# What is Challenge: Definition and 941 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. ### An Algorithm Challenge (finding the five fastest horses out of a large group)

As a Bedouin schiek you own twenty-five horses. You want to find the three fastest. You have no clock or other device that measures time. Your racing field is wide enough that five horses can race unimpeded, so you can race five at a time and see how they place. You don't want to abuse your...
2. ### How to find integrals of parent functions without any horizontal/vertical shift?

TL;DR Summary: How to find integrals of parent functions without any horizontal/vertical shift? Say you were given the equation : How would you find : with a calculator that can only add, subtract, multiply, divide Is there a general formula?
3. ### A Combination theory challenge

Hello All, Not sure if this belongs in general math but lets start here and see where it takes us. In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. As an example , say we have digits 1 to 10. And we want to select 3...
4. ### Engineering Calculating a) and Baffled by b): A Math Challenge

I was able to calculate a), and got 0.7mm But I have no idea where to even start with b)
5. ### I ChatGPT challenge of the day

Chatgpt is actually pretty good at generating math problems. It's awful at solving them. I guarantee every question posted here cannot be solved by chatgpt, but maybe can be solved by a human? My plan is to spend a couple minutes getting a question I think it's cool and then posting it here -...
6. ### NASA Could Mars have supported life? NASA challenge wants your help

Deadline April 18, 2022 Competition Eligibility at: https://www.drivendata.org/competitions/93/nasa-mars-spectrometry/rules/ HeroX Challenge page: https://www.herox.com/MarsSpectrometry Brief article: https://www.space.com/nasa-mars-habitable-herox-competition Good Luck, and have Fun! Tom
7. ### Map Colour Design Challenge

OK, I'm stuck on a problem implementing this map. (It'll be built in HTML with JavaScript and CSS and is interactive but that's just context - this is really about map-colouring.) The function of the map is to help users see at-a-glance what regions/counties of the province are serviced by...
8. ### I How would you have answered Richard Feynman's challenge?

Fun question on mathoverflow: How would you have answered Richard Feynman's challenge?
9. ### Challenge Math Challenge - December 2021

This month's challenges will be my last thread of this kind for a while. Call it a creative break. Therefore, we will have a different format this month. I will post one problem a day, like an advent calendar, only for the entire month. I will try to post the questions as close as possible to...
10. ### Challenge Math Challenge - November 2021

Summary: Analysis. Projective Geometry. ##C^*##-algebras. Group Theory. Markov Processes. Manifolds. Topology. Galois Theory. Linear Algebra. Commutative Algebra. 1.a. (solved by @nuuskur ) Let ##C\subseteq \mathbb{R}^n## be compact and ##f\, : \,C\longrightarrow \mathbb{R}^n## continuous and...
11. ### Challenge Math Challenge - October 2021

Summary: Functional Analysis. Project Management. Set Theory. Group Theory. Lie Theory. Countability. Banach Algebra. Stochastic. Function Theory. Calculus. 1. Prove that ##F\, : \,L^2([0,1])\longrightarrow (C([0,1]),\|.\|_\infty )## defined as $$F(x)(t):=\int_0^1 (t^2+s^2)(x(s))^2\,ds$$ is...
12. ### 2-D kinematics challenge problem help please

Hi! I can't solve this. Please someone give me a hint and help? I'm unsure what equation to use. Thank you!🙏🙏🙏 An artillery crew demonstrates its skill by firing a shell at an angle of 49 deg and then lowering the gun barrel and firing a second shell at a smaller angle of 20 deg in such a way...
13. ### Challenge Math Challenge - September 2021

Summary: Gamma function. Combinatorics. Stochastic. Semisimple Modules. Topological Groups. Metric spaces. Logarithmic inequality. Stochastic. Primes. Approximation theory. 1. (solved by @julian and @benorin ) Let ##f## be a function defined on ##(0,\infty)## such that ##f(x)>0## for all...
14. ### A Samalkhaiat's challenge #002

