Puzzle Definition and 618 Threads

Find an elegant solution to this question: if 4 players are playing a game where they each are given a random number from 1 to a million, and the largest number wins, what is the expectation value of the winning number?

I don't know if this already been posted but here it goes: What is the Cost of a book that costs 1$ plus half of its price?

You have a pile of N stones. You do the following: you take a pile and separate it into two smaller piles, multiply the numbers of stones in these two piles, and write this number on the blackboard. You do that until there is N piles with only one stone in each. Then you take a sum of all...

I'm an avid Geo Cacher (for more info on it visit www.geocaching.com) and I'm trying to solve a problem to find a geo cache. Can anyone help me with it? A Happy Buddha stops to take a rest while ascending an incline. As he rests on the incline, the coefficient of static friction (mu) is...

Homework Statement I was flicking through the newspaper the other day and noticed there is a type of puzzle where words are added together to form a sum. Each letter represents one of the digits 0-9, for example: FUN +JOKE =HAHA and the aim of the puzzle is to find which...

Hi every one. Im new on this forum,and my question is my reason for joining. iv seeked this question for a long time now,and it confuses me.The answer may be very simple to a peron that already knows the answer,me on the other hand... ! hasnt got a clue...

Right this is the question, Determine the yield