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Does anyone have any ideas on this one?Any hints are appreciated.

**Mario23**- Replies: 3

What is the ratio between the lengths of a rectangular pool table if a ball launched from one of the sides under an angle of 45° passes through the starting point after 6 reflections?(when I say reflection I mean that the ball hits the side of the table)

iamaditya wrote:

But, the semi-circles and the circles may be of different sizes also. The size is not specifies in the question.

I think the size doesn't matter as 3 will be needed as greg said.I don't know yet if the answer is the same for a sphere.

bob bundy wrote:

??? No, still don't get it. What's the difference between a circle and a disk? If two semicircles meet what does it matter if they're open?

Here's my solution.

http://i.imgur.com/sXx6Z60.gif

You cannot see the original circle (it is red) because it's covered.

Bob

The disk is the inside of the circle

@greg1313 how do I extemd this to a sphere?Will I need 3 hemispheres like here?

The problem says nothing about their size,it only says that an open secircles is a semicircle without its ends.

**Mario23**- Replies: 12

a)How many open semicircles are needed to fully cover a circle?

b)How many open hemispheres are needed to fully cover a sphere?

It is the first time I've ever seen questions like this and I don't know how to approach them.Please help me!

**Mario23**- Replies: 0

Hi guys! I need some help with this exercise I am trying to do so as to be prepared for the math olympiad:

Be n>=2 a natural number.Prove that the equation

has an infinity of solutions in N*.

My idea initially was to use mathematical induction to prove it,but then I thought that maybe it is a diophantine equation.I need some help with it

How did you get it thickhead?

**Mario23**- Replies: 7

Be the numbers

.If find the minimum of the sum .I tried to show that sum is >= than something but no luck.I tried using all the inequalities I know but I didn't use any which help,so I need your help guys

Just wondering,how did you find all those numbers above?

Oh my God that's a lot of numbers.Which are the relationships you are thinking at?

Well the only thing I did not include is that x,y and z are distinct from one another

**Mario23**- Replies: 7

Hey guys,here I am with another exercise I can't solve.

Find all the triplets of distinct real numbers (x,y,z) for which:

I remember this problem as an exercise for integers.There I would use that xyz=1 but how do I do it for reals?

They are right,I checked them

Thank you for your help !

Okay,I am looking forward to seeing your ideas

My best try at proving that using that relation was that

where m is a rational number.I used then that the other frac is mq and I tried to square them,divide the ecuations etc but it is definitely not working.

Well I don't know.There are usually more .And I don't know how to prove there aren't.

Yes,I managed to guess it too but I don't know how to find all of them.

**Mario23**- Replies: 13

Hey! I've come across an exercise I can 't seem to solve.

Find all the n integers that satisfy :

is a rational number.

I can't see how to find them because 4n-2 can't be a perfect square and that's why I need some help on it.

Yeah,I managed to finish it from that point.Thank you all for your help!

Hey! I have some c++ knowledge maybe I can help you

So I should prove that

is independent of n?

EDIT:That's the only thing I can't prove so I could use a hand

Ok so from that point I applied that theorem but what should I do next?