To get you started I will derive the Lorentz force law from the QED Lagrangian \begin{equation}\mathcal{L} = \frac{i}{2} \bar{\psi}\gamma^{\mu}D_{\mu}\psi + h.c - \frac{1}{16\pi}F_{\mu\nu}F^{\mu\nu} ,\end{equation}D_{\mu} = \partial_{\mu} + ieA_{\mu}, and then, I let you do the same to a SM-like...
15. ### Challenge Math Challenge - August 2021

Summary: countability, topological vector spaces, continuity of linear maps, polynomials, finite fields, function theory, calculus 1. Let ##(X,\rho)## be a metric space, and suppose that there exists a sequence ##(f_i)_i## of real-valued continuous functions on ##X## with the property that a...
16. ### I Would this violate or challenge Newton's laws?

The phenomenon of diffusion is a transport phenomenon based on the thermal motion of molecules, a process in which molecules are transported from a region of high concentration to a region of low concentration by Brownian motion. Let's assume that there is a car, the road under the wheels is...
17. ### MHB Can You Solve This Isosceles Triangle Challenge?

Hello MHB, I saw one question that really tickles my intellectual fancy and because of the limited spare time that I have, I could not say I have solved it already! But, I will most definitely give the question more thought and will post back if I find a good solution to it. Here goes the...
18. ### Challenge Math Challenge - July 2021

Summary:: Group Theory, Lie Algebras, Number Theory, Manifolds, Calculus, Topology, Differential Equations. 1. (solved by @Infrared ) Suppose that ##G## is a finite group such that for each subgroup ##H## of ##G## there exists a homomorphism ##\varphi \,:\, G \longrightarrow H## such that...
19. ### Physics 'challenge' type problems, High School (16-18) level

Hi all I've long been a fan of the nrich site for maths and in recent years it has started to add a section on physics here. I also like IsaacPhysics although I haven't used it much in the past year so am still trying to get used to the new layout. I'm looking for other resources along this...
20. ### Challenge Experimental Physics Challenge, June 2021

Trying this out for fun, and seeing if people find this stimulating or not. Feedback appreciated! There's only 3 problems, but I hope you'll get a kick out of them. Have fun! 1. Springey Thingies: Two damped, unforced springs are weakly coupled and obey the following equations of motion...
21. ### Challenge Math Challenge - June 2021

Summary: Lie algebras, Hölder continuity, gases, permutation groups, coding theory, fractals, harmonic numbers, stochastic, number theory. 1. Let ##\mathcal{D}_N:=\left\{x^n \dfrac{d}{dx},|\,\mathbb{Z}\ni n\geq N\right\}## be a set of linear operators on smooth real functions. For which...
22. E

### Challenge May Physics Challenge

Just for fun! :smile: Feel free to have a go at any of the problems. Problem 1 A spherical ball of radius ##a## and centre ##C## rolls on the rough outer surface of a fixed sphere of radius ##b## and centre ##O##. Show that the radial spin ##\boldsymbol{\omega} \cdot \mathbf{c}## is conserved...
23. ### MHB Sequence Challenge: Prove $a_{50}+b_{50}>20$

The sequence $\{a_n\}$ and $\{b_n\}$ are such that, for every positive integer $n$, $a_n>0,\,b_n>0,\,a_{n+1}=a_n+\dfrac{1}{b_n}$ and $b_{n+1}=b_n+\dfrac{1}{a_n}$. Prove that $a_{50}+b_{50}>20$.
24. ### Challenge Math Challenge - May 2021

Summary: Group Theory, Integrals, Representation Theory, Iterations, Geometry, Abstract Algebra, Linear Algebra. 1. Integrate $$\int_{0}^\infty \int_{0}^\infty e^{-\left(x+y+\frac{\lambda^3 }{xy}\right)} x^{-\frac{2}{3}}y^{-\frac{1}{3}}\,dx\,dy$$ 2. (solved by @Infrared , basic solution...
25. ### MHB Trigonometric challenge

Prove $\sin^2(x+a)+\sin^2(x+b)-2\cos (a-b)\sin (x+a)\sin (x+b)$ is a constant function of $x$.
26. ### Challenge Math Challenge - April 2021

