# challenge

1. ### Geometric puzzle challenge

Due to problems with two members I will not be posting or commenting anymore. I find these members insulting. Though these people insulting me, cannot solve a seemingly simple geometric puzzle. I hope others with less ego will solve it. Here it is. You must design two geometric shapes...
2. ### Geometric puzzle challenge for you

Hello math lovers. Here is a geometric puzzle for someone to try to solve. The answer leads to knowledge of how cubes relate directly to spheres. Though this is a 2D puzzle, it can also relate on a 3D level, where your interest may be more directed. Here it is. You must design two...
3. ### Geometric puzzle challenge

Here is a great geometric puzzle. that has led to new geometric shapes. This is the puzzle. You must design two geometric shapes. With these two geometric shapes, you must be able to construct either a circle or a square. You must use both shapes in the construction of the circle or the...
4. ### I challenge you to a debate!

400 Mathematicians leading of mathematical institutions in the world (to whom were sent personal letters) I challenge you to a debate! Dear Sirs Over the past 70 days, I sent you the text of a single-page elementary proof of Fermat's Last Theorem. In fact, its mathematical apparatus...
5. ### Geometry challenge problem

This is from Mensa. I figured it out using calculus and then discovered that it can be solved with an easy geometric proof. While the calculus solution is not particularly difficult, the geometry solution is cooler and accessible to high school students. I have selected a site for my house...
6. ### Challenge Problem

One day you decide to write a letter to 3 friends.When you finish, you write each address on an envelope and put a stamp on each. If you were to put a letter into each envelope without looking, how many ways are there of putting AT LEAST one letter in the wrong envelope? What is the chance you...
7. ### Trigonometry Challenge = cotangent product

Prove \prod_{n=1}^{m-1}\cot\frac{n\pi}{2m}=1 for all integers m>1.
8. ### My Number Puzzle Challenge

Use the digit 3 exactly one time each and no other digits. You can use unlimited pairs of parentheses, except that if you can remove any pairs and still have a valid solution, then you must use the least number of them. You can use unlimited pairs of floor function symbols, except that...
9. ### ODE - third challenge

So i'm stucked with this equation, and need help.. i've started solve it but than it arrived to an integral of 1/lnc1y- which i don't know how to solve - the equation is: 1/y(y'^2)y''+2y''^2+y'y'''=0 thanks a lot :unsure:
10. ### Trigonometry challenge

If $T_n = \sin^n \theta + \cos^n \theta$, prove that $6T_{10} - 15T_8 + 10T_6 - 1 = 0$
11. ### Differential equation challenge

Hi I can't figure out how to solve this equation :( . Can anybody help me? :D The equation is: y''=8y^3 \qquad , \qquad y(0)=1 \quad \text{and} \quad y'(0)=2 Then the book hints you to multiply with y' on both sides. Furthermore, I use Leibniz notation and multiply with dx on both sides...
12. ### Challenge problem -- estimate the sum

. . Given (meaning you can use these): -------------------------------------------- The natural logarithm of 10, that is, ln(10), equals 2.3 when rounded to the nearest tenth. \int \ln(u)du \ = \ u*ln(u) \ - \ u \ + \ C...
13. ### Help me build an equation.

Alright, so I'm looking for some help with creating an extremely complex and time-consuming equation that has a solution of 2108237118. Any help would be greatly appreciated.
14. ### 3 8's to make 24 -- my challenge puzzle

In each expression: Use exactly three 8's. Use at most three square root symbols. If you can't access the square root symbol, then you can type "sqrt" as in the form "sqrtX" or "sqrt(X)," where appropriate. Here, "X" might be one or more characters in length. Use at most two...

Can anyone solve this? I asked my peers for help, and none of us were able to solve this. -Suppose you have a scientific calculator where some of the buttons are broken. In fact, the only working keys are the digits [0] to [9], [+],[-],[x],[*division sign*/], [ln], and [e^x]. Explain how...
16. ### Beal challenge counter example

The beal challenge is that if A^x+B^y=C^z This is my counter example: 79^40 +3^90 =3077056399^8 This follows all the rules except A(79),B(3) and c(3077056399) = don't have a common prime number as 79 and 3 are both prime numbers. This therefore disproves the Beal prize conjecture.
17. ### Help Adam with this simple challenge

Hi, hope you're good. I've a little problem I find confusing and I'm hoping one of you finds it fun. Would you be up for cracking it/simplifying it for me please? Here it is, in hope.. I run a music booking agency where an act gets a fee, which has a VAT amount charged of 20% onto it. We take...
18. ### Integration Challenge

\int\frac{dx}{\sec x+1}
19. ### A challenge, to find the equation for a function

So after really considering this album cover (titled 'AM'), I decided that I really wanted to come up with a function that resembled it. Even with my relatively limited understanding of functions, I decided to give it a shot. However, the best thing I could come up with is this: f(x) = sin(x) *...
20. ### Which side is greater? my challenge #2

\sqrt{2} \ + \ \sqrt{3} \ + \ \sqrt{5} \ + \ \sqrt{7} \ \ \ versus \ \ \ 8 I am not asking to do the actual work to determine which side is larger. The question is: At any given step, is it possible to eliminate one of the four radicals that will be present in that step after squaring...