Bignose

Did you guys all forget that this is a discussion forum? The OP starts a thread on a forum, by definition, because they want to discuss something. Then OP in a matter of a very short time says (paraphrasing) "well, actually I can't discuss it". So... if there isn't anything to discuss, why are we surprised that the thread was closed? There is little need to document everyone asking questions and providing critiques that OP has stated they cannot or will not answer. Thread closure is the logical next step; if there is to be no discussion, then there is no point on a discussion forum.

If all 11 variables and all experiments are independent and identically distributed, then you can use the binomial distribution to calculate what you need https://en.wikipedia.org/wiki/Binomial_distribution

And what I'm saying is that no equation can ever give you something correct if you ask the impossible... There is no correct equation to tell you what the odds are to do something impossible, in your case it is impossible to draw more cards than what are left in the deck. If you are programming this in a system somewhere, you need to check the inputs to limit the calculation only to actually feasible scenarios. If someone asks the impossible, you return an error, or 0, or a message explaining the impossibility, or whatever is appropriate to your system. You're fundamentally asking of the math an question it cannot answer. It is like asking 'how heavy is the color blue?' or 'how many candle lumens in a hogshead?' or 'how do I pay a $100 electricity bill when I only have $15 in my account?' Math is not the solution to impossibilities.

Well, sure. The math says something is wrong when you attempt the impossible: to draw more cards from the remaining deck than are in the deck, H > (D - T). Its no different than asking what happens when you try to lift a boulder with infinite mass or try to divide by zero. The fact that the math can't be done indicates that you're asking for something impossible and you need to check that what you've set up the problem to do is correct.

I think your investigation should begin with studying the spherical coordinate system: https://en.wikipedia.org/wiki/Spherical_coordinate_system Understanding that will go a long way toward answering your questions.

1) I am specifically asking WHERE the 'center' of a vector is? Because you need to know where that is before you drag anything through it. I have never heard the term 'center of a vector' before, and just wanted to understand. As near as I can tell, this is term you made up and didn't bother to define. 2) no need for name calling. Just asking a question. If you are going to name call when someone asks a question, then expect your time here to be short.

Was this supposed to address wtf's comments? Because not only have you failed to define what is meant by 'inverting a sphere' you introduced another meaningless mathematical term -- the center of a vector. Please define both of these terms explicitly.

no. not ok. Firstly, this is a forum. Everyone who follows the rules is allowed to post. Secondly, it is just advice. It is worth exactly what you paid for it. Feel free to take it or not. I am simply trying to help you by showing you the tools that, well, every other person who does math uses. Again, if you have ideas on a certain subject, it usually helps to learn the terminology and language of that subject. One would think that being able to better describe an idea would be a good thing. But hey, you do you. Do whatever you want.

then, mathspassion, you need to go and learn some algebra. Because the 'proof' is simply variable manipulation. If your namesake is true, and you have a passion for maths, you should be trying to learn as much of it as you can. And algebra is a very fundamental building block of math. Not only that, but if you learn algebra, you'll be able to express ideas -- like the one that started this thread -- into a more succinct and generally understandable format. Strange was not the only one who struggled to understand what you were trying to say. Learning the terminology and nomenclature that you will learn in algebra will help you convey your messages much, much easier. It is worth the effort.

Dude. Just multiply it out. This is like basic algebra. Post here if you need help, but if you just expand each term on the right hand side, you'll see the terms cancel and prove the identity.

So... you've converted 1 number lookup (the N) and 1 multiplication (N*N) into 4 number lookups (have to find the numbers on the square snake thing), 2 multiplications, and 1 addition. I guess I fail to see any practical reason for it, tho that has been said about a lot of math.

I didn't think that there was much mystery about Buffon's needle, except the fact that so many so-called 'real world' experiments of the problem ended up just a little too perfectly in line with predictions many, many times throughout the years. In my opinion, if you want something that is a bit more mysterious, check out Bertrand's paradox. https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) It is my favorite example of 'probability requires you to be extremely careful in your definitions'

272 integer results... do x, y, and z have to be integers? The original problem statement did not state that.

Um, 1200-980 = savings of 220? If it cost more to get two quotes, then that comes off the savings.

How do you handle the fact that there are mathematical proofs that there is only one unique zero that obeys the axiomatic rules for how a zero operates?