Summary: Differential Equations, Linear Algebra, Topology, Algebraic Geometry, Number Theory, Functional Analysis, Integrals, Hilbert Spaces, Algebraic Topology, Calculus. 1. (solved by @etotheipi ) Let ##T## be a planet's orbital period, ##a## the length of the semi-major axis of its orbit...
27. ### MHB Trigonometric challenge

Let $x$ be a real number such that $\dfrac{\sin^4 x}{20}+\dfrac{\cos^4 x}{21}=\dfrac{1}{41}$. If the value of $\dfrac{\sin^6 x}{20^3}+\dfrac{\cos^6 x}{21^3}$ can be expressed as $\dfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers, find the remainder when $m+n$ is divided by 1000.
28. ### Challenge Math Challenge - March 2021

Summary: Lie Algebras, Commutative Algebra, Ordering, Differential Geometry, Algebraic Geometry, Gamma Function, Calculus, Analytic Geometry, Functional Analysis, Units. 1. Prove that all derivations ##D:=\operatorname{Der}(L)## of a semisimple Lie algebra ##L## are inner derivations...
29. ### Challenge Math Challenge - February 2021

Summary: Calculus, Measure Theory, Convergence, Infinite Series, Topology, Functional Analysis, Real Numbers, Algebras, Complex Analysis, Group Theory 1. (solved by @Office_Shredder ) Let ##f## be a real, differentiable function such that there is no ##x\in \mathbb{R}## with ##f(x)=0=f'(x)##...
30. ### MHB Trigonometric Challenge

If $x\in \left(0,\,\dfrac{\pi}{2}\right)$, $0\le a \le b$ and $0\le c \le 1$, prove that $\left(\dfrac{c+\cos x}{c+1}\right)^b<\left(\dfrac{\sin x}{x}\right)^a$.
31. ### Challenge Math Challenge - January 2021

Summary: Linear Programming, Trigonometry, Calculus, PDE, Differential Matrix Equation, Function Theory, Linear Algebra, Irrationality, Group Theory, Ring Theory. 1. (solved by @suremarc , 1 other solutions possible) Let ##A\in \mathbb{M}_{m,n}(\mathbb{R})## and ##b\in \mathbb{R}^m##. Then...
32. ### MHB New Year Challenge: Find Real Number Triples

Find all triples $(a,\,b,\,c)$ of real numbers such that the following system holds: $a+b+c=\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\\a^2+b^2+c^2=\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}$
33. ### Do you consider writing this program a bit of a challenge?

Do you consider writing a program that takes 3 integer inputs and orders them in ascending order (accounting for same numbers) difficult? You can only use if statements (if, else if, else). I know there is some thing called "sort" that does the tedious work for you but do you find this simple...
34. ### MHB Summation Challenge: Evaluate $\sum_{k=1}^{2014}\frac{1}{1-x_k}$

Let $x_1,\,x_2,\,\cdots,\,x_{2014}$ be the roots of the equation $x^{2014}+x^{2013}+\cdots+x+1=0$. Evaluate $\displaystyle \sum_{k=1}^{2014} \dfrac{1}{1-x_k}$.
35. ### I What is the main challenge of high energy physics?

Hi, my question is that what is the main challenge of high energy physics? what is the best theory that maybe explain it and why it would not be accepted?
36. ### Challenge Math Challenge - December 2020

Summary: Circulation, Number Theory, Differential Geometry, Functional Equation, Group Theory, Infinite Series, Algorithmic Precision, Function Theory, Coin Flips, Combinatorics. 1. (solved by @etotheipi ) Given a vector field  F\, : \,\mathbb{R}^3 \longrightarrow \mathbb{R}^3\, ...
37. ### MHB Prove Triangle Inequality: $\sqrt{2}\sin A-2\sin B+\sin C=0$

In a triangle $ABC$ with $\sqrt{2}\sin A-2\sin B+\sin C=0$, prove that $\dfrac{3}{\sin A}+\dfrac{\sqrt{2}}{\sin C}\ge 2(\sqrt{3}+1)$.
38. ### MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$

