Riddles, brain puzzles and mathematical problems

[MyRedNeptune]

@BAndrew

I think we have twin brains.

[BAndrew]

Hahahaha

I have another riddle/problem, but I haven't solved it yet. I'll inform you when I have. I'll start trying it now.


EDIT:

Spoiler below!

OH MY GOD! I solved it! The problem is REALLY hard. If I didn't know calculus I wouldn't be able to solve it. The problem requires some Math knowledge. I don't know if anyone wants to try, but whatever, here's the problem. I will provide the knowledge you probably don't have.

Problem:
Consider a bone with length 1. We break it randomly in two pieces*. Find the average value of the ratio of the length of the largest to the smallest piece.

---

in other words find the
average = length of large piece / length of small piece

I am not here to test how good or bad you are at math so here are the
Things you need to know, but probably don't:

The middle value of a continuous function f is:



How to calculate an integral:
If you don't already know then it is not so simple so go here
and type:
integral from "bottom_number" to "top_number" of "write_function_here" dx

With the help I provided you should be able to solve it like a normal problem.

*It is equally likely to break it on any point.

When I first saw it I thought it didn't have so advanced math, but I was plane wrong.

[DavidS]

Does learning how to solve a Rubik`s Cube still count as a brain puzzle or is it widely regarded as the "easy mode" in these parts? In any case, it is funny how hooked you can get on these little 3D puzzles. Once I got the 3x3x3 down, should I either try a bigger one or better play around with another of Rubiks contraptions?

[BAndrew]

Does learning how to solve a Rubik`s Cube still count as a brain puzzle or is it widely regarded as the "easy mode" in these parts? In any case, it is funny how hooked you can get on these little 3D puzzles. Once I got the 3x3x3 down, should I either try a bigger one or better play around with another of Rubiks contraptions?

It does count of course.

I was interested in the past to come up with an algorithm or a strategy to solve rubic cubes puzzles, but I never actually worked on it. Feel free to post Rubik's cube puzzles.

[DavidS]

I bought a cube a while ago, but here is an online game that also has a "solve" button which is nice once you get stuck somewhere. http://www.agame.com/game/rubix-cube

Right now I am trying to memorize the algorithms in the official guide http://eu.rubiks.com/uploads/general_con...ion-en.pdf nice to keep hands and brain busy while commuting or in a waiting room.

[Bridge]

Of course, while memorizing algorithms and being able to apply them on the fly takes some highly developed cognitive skills it is not even remotely comparable to solving the cube yourself which requires formidable spatial intelligence.

[7heDubz]

Learned how to do it, and now i don't remember the algorithms. I only used them as a basis for my hands learning the movements. Of course i still look at the cube and have to line pieces up correctly but I couldnt do the cube slowly step by step if i tried to.

[DavidS]

@Bridge: Haha, yeah you are right. I am already satisfied if I solve it at all without looking at a guide, no matter the method.

[BAndrew]

Using the appropriate symbols (+,-,*,/,^,etc) between the numbers make the following true:

2 2 = 24
3 3 3 = 24
4 4 4 4 = 24
5 5 5 5 5 = 24
6 6 6 6 6 6 = 24
7 7 7 7 7 7 7 = 24
8 8 8 8 8 8 8 8 = 24
9 9 9 9 9 9 9 9 9 = 24


NOTE: Square (or any other) root is not allowed. Also you can use exponentiate if and only if you use the numbers specified so for example:

2^2 --> allowed
2^4 + 2^2 --> not allowed
4^4 + (4*4)^4 --> not allowed (because you used one more 4)
9^9 + (9*9+9)^9 +... --> allowed
5^7 --> not allowed


Also you are not allowed to combine 2 digits in one number. So for example you cannot make "44" just by combining the two 4.

PS
I am so bad at Rubik's cube :/

[Froge]

4^4 + (4*4)^4 --> allowed

But there are four 4s and five here?