Counting Definition and 392 Threads

I've been playing with a computational system that represents numbers in their simple continued fraction form. That is, CF([a0,a1, ... , an]) =a0 + \frac{1}{ a_{1}+\frac{1}{a_{2}+\ddots\frac{1}{a_{n}}} }Considering what types of numbers such a system can represent, the finite CF's correspond to...

Homework Statement Consider a system composed of 2 harmonic oscillators with frequencies w and 2w respectively (w = omega). The total energy of the system is U=q * h_bar * w, where q is a positive negative integer, ie. q = {1, 3, 5, ...}. Write down the number of microstates of the system...

I am examining the conjugacy classes of S_5. I know that two elements in S_5 are conjugate if and only if they have the same structure when expressed as products of irreducible cycles. Thus, the conjugacy classes are [(1 2 3 4 5)], [(1 2 3 4)], [(1 2 3)], [(1 2 3)(4 5)], [(1 2)(3 4)], [(1 2)]...

Hey peeps, I was bored the other day and wanted to paint something, so I started tweaking images in mathematica to make them eaiser to paint/draw and I came across de jong attractors and the following http://flam3.com/flame.pdf" . Basically I immediately remembered I had forgotten most of...

Homework Statement A poker hand conatins 5 cards chosen from a deck of 52. 1. How many hands are possible a. 4 of a kind b.3 of a kind c. flush d. full house e. straight f. straight flush The Attempt at a Solution When i write (5,2) I mean 5 choose 2 . 1. (52,5) a. I have 13...

Hi, I want to understand the meaning of orbifold counting. Could anyone help me? Background: I will begin my third undergraduate year in Physics in September.

Homework Statement 100 hundred people are to be divided into 10 discussion groups with 10 people in each group how many ways can this be done. The Attempt at a Solution So if we think of it as people on a 10 by 10 grid their are 100! ways of populating the grid and then 10! ways or...

Homework Statement A software company uses a 20 character product key that new buyers of their product must use during installation to successfully install the software in their computers. The structure of these product keys is as follows. Repetitions are allowed unless explicitly...

Homework Statement A computer operating system allows files to be named using any combination of uppercase letters (A-Z) and digits (0-9) But the number of characters is at most 4 , And there must be at least 1 letter in each file name. The Attempt at a Solution So I break this up into 4...

Homework Statement Let r be a positive integer. For any number x, let (x)r = x(x-1)(x-2)...(x-r+1) Show that (-1/2)r = (-1)rr!2-2r(2r take r) Homework Equations by "2r take r" I mean what is usually denoted by (n / r) (written like a fraction but without the bar) and is calculated...

Homework Statement social security number is a 9 digit number. the first digit may be 0 a. How many numbers are available b. How many are even c. How many have all of their digits even d. How many read the same forward and backward e. How many have none of their digits equal to...

I am attempting to write a program to do the work for me. I started in the process by hand and it took about an hour to get through the letter a. So I have a folder with many sub-folders and each sub-folder has at least one sub-sub-folder and then in theses many sub-sub-folders are the...

I stopped posting outside of general discussion when I hit 314 posts. I figured pi was a cool number to stop at and I knew I wasnt going to hit Avagadro's, so why do I now have 618 posts?

Homework Statement ----1. From the digits 0, 1, 2, 3, 4, 5, 6, how many four-digit numbers with distinct digits can be constructed? How many of these are even numbers? ----2. How many integers between 1000 and 9999 inclusive have distinct digits? Of these how many are odd numbers...

Box counting dimension! please help! Hi all, I am working on a problem from Chaos theory, I have to find the box counting dimension of the set {0}U{n^-p} where n is an integer and p>0. I started this problem by considering p=1. So, the set looks like {0,1,1/2,1/3,...}. If I take intervals...

Homework Statement How many was can 3 identical prizes be awarded to 98 potential winners? Homework Equations The Attempt at a Solution Well. I know that if the prizes were unique, the first prize would have 98 possible winners, the second prize would have 97 possible winners...