Let $x,\,y,\,z$ be integers such that $(x-y)^2+(y-z)^2+(z-x)^2=xyz$, prove that $x^3+y^3+z^3$ is divisible by $x+y+z+6$.
39. ### Challenge Math Challenge - November 2020

Summary: Diffusion Equation, Sequence Space, Banach Space, Linear Algebra, Quadratic Forms, Population Distribution, Sylow Subgroups, Lotka-Volterra, Ring Theory, Field Extension. 1. Let ##u(x,t)## satisfy the one dimensional diffusion equation ##u_t=Du_{xx}## in a space-time rectangle...
40. ### Solving an Electrical Engineering Challenge with a Tank of Electrolyte Liquid

So I am working on a project where I have a tank, which has a volume of electrolyte liquid inside it. This is coupled to a battery which charges it, and gives it energy. I will have a copperband arround it, so i can measure a potential voltage from the electrical field. So what I need to...
41. ### MHB Sine function challenge

Let $a,\,b$ and $c$ be real numbers such that $\sin a+\sin b+\sin c\ge \dfrac{3}{2}$. Prove that $\sin \left(a-\dfrac{\pi}{6}\right)+\sin \left(b-\dfrac{\pi}{6}\right)+\sin \left(c-\dfrac{\pi}{6}\right)\ge 0$.
42. ### MHB Inequality challenge

Prove that $\sqrt[n]{1+\dfrac{\sqrt[n]{n}}{n}}+\sqrt[n]{1-\dfrac{\sqrt[n]{n}}{n}}<2$ for any positive integer $n>1$.
43. ### Challenge Math Challenge - October 2020

Summary:: Functional Analysis, Algebras, Measure Theory, Differential Geometry, Calculus, Optimization, Algorithm, Integration. Lie Algebras. 1. (solved by @julian ) Let ##(a_n)\subseteq\mathbb{R}## be a sequence of real numbers such that ##a_n \leq n^{-3}## for all ##n\in \mathbb{N}.## Given...
44. ### Challenge Math Challenge - September 2020

Summary: group theory, number theory, commutative algebra, topology, calculus, linear algebra Remark: new solution manual (01/20-06/20) attached https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/ 1. Given a group ##G## then the intersection of all maximal...
45. ### MHB Algebra Challenge: Proving $p,\,q,\,r,\,s,\,t$ Satisfy Equation

Let $p,\,q,\,r,\,s,\,t \in \mathbb {R_+}$ satisfying $p^2+pq+q^2=s^2\\ q^2+qr+r^2=t^2\\r^2+rp+p^2=s^2-st+t^2$ Prove that $\dfrac{s^2-st+t^2}{s^2t^2}=\dfrac{r^2}{q^2t^2}+\dfrac{p^2}{q^2s^2}-\dfrac{pr}{q^2ts}$
46. ### MHB Challenge involving irrational number

Let $x$ be an irrational number. Show that there are integers $m$ and $n$ such that $\dfrac{1}{2555}<mx+n<\dfrac{1}{2012}$.
47. ### MHB Nature of roots challenge

Prove that the polynomial equation $x^8-x^7+x^2-x+15=0$ has no real solution.
48. ### MHB Summation Challenge: Evaluate $\sum_{n=0}^\infty \frac{16n^2+20n+7}{(4n+2)!}$

Evaluate $\displaystyle \sum_{n=0}^\infty \dfrac{16n^2+20n+7}{(4n+2)!}$.
49. ### MHB Continuous Function Integration Challenge

Find all continuous functions $f:[1,\,8] \rightarrow \mathbb{R}$ such that $\displaystyle \int_1^2 f^2(t^3)dt + 2\int_1^2 f(t^3)dt=\dfrac{2}{3}\int_1^8 f(t)dt-\int_1^2 (t^2-1)^2 dt$
50. ### Challenge Math Challenge - August 2020

1. (solved by @nuuskur ) Let ##K## be a non-empty compact subset of ##\Bbb{C}##. Construct a bounded operator ##u: H \to H## on some Hilbert space ##H## that has spectrum ##\sigma(u) =K##. (MQ) 2. Let ##f,g:[0,2]\to\mathbb{R}## be continuous functions such that ##f(0)=g(0)=0## and...