Puzzle Definition and 618 Threads

I am given that The kth moment of an exponential random variable with mean mu is E[Y^k] = k!*mu^k for nonnegative integer k. I found m^2 (0) = (-a)(-a-1)(-beta)^2. The answer I found is however mu^2+a*beta^2 which is different from the k! From the given formula. Could someone help me figure it...

Would it be possible for 2 identical objects to orbit their center of gravity in an otherwise empty universe? I am guessing that the answer is no, but how would GRT address / answer that question? Would the objects’ spins affect the answer?

I am reading H. Croom's Principles of Topology and in page 139, he gave an example 5.2.5 to show that two points in the same member of any separation of the topological space X, might not belong to the same component of X. In this example, the space X is a subspace of 2 dimensional Euclidean...

Homework Statement Two trains, A and B, are moving towards each other with relative speed 0.8c. The passing of the two trains (from when their fronts align to when their backs align) takes 20% longer as observed from train A as is does as observed from train B. What is the ratio of the length...

Find two sets P and Q satisfying I) P and Q are completely contained in the square, in R2, with vertices (1, 1), (1, -1), (-1, -1), and (-1, 1). II) P contains the ponts (1, 1) and (-1, -1) while Q contains (-1, 1) and (1, -1). III) P and Q are disjoint. IV) P and Q are both connected sets.

There are 111 people in a competition. The competition has 4 boxes and 4 jewels. Each box is identical and is completely opaque (i.e. you cannot see inside the box once it is closed). The jewels are all different: diamond, ruby, emerald and topaz. Everyone in the competition knows this. The host...

$\dfrac{\square}{\square \square}+\dfrac{\square}{\square \square} +\dfrac{\square}{\square\square}=1------(*)$ fill in the above 9 blanks with 1~9 without repetition and satisfy (*) (you should find it using mathematical analysis,and show your logic,don't use any program) in fact there...

Homework Statement I can't follow the math of the very last line. It's really annoying me because I know its not supposed to be hard, I have tried multiplying top and bottom by k1+k2 and all kinds of rearranging but I'm not sure how they get from w1 - w2 / k1 - k2 = c (k1-k2) / (k1-k2)...

This is question 2.30 from the 2nd edition of the Purcell book on Electricity and Magnetism. It's an interesting puzzle, and I've been thinking about it for a while, but I can't make any headway, so maybe you guys can do better. Suppose you have a uniformly charged cube (charge density ρ) of...

NEW CHALLENGE: This challenge was a suggestion by jgens. I am very thankful that he provided me with this neat problem. A 15-puzzle has the following form: The puzzle above is solved. The object of the game is to take an unsolved puzzle, such as and to make a combination of...

the 4 pictures to the left follow a pattern. 1 of the 3 pictures to the right matches that pattern. which one?

If f(x) is a square-integrable real-valued function on the reals, then we can define an auto-correlation function C(\theta) via: C(\theta) = \int dx f(x) f(x+\theta) I'm trying to get some insight on what C(\theta) is like, for small values of \theta in the case in which f(x) is highly peaked...

Homework Statement Johnny is swinging (on a swing) at a velocity of 4m/s when he is 56 cm above the ground. What is his maximum height? Johnny is 45 Kg. Homework Equations Pe = mgh Ke= (1/2)(m* v^2) Total energy= Pe + Ke The Attempt at a Solution I tried setting the Ke equal to the Pe...

Hi guys , this topic is specialized to post some puzzles and challenge members to solve them. I will post the first puzzle and anyone solves it should try to post another one . If he/she didn't have any, in half a day anyone is allowed to post another challenging problem The scope of...

Homework Statement A bus travels 650km in 3 hours less than the other bus whose speed is 15 km/h slower than the speed of the first bus. A. Assemble the equation. B. Solve the equation and state the speeds of the buses. Homework Equations The Attempt at a Solution V = d / t...

An airplane was carrying 80 bricks. One fell off from the plane. How many bricks will be there in the plane?

Arrange the numbers: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 such that the summation of each two successive numbers is a complete square easy interesting question

There was a thread on another forum that I'd like to share. Is $f(x,y) = x \sqrt{1+y^2} + y \sqrt{1+x^2}$ associative?

You're in an empty room. You have a pen and paper. Every 10 seconds you have to write what you did for the last 10 seconds. What would you write after 20 seconds? Think 'outside' the box (no pun intended).

"... the first direct evidence of pear shaped nuclei in exotic atoms. The findings could advance the search for a new fundamental force in nature that could explain why the Big Bang created more matter than antimatter—-a pivotal imbalance in the history of everything." Any insights...

Imagine a 8x8 chess board, is it possible to place 8 pawns such that they are of different distances from one another?

came up with a different answer than someone posted on this, what do you all think? Say you have one bacterium now. In any minute, each living one has a quarter chance of dying, a quarter of staying still, a quarter of splitting into 2, and a quarter of splitting into 3. What is the...

I posted this on my website a couple days ago. I like puzzles a lot, so I figured I would share it here and see how many people could figure it out; enjoy!;) A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those...

Hello Everyone, This forum is for the posting of problems and puzzles which our members find challenging, instructional or interesting and who wish to share them with others. As such, the OP should already have the correct solution ready to post in the event that no correct solution is given...

This is a puzzle based on a purported "refutation of GR" on http://finbot.wordpress.com/2008/03/05/no-black-holes/, which is also the subject of a subthread in this Hacker News discussion. (Btw, the Hacker News discussion contains my answer to the puzzle if you scroll down enough, so you're on...

Here's a nice challenge that I made up thinking about compressing data one night... Print out a number that you can read within it: The numbers 1 to 20(easier) or 1 to 99(very hard) Rules: →Can be read forward or backwards and use same numbers eg. 123 you can read...

I need help with the following puzzle. Thanks. :smile: Of the following I am none; Mozzarella, Swiss, and Monterey Jack. However, I will always be made When you begin at the end. What am I?

For few days I am thinking to write a code in FORTRAN to solve the sudoku puzzle. At first it seams simple but I have no luck writing this code. I am wondering if there is any written code to solve this puzzle. I hope Sudoku puzzle is known for members here. en.wikipedia.org/wiki/Sudoku

Homework Statement http://web.stagram.com/p/362176186041336029_243276631 this is a link to the question. I'm stuck on 2a and b Homework Equations I don't understand if the voltmeter is reading 6v why the light is not receiving 6v? And why would a transistor help this problem? The...

Homework Statement This is the diagram http://s1302.beta.photobucket.com/user/Rameel17/media/dd_zps43d04d44.png.html A single large circular Olympic ring hangs freely at the lower end of a strong flexible ring which is firmly supported at the other end. Two identical beads each has a mass...

Hello, I need some help with this question, it is not very clear and I find it hard to translate from text to math... Some company has found that x units of it's product can be sold for p$ a unit when x=1000-p. The cost of producing x units in a day is C(X)=3000+20x. A. Found the income...

There's an well-known puzzle that goes as follows: You have 12 balls. They look identical, and 11 of them have the same weight but one of them, you don't know which, has a different weight. You don't even know whether the odd ball is heavier or lighter than the others. You have an...

Hi everyone, I am a student studying semiconductors and solid-state physics. I have a question which is haunting for several years. That is about the definition of electron affinity in solid-state physics. Its definition in solid state physics may be quite different from that in chemistry...

Quasar Mass-Luminosity High Mass Turnoff Evolution and a Synchronization Puzzle It is unusual that a generation of researchers has the opportunity to completely rewrite, to replace major established scientific theories. The observation that quasars are turning on and off, at a specific mass...

A number of aliens, who have just dropped in from another planet, emerge from the spacecraft . (i) There is more than one alien (ii) each alien has the same number of fingers (iii) each alien has at least one finger on each hand. (iv) the total number of fingers of all the aliens is...

I came across this little teaser on Another Forum. I found a solution, more or less by trial and error. I don't know if there is a more systematic way to tackle it.

This exercise is from my Discrete Mathematics course and it requires a step by step solution, backed up by logical equivalences or deductions made based on the rules of logic. 5 students, Oliver, Simon, Peter, Bob and Christie all seniors at Harvard, come from one of the following cities...

Found this challenging: A,B and C work at same speed. When all 3 of them plant a field with D, the job gets done in 5 hours. When all 3 of them plant the same field with E, the job gets done in 6 hours. The field was divided between the 5 workers in proportion to their 5 work rates, into a...

I was taught that a particle is assigned to a unique quantum state. As a specific example, two bound electrons can't have the same quantum numbers in an atom. And likewise one and only bound electron is assigned to one quantum state in an atom. Yet, I am reading several solid state books and...

So I was browsing the Wikipedia article concerning The Monty Hall Paradox, and I seem to take great issue with the assumption that switching results in a 2/3 probability of winning a car. (hold on pressed enter by mistake... editing now watch this space) My reasons are as follows (and I don't...

I am trying to fill in some of the gaps in wikipedia's proof of Godel's diagonal lemma, which is a crucial step in proving his first incompleteness theorem. There is a step that the wiki proof just takes for granted, perhaps because it looks obvious. But I am unable to find a formal proof of...

I was doing a brain treaser where the letters A-H had to be put into an array 2 by 4 such that no letter is adjacent or diagonal to a letter one unit different. That is a C can't be above, below, to one side of, or diagonal from a B or D. I solved the problem but the thought...

Hello, This is a question I've been working on out of blundell and blundell, http://imageshack.us/a/img560/3342/entwopy.jpg The red box is my answers to the question which I am pretty sure are ok. I am having trouble with the very last part of the question. By the logic of the...

Homework Statement The A-string (440Hz ) on a piano is 38.9cm long and is clamped tightly at both ends. If the string is under 667-N tension, what is its mass? I can't figure out which equations to use. Anybody know?

Homework Statement A basketball player is standing 9.5 m from the basket, which is at a height of 3.1m. she throws the ball from a initial height of 2m at an angle of 35 degrees above the horizontal. The ball goes through the basket. Determine intial velocity. PS Assume the max height of the...

Hi, I am searching for a smart way of calculating all numbers in a special matrix kind of game. The game board consist of numbers between 1 and 9 in a 4x4 matrix. Swiping over numbers will either add up (swiping left or right), subtract (swiping up or down) or do nothing (diagonal...

Hi, I am struggling with the following puzzle. Six people, on their way out from a restaurant, waiting to collect their hats. The attendant mixes up the tags and hands the hats over randomly. What are the chances that at least one of them gets the right hat? I tried to find the...

Homework Statement lim_{x→∞}( \frac{x^x}{(x+1)^x} )^2 2. The attempt at a solution Well this limit is actually my most recent step to solving this problem. The initial problem was determining whether or not the following infinite series converges: \sum{(\frac{k}{k+1})^{2k^2}} The...

Hi, I feel really out of my depth and this is just to satisfy a personal frustration. I can see that the light from both flashes should reach a passenger on board the train at the same time and also that it should hit from the front first, but I just can't seem to make it work in my head. Are...

I'm drawing a scene with, trying to size my font correctly. I have both a big and small version of the layer on the screen at the same time. I want to set the font in a label on this layer (both the thumbnail and the full size version) to, for example, size 30. This works fine for the full...