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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 Re: Help Me ! » Sum problem with exponent factor and unknown n » Today 14:05:32

You can get those neat looking formulas using LaTeX.

To use it, you need the math tags:

[math][/math]

You can click any formula to see how it was written. Also, there are a lot of them here

#2 Re: Help Me ! » How to name a plane » Today 06:27:45

But, if we are looking at 3D space, spherical geometry wouldn't be placed on the surface of a sphere, but rather on the surface of a hypersphere. smile

Also, after your post I realised that I wanted to say "in polar coordinates". But this way it's more interesting.

#3 Re: Help Me ! » How to name a plane » Today 06:06:26

How do you define a plane in spherical geometry?

#4 Re: Jokes » Poem by a student » Today 04:24:33

Now you're copying me? You are stone dead to me.

#6 Re: Jokes » Poem by a student » Today 04:00:39

If I cannot think of another pun, my name will be in mud.

#7 Re: Jokes » Poem by a student » Today 03:57:58

Sticks and stones may break my bones, but jokes will never harm me.

#8 Re: Jokes » Poem by a student » Today 01:00:47

No problem. No member here has a heart of stone. smile

#9 Re: Jokes » Poem by a student » Yesterday 23:22:23

Hi GreatSandy

It's a pun on the word "deep". It can be used to mean that it's very philosophical, but also to refer to "deep" as in "deep under the earth".

You can see the rest of us followed by even more puns with words related to dirt and mud.

#10 Re: Exercises » Bitter die » Yesterday 13:47:04

Will do. Thank you for posting it!

I hope for more of these in the near future.

#11 Re: Exercises » Bitter die » Yesterday 13:43:01

Ah, okay. I will try getting something out of the chain.

#12 Re: Exercises » Bitter die » Yesterday 13:34:47

Hm, so you did it the same way I did?

#13 Re: Exercises » Bitter die » Yesterday 13:32:26

It seems right for infinite throws. I think it's different for finite.

#14 Re: Exercises » Bitter die » Yesterday 13:24:57

Hm, is expected time calculated as P(I-P)^(-2)?

#15 Re: Exercises » Bitter die » Yesterday 13:11:47

So, you cannot do it by Markov chain?

Fixed my matrix above, forgot that 654321 is not an absorbing state.

#16 Re: Exercises » Bitter die » Yesterday 12:52:57

" "
6
65
654
6543
65432
654321

#17 Re: Exercises » Bitter die » Yesterday 12:39:03

{{5/6,1/6,0,0,0,0,0},{2/3,1/6,1/6,0,0,0,0},{2/3,1/6,0,1/6,0,0,0},{2/3,1/6,0,0,1/6,0,0},{2/3,1/6,0,0,0,1/6,0},{2/3,1/6,0,0,0,0,1/6},{5/6,1/6,0,0,0,0,0}}

#19 Re: Exercises » Bitter die » Yesterday 12:27:47

Hm, let's try the second option. I put my hands together and say the magic words.

#21 Re: Exercises » Bitter die » Yesterday 12:10:54

Yes, but I do not know how.

#22 Re: Exercises » Bitter die » Yesterday 12:08:31

I wanted to do it with a Markov chain, but I couldn't find the formula for the expected number of visits to a state.

#23 Re: Exercises » Bitter die » Yesterday 12:01:10

Which method?

I used the independence of expectation trick.

#24 Re: Exercises » Bitter die » Yesterday 11:57:48

Anyway, this wasn't as hard as you said it would be.

How did you do it?

#25 Re: Exercises » Bitter die » Yesterday 11:50:24

Thanks. I have miscounted something, that's why I got the first answer.

I wouldn't have been so sure of either answer if it wasn't for the simulation.

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