Counting Definition and 392 Threads

Hi Is there a relatively easy way to calculate the number of partitions of a number given the maximum term and the count of terms? A couple of examples: 25 has four partitions with five terms where each term is unique and the largest term is 8 {8,6,5,4,2} {8,7,5,3,2} {8,7,5,4,1} {8,7,6,3,1}...

Homework Statement 1) 100 of the 5-element subsets of {1, . . . , Y } have the same SUM. (Fill in Y . Make Y as small as you can, however you need NOT prove that it is smallest possible. You might need a calculator.) 2) Let FUNC be the set of all FUNCTIONS from N to N. Show that FUNC is...

Let me prefix by stating that this is not really a homework problem, just something I am curious about. I posted it here because it is probably too easy to go into the "big boy" forums :smile:. Last night my wife said she needed a 23% on her final to maintain a grade of A in her course. I...

Consider line segments oriented vertically, horizontally, and either diagonally. The individual segments may be seen as stretching between an imaginary 12 and 6 o'clock; or 1:30 and 7:30; or 3 and 9; or 4:30 and 10:30. Thus give them singly or doubly a common center. By using them so -...

[SOLVED] Counting Seating Arrangments of Couples at a Round Table I'm reading this example in my probability book which is I'm not understanding. It says: There are 19! ways of arranging 20 people around a table. The number of arrangements that result in a specified set of n men sitting next...

for example...is there some software that will let me do all my calculations mod 2 or something? free software would be preferable thank you

let's say for example, I am interested in using mod 2 integers ({0,1}) to get rid of certain coefficients. Now, I am most interested in eigenvalues. How will this affect my eigenvalues compared to the original matrix (normal counting)? Is there anyway I can "retrieve" the original eigenvalues?

Homework Statement How many 3 digit numbers can be constructed from digits 1, 2, 3, 4, 5, 6, and 7 if each digit may be used once only and the number is odd? 2. The attempt at a solution What number do they speak of? The resulting 3 digit number? How do I approach this equation?

[SOLVED] Funky Counting Question Problem. We have 20 thousand dollars that must be invested among 4 possible opportunities. Each investment must be integral in units of 1 thousand dollars, and there are minimal investments that need to be made if one is to invest in these opportunities. The...

Beta particle counting efficiency?? Hi! Can anyone tell me what counting efficiency means? For example if it's put into a question as: "shielded beta counter with 85.7% counting efficiency, 845 counts are accumulated in one week" what does it mean? How I understand it so far is that it's...

So today I was doing a problem out of my book for practice, and I came across some interesting results. Show that among any group of five (not necessarily consecutive) integers, there are two with the same remainder when divided by 4. a set of consecutive integers 1 mod 4 = 1 2 mod 4...

I am in my final year at high school and i have choosed physics exam, there left only two weeks until it, have anyone ideas how to prepare for it in such a short time?

To open a safe, 4 number buttons must be pressed, in the correct order. Over time, the 4 numbers buttons of the code fade. A thief notices the faded buttons, so knows that the code consists of those 4 numbers. How many possible codes are there? 4 numbers can be arranged in 4! different...

show that there is a normal subgroup of G of order 5 when G is a group of order 30. My friend just called me with this problem, he said the usual method of solution fails. (i.e. using sylow and then showing that the subgroup is unique and deducing that it must therefore be normal), I told him to...

Still awake, and not even drowsy at the moment! Maybe it's the cumulative lethal dose of caffeine, or the painful frostbite on my ear (-8C outside, very windy), or the pleasant warm glow of the gray PF background - I'm still going after 90,000+ seconds of wakefulness! (okay, excluding the brief...

Homework Statement There are 285 math students. First homework was completed by 166 students, second by 148 and third by 129. First and second was completed by 108 students, first and third by 83 and second and third by 25 students. How many students have not completed at least one homework...

Way back in July 2004, kurious asked: Just thought I'd mention that Einstein himself proposed an interesting method for "counting" the solutions of a PDE which may have been indirectly inspired by the landmark work by his colleague David Hilbert on what is now called "the hilbert polynomial"...

Suppose you pick a k-element subset of {1, 2, ..., n}, call it A. How many of the other k-element subsets have k-1 elements in common with A? I've been at this for quite some time, but I always overcount. Can anyone help me out? My last attempt gave me (n-k+1)k - \frac{k(k-1)}{2}, which isn't...

Hello everyone. I'm not sure if I'm doing this right or not. The problem asks: Consdier the set of all strings of a's, b's, and c's. a. make a list of all of these strings of lengths zero, one, two, and three that do not contain the pattern aa. Okay so i have the following: note e: stands...

Hello everyone, I'm having some issues on this problem: A coin is tossed ten times. In each case the outcome H (for heads) or T (for tails) is recorded. (One possible outcome of the ten tossings is denoted THHTTTHTTH.) I got a, d right i believe. but I need someone to check if i did the...

I am going through Hardy's book on number theory.The following theorem I do not understand. theorem 10: pi[x] >= loglog x where pi[x] is the prime counting function and >= stands for greater than or equal to The arguments written in the book are very compact.please help .

Can anyone tell me if Riemann's Prime Counting function can be solved by residue integration? Here it is: J(x)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{ln(\zeta(s))x^s}{s}ds which has the solution: J(x)=li(x)-\sum_{\rho}li(x^\rho)-ln(2)+ \int_x^{\infty}\frac{dt}{t(t^2-1)ln(t)} I...

I have very disappointed myself. I am forgot how count time, if car drives example 45 km(kilometre) distance and it's speed is 100km/h ( kilometre per hour). How i know what is time? equation is t = s/v (t = time, s = distance and v = speed) and now equation is t = 45km...