I need help with this math problem: Show that the set of rational numbers, Q, is countable. and Show that the set of irrational numbers is uncountable.

Hello I am new in string theory and I am wrestling with a paper in Beltrami parametrization. Although I have spend time studying ghosts, brs symmetry etc my knowledge in differential geometry is very limited (for string theory). My question is how do I count practically the grading of an object...

The guiding premise of this thread is the following proposition: If fractals play a role in the behavior of partitions, then maybe, just maybe, they play a role also in the positioning of the primes; and if they do, then who is to say that the two, prime numbers and partition numbers, cannot at...

I don't remember any probability from high school which was over nine years ago. This semester I'm taking Thermal Physics and Probability. So, I'm having to catch up with counting techniques and so forth and make sense of the logic behind the techniques...

Homework Statement Either People of different heights are to be seated in a row. The shortest and tallest in this group are not seated at either end. What is the probability that: a) the tallest and shortest persons are sitting next to each other? (Ans: 1/3) b) there is one person sitting...

Suppose an ant is on a vertex of a cube. On one of the three vertices neighboring the ant, there is a black hole. On each move, the ant travels to one of it's neighboring vertices, being careful not to pass through the black hole. The ant makes N moves in total. How many different paths lead the...

what is "counting rate"? Homework Statement Is "counting rate" the same as "rate of decay"? This problem asks about counting rate, but i can't see this term anywhere in my physics book.. Is it like an alternate term for "rate of decay" (also, counting rate isn't even on wikipedia)...

Hello all, I am in a circuits class now and we are doing our end of the year project. I have decided that I want to do some sort of circuit that counts things. For the actually counting portion of the circuit I am just busting open a cheap little calculator and connecting two leads to the =...

Hi all. If I read in variables entered by the user, how can I check to make sure the correct number of variables were entered? For example, after reading in a data file and making it into an array, I have: echo "To check the data, enter the first element number, last element number and...

Hi all, Entropy uses the 6N dimensional phase space. But ... Roger Balian in "Scientific American" takes one liter gas in a cube and he writes: I can replace the continuous volume by Q = 10^100 sites after having evacuated the speeds (he says this is possible with quantum mechanics) He...

I'm working through Srednicki's QFT text, and I'm continuously vexed by the various numerical factors in diagrams and vertices, as well as the grouping of diagrams. For example, in Chapter 10 (pg 75) Srednicki treats basic \phi\phi\rightarrow\phi\phi scattering processes in \phi^3. He claims...

Hi everyone, I have trouble depicting the difference between these two problems. The first problem uses the multiplication rule to solve while the second problem uses the counting rules (combination) to solve. To me, it seems like both problems could be solved using the multiplication rule so I...

Hello all, I am going through some sample problems exercises in Paul Sally's Tools of the Trade, and am being asked to prove the Fundamental Counting Principle. That is, If A has m elements and B has n elements, then A X B has mn elements. Sally goes on to write that "this is simple to prove...

Homework Statement A license plate has three letters followed by three numbers. Suppose the digits from 0...9 can be used, except all three digits cannot be zero, and that any letter from A-Z with repeats can be used. How many plates are possible? Homework Equations My question is on...

Homework Statement A football team consists of 20 offensive and 20 defensive players. The players are to be paired to form roommates. They are paired at random. What is the probability that there are exactly 4 offensive/defensive pairs. Homework Equations The Attempt at a...

Hi, I have a question about counting (how difficult should that be ;) ) I have the set of tensors in D dimensions \{h_{\mu\nu}, H^{\mu\nu}, t_{\mu}, T^{\mu}\} with the relations H^{\mu\nu} h_{\nu\rho} = \delta^{\mu}_{\rho} - T^{\mu}t_{\rho} T^{\mu}t_{\mu} = 1...

