) transcendental?

    Here's your challenge - is $\displaystyle \begin{align*} \cos{ \left( \frac{\pi}{60} \right) } \end{align*}$ transcendental, or does it have an exact surd value? If it has an exact surd value, what is it?
  12. I

    Downforce-aerodynamics-fluid dynamics *Challenge*

    In basic car aerodynamics car manufactures know the basic design in every car creates lift. Let's take the Prius for example, very aerodynamic but does not have any downforce due to the shape of the vehicle (air travels farther on top of the car) being shaped like a wing of an airplane. My...
  13. Greg

    MHB Trigonometric Product Challenge sin(π/m)sin(2π/m)sin(3π/m)⋯sin(m−1)π/m=m/2^(m−1)

    Prove that for $m=2,3,...$ $$\sin\frac{\pi}{m}\sin\frac{2\pi}{m}\sin\frac{3\pi}{m}\cdots\,\sin\frac{(m-1)\pi}{m}=\frac{m}{2^{m-1}}$$
  14. 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...
  15. Evo

    News Florida law lets anyone challenge what’s taught in science

    New Florida law let's any resident challenge what’s taught in science classes. https://www.washingtonpost.com/news/speaking-of-science/wp/2017/07/01/new-florida-law-lets-any-resident-challenge-whats-taught-in-science-classes/?utm_term=.0104dd426ae7 I'm wondering if soon teaching actual science...
  16. lfdahl

    MHB Binomial coefficient challenge

    Prove the following identity:\[\sum_{n =1}^{\infty }\frac{1}{\binom{n+r}{r+1}}=\frac{r+1}{r},\: \: \: \: r,n \in \mathbb{N}.\]
  17. bhobba

    A What's Your Answer To Dyson's Challenge

    I had been meaning to go into Feynman's derivation of Maxwell's Equations for a while now. I finally got around to it: http://signallake.com/innovation/DysonMaxwell041989.pdf He didn't make use of gauge invariance which Schwinger showed is its real basis and I know that derivation, as well as...
  18. mfb

    Challenge Math Challenge by mfb #1

    Greg asked me to post it myself. 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...
  19. 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...
  20. R

    Calculating Friction between Tapered Cylinders: A Math & Engineering Challenge

    Hi everyone: I need the brain of an engineer if anyone out there cares to help. I have a masters in Math from UofT but could use some knowledge from the smartest people- Engineers, I am now an experienced builder and yes everyone, we need smart people doing construction too- my math degree has...
  21. Mateus Buarque

    Area of Hexagon - Geometry Challenge

    Determine the area of the painted hexagon, knowing that the area of triangle ABC is 120cm^2 IMG Link: https://m.imgur.com/a/WtdsW I tried using Heron´s formula, but just ended up with a bunch of terms and one more variable. Sidenote: I guess part of it is figuring out that the side lenghts...
  22. 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...
  23. Greg Bernhardt

    Challenge Math Challenge by Andrewkirk #1

    Submitted and judged by: @andrewkirk Solution credit: 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...
  24. J

    MHB Solving Kaliprasad's Challenge: Finding x Mod p

    A recent challenge problem by Kaliprasad was: x=2*4*6...*(p-1) and y=1*3*5...*(p-2); find x-y mod p. I first thought of Wilson's theorem: for any prime p, (p-1)! is -1 mod p. So I then thought about the exact values of x and y mod p. By writing the factors of x in reverse order, one gets x is...
  25. T

    B A Possible Challenge To Chronology Protection Conjecture?

    Correct me if I am wrong, but my basic understanding of how the Chronology Protection Conjecture (CPC) would work is that, as virtual particles created from the quantum fields of the vacuum would traverse a wormhole and arrive in the past, they would then travel back into the wormhole alongside...
  26. 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...
  27. A

    Comp Sci Make an array with this series (java challenge)

    Homework Statement Given n>=0, create an array length n*n with the following pattern, shown here for n=3 : {0, 0, 1, 0, 2, 1, 3, 2, 1} (spaces added to show the 3 groups). Homework EquationsThe Attempt at a Solution public int[] squareUp(int n) { int length = n*n; int[] completeArry...
  28. Greg Bernhardt

    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...
  29. 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...
  30. 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...
  31. Greg Bernhardt

    Challenge Math Challenge by QuantumQuest #1

    Submitted by: @QuantumQuest Credit to: @stevendaryl 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...
  32. zwierz

    A Classical Mechanics challenge for fun

    I composed a problem and propose it here. I know the solution so it just for fun of the participants. There is a cylindrical bobbin of radius ##r##; the bobbin rotates about its central axis with angular velocity ##\omega=const>0##. An inextensible weightless string is coiled around the...
  33. Greg Bernhardt

    Challenge Math Challenge by Charles Link #1

    Submitted by @Charles Link Solved by: @MAGNIBORO and @maline 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...
  34. gmalcolm77

    B Funneling Light to an Electron: A Size Challenge

    Assuming that the photon packet size is generally related to the wavelength of the light, say 500 nanometers and the electron approximate size of 2.82x10<-15 meters, how does the huge wavelength funnel it's packet energy to an electron approximately 1/17,730 th of it's size?
  35. Albert1

    MHB Trigonometric inequality challenge

    Acute triangle ABC Prove :Sin A +Sin B +Sin C>Cos A + Cos B + Cos C
  36. J

    I How to Prove the Partial Fraction Formula for Distinct Complex Numbers?

    I have figured out a nice way to prove that if the complex numbers z_1,z_2,\ldots, z_N\in\mathbb{C} are all distinct, then the equation \prod_{n=1}^N \frac{1}{z - z_n} = \sum_{n=1}^N \frac{\alpha_n}{z-z_n} is true for all z\in\mathbb{C}\setminus\{z_1,z_2,\ldots, z_N\}, where the alpha...
  37. lfdahl

    MHB Is it Possible to Prove this Trigonometric Inequality?

    Prove the inequality: \[\left | \cos x \right |+ \left | \cos 2x \right |+\left | \cos 2^2x \right |+...+ \left | \cos 2^nx \right |\geq \frac{n}{2\sqrt{2}}\] - for any real x and any natural number, n.
  38. Theia

    MHB What is the Differentiation Challenge?

    Let's have a snack challenge for a while. ^^ Let x and y be real numbers (with restrictions y \ne 0, \ y \ne -x) and \frac{x - y}{x + y} = \frac{x + y}{y}. Find \frac{\mathrm{d}y}{\mathrm{d}x} in whatever form you like most. I mean, for example forms \frac{\mathrm{d}y}{\mathrm{d}x} = f(x, y)...
  39. anemone

    MHB Can You Successfully Factorize x^2+y^2+z^2-2xy-2yz-2zx?

    Factorize $x^2+y^2+z^2-2xy-2yz-2zx$.
  40. Alex_C

    Difficult Practice Questions for Gravitational and Electric Fields

    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...
  41. M

    Egg Drop Challenge: Designing a Way to Keep an Egg Intact

    For my physics assignment we have to design and test a way to allow an egg to fall from a three storey building and not crack. The only requirments are the egg must be visible in atleast one place and the smallest design wins. I tried making a crumple area and then protecting the egg with...
  42. L

    I The statistics of 'psychic challenge'

    This is a problem that I thought I 'solved' many years ago. In actual fact there are many things about it that are not clear to me, and I would like to hear your opinion, please. Very briefly, there was this TV programme where a (supposedly psychic) guy had to match 5 (husband-wife) couples...
  43. Jonathan Scott

    Can you crack GCHQ's code-breaker challenge?

    Nice little puzzle: http://www.bbc.co.uk/programmes/articles/5m5cv4NM5dWx108YgCQXj9J/can-you-crack-gchqs-code-breaker-challenge I didn't find it particularly difficult (less than a minute to spot how to do it, and a few minutes to actually work through it), although Google translate thinks the...
  44. anemone

    MHB Solve Algebra Challenge: $(x+1)(y+1)/(x+y)+\cdots

    Given that $x,\,y$ and $z$ are non-zero real numbers such that $x + y + z = 3$ and $xy + yz + zx = −1$. Evaluate \frac{(x + 1)(y + 1)}{x + y}+ \frac{(y + 1)(z + 1)}{y + z}+ \frac{(z + 1)(x + 1)}{z + x}.
  45. I

    B Strategies for Solving Mathematical 'Riddles' in Scholarship Tests

    I took a test for a scholarship that had mathematical "riddles" just like Micromass' challenges. It was multiple choice and I guessed for some, but others I was able to do or at least use process of elimination. I didn't think I did that well, but I advanced to the second round. Could I have...
  46. gleem

    What is Energy? Join the Flame Challenge 2017 and Explain it to 11 Year Olds!

    In 2012 actor Alan Alda started a competition in which scientists are asked to explain by whatever means a designated phenomenon or concept to 11 year olds. The explanations are judged by students whose schools are participating in the competition worldwide some 26,000 students so far. This...
  47. lfdahl

    MHB How to Prove the Inequality for a, b, and c in the Range of 0 to 1?

    Prove the inequality: $\sqrt{a(1-b)(1-c)}+\sqrt{b(1-a)(1-c)}+\sqrt{c(1-a)(1-b)} \le 1 + \sqrt{abc}, \;\;\;\;a,b,c \in [0;1].$
  48. 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...
  49. lfdahl

    MHB Integral Challenge II: Calculate Int. 2 to 7

    Calculate the definite integral\[ \int_{2}^{7} \frac{x}{1-\sqrt{2+x}}\,dx \]- without the use of an integral calculator
  50. lfdahl

    MHB Solve Indefinite Integral: 3 Ways

    Solve the indefinite integral \[\int \frac{dx}{\cos x+\sin x}\] - in three different ways.
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