What's the closest way that nature counts or does math? I was thinking either symmetry (perhaps crystal growth or structure) or population (maybe by equilibrium?), but that just doesn't feel complete. I guess those could be considered to be numbers, but there isn't any computation going on...

This is the question, and we're supposed to answer if it's true or false: If A is a countably infinite set, and A is a proper subset of another set B, then B is uncountable. I thought this was false, because if A is infinite and countable, then B should also be infinite and countable in...

How I can write a program which reads a sequence of integers and counts how many there are. Print the count. For example, with input 55 25 1004 4 -6 55 0 55, the output should be 8 because there were eight numbers in the input stream. Please help.

Hi guys! I made a program in C, which count vowels on text, but it doesn't work. Thats the code i have writed: #include <stdio.h> #include <string.h> int main() { char buffer[80]; int counter; printf("Enter a line of text: "); fgets(buffer, sizeof(buffer), stdin)...

Hi, I've done more questions. Hopefully the wordings on these word problems aren't vague. Could someone take a look? I'm not sure if I've thought about the problem the right way. :smile: Thanks v. much in advance.

Hi All, I'm taking discrete math as part of my computer science course. i don't quite understand why i didn't get the answer in the book. Please take a look at my attachment and see where have i gone wrong. Thanks. :blushing:

The doughnut shop has 5 kinds of doughnuts: a, b, c,d and e. There are unlimited supply of each kind. In how many ways can you order a dozen doughnuts? Well, my first instict is to simply 5^12. But then I realize aaaab is the same as baaaa... hence the order doesn't matter. I'm trying...

1.The integer 388,800 can be factored with primes as 2^6 × 3^5 × 5^2 (a) How many unique divisors does 388,800 have? (b) How many of these factors are even? odd? I have no clue how to do this. There are no similar examples in our textbooks or notes. I searched up counting divisors on the...

I want to find out how many paricles on random move passing through a little hole ? There is no condition or force acting on eachof them. :biggrin: :biggrin:Thanks guys:biggrin: :biggrin:

Please help I have ALOT of questions! 1.)Starting at 888 and counting backward by 7, a student counts 888, 881 and 874, and so on. Which of the following numbers will be included? a) 35 b) 34 c) 33 d) 32 e) 31 Ok, so I by using the calcuator the aswer is 34, but how would you calcuate...

[SIZE="3"]Counting Game This forum word game is simple. You start of with "1" and the next person posts the number following it (2), the next posts the number following it (3) and so on. No double posting If an incorrect number is posted, then carry on with the correct number. I'll...

Do you know of an attempt to disprove the existence of a formula which predicts all prime numbers, as opposed to the accustomed attempt to derive one?

I am working on a problem in which there are 100 widgets. I need to find how many samples of size 5 there are, which I found to be 75,287,520. No problem there. I am not sure how to go about the next part, however. In the original set of 100 widgets, 3 are broken. How many of the samples of...

I hope that some of the folks (Mike, Howard, Patrick, Robin) who have engaged in the other threads [1][2][3] on outcome counting (ie Patrick's APP) see this thread. Starting with the Feynman path integral formulation of ordinary quantum mechanics, it is pretty straightforward to derive...

I need java to read a string and count how many characters are in it. I know there's some class that can do this. What is it?

imagine a 8 letter word, how many possibilities are there to arrange letters in the alphabet (26) that start with BO(in that order) OR end with BO (in that order), if letters can be repeated? This is my work: 1 * 1 * 26 * 26 * 26 * 26 * 26 * 26 = 26^6 + 26 * 26 * 26 * 26 * 26 * 26 *...

So, I'm currently looking for a job. I've been telling myself all through school that my current car has to last me, and it has... barely. It currently has no ABS (the modulator is bad, but the brakes still work) so it can't go through the Maryland emissions test which is due. It is leaking oil...

Some my puzzles of “coincidence counting” When I read literatures concerning with two-photon interference experiment, the “two-photon interference patterns” are always got by means of so called” coincidence counting”. My questions are: What is the coincidence counting? What the essential is the...

hi, I have been trying to solve the following questions (and similar) for 2 hours now without any major success. the questions are: 1) In how many different ways can 7 different books be arranged in a row if a. 3 specific books must be together b. two specified books must occupy the ends (I...

http://www.gamespot.com/news/6141517.html Is it just me or is that a lot of people playing one game. Whats so special about World of Warcraft anyway? Any hardcore WoW players on PF.

I have the definition that if F is a finite field then a \in F is a primitive root if ord(a) = |F|-1. Now what I don't understand is how exactly are there \phi(|F|-1) primitive roots? (Note: This material is supposed not to use any group theory.)

Is there a way to systematic way of counting the number of distinct homomorphisms from one ring to another?

Attempts to make the Born rule "emerge" explicitly from outcome counting I would like to compare and contrast the various attempts to date to reconstruct the MWI so that it: 1) assumes outcome counting instead of the Born rule, but also 2) makes correct experimental predictions. This is an...

A typical stat mech. question is the following: If I have 5 bosons and energy E to divide among the bosons, what is the total number of possible configurations? I can't remember this answer, so if someone reading this can post it that would be appreciated. Now, I want to ask a slightly...

Prime counting function-- no error. I have developed a prime counting function with no error; it returns the exact number of primes equal to or less than any number one chooses. I am rather ignorant of progress in this field... Has this been done before? Please, ignore any skepticism you...

I have a question about an example in my physics notes. It considers Nitrogen at room temperature and calculates p*r and finds this to be greater than h-bar and so it is consistent with the uncertainty principle: p*r = 2.4*10^-26 > hbar = 1*10^-27 It says at room temperature the momentum...

How many americans still drive thoughs old V8 tanks ??