Homework Statement How many different bit strings can be formed using six 1s and eight 0s? Homework Equations C(n,r) = n!/(r!*(n-r)!) The Attempt at a Solution since there's six 1s and eight 0s there are 14 slots. So I'm guessing for the possible six 1s it would be C(14,6)...

nvm i got it

We got some cool weather today along with some scattered showers. My wife was sitting there in deep concentration so I asked her what she was thinking. She said she was counting the seconds between the lighting flash and the thunder. She said that the light gets here much faster than the sound...

In an electric circuit a branch is a part of the network between two points or junctions... I have attached a circuit diagram...Can anyone please confirm how many branches are there in the circuit.I m getting a little bit confused. I think the answer is 7. Plz tell me. V1=Emf source 1...

can someone tell me what is wrong with my code? i am trying to make a code that has 1000000 randomly choosing A or B 1000 times. if A is bigger than B, i want to increment the variable called 'aWins'... when i try to get it to print the screen is blank. i left out the int main and #include parts...

Hi I want to know how astronomers count the number of stars (or any other celestial object for that matter) in the sky. Will they take a photograph and do some signal processing like counting the number of brightest spots? Is it possible to count accurately since there are billions and...

Dear Friends, I have a question and would be pleased if you help me by suggesting a paper or book to study. Let A={1,2,...,n}. We consider all the subsets with k elements. How many of these sets have a sum of r ? e.g. for n=6, k=3, r=10 {1,3,6} {1,4,5} {2,3,5} Hense the...

So I am taking intro to stats and probability and I am having trouble understanding something that may be quite difficult to explain in counting. Let me start by telling you what i understand The choose function i.e (6 C 2) will take six elements and create a SET of 15 TUPLE's, in which...

Homework Statement #include <stdio.h> main() { long nc; nc=0; while (getchar() !=EOF) ++nc; printf("%ld\n", nc); } Homework Equations The Attempt at a Solution I'm trying to learn C and am using the book "C Programming Language". It says that...

Homework Statement Z plays a game where independent flips of a coin are recorded until two heads in succession are encountered. Z wins if 2 heads in succession occurs. Z loses if after 5 flips, we have not encounter two heads in succession. 1) What is the probability that Z wins the game...

Homework Statement Let A = {1,2,3} and B = {1,2,3,4,5} Find the number of functions f: A -> B so that f(1) = f(2) Homework Equations The Attempt at a Solution I'm just reviewing random questions for my final on Tuesday and I came upon this question. Seems to be a counting...

Homework Statement 1. How many strings of eight English letters are there if no letter can be repeated? 2. How many strings of eight English letters are there if X is the first letter and no letter can be repeated? 3. How many strings of three decimal digits do not contain the same digit...

I was confonoted with the following problem today, and thought it was interesting enough to discuss it here: Homework Statement You have a box with balls numbered 1,2,3...n. Suppose you began, by taking out balls numbered 1–100 and then put ball 1 back. Suppose you then removed balls...

Homework Statement Prove that, in any set of n + 1 positive integers (n ≥ 1) chosen from the set {1, 2, . . . 2n}, it must be that two of them are relatively prime (i.e. have no common divisor except 1). ( Hint: two consecutive integers are relatively prime. Make boxes labelled by pairs of...

Let K1, K2, K3, . . . be an infnite sequence of sets, where each set Kn is countable. Prove that the union of all of these sets K = Union from n=1 to infinity, Kn is countable. I tried to start, but I don't even understand the question Need some idea on how to start

Hi, I wondered if anyone can help. I have some linear equations in which I've found various possible solutions to the variables using NSolve function. For example, for x1, x2, x3 and x4, it has given me ~14 different possible combinations for each x. Is it possible to do a count so if the...

I'm taking a course that uses matlab, and for one assignment, we need to write a function that, among other things, counts the number of rows and columns in any given numeric matrix. The thing is that we're not allowed to use any built-in functions. No x = size(mat). No length(mat). It all...

Homework Statement Specifically, How many ways can you divide up 20 distinct balls into 5 distinct boxes so that no box contains more than 10 balls? Homework Equations This is similar to another problem in which we have to find the number of ways to divide up r balls into k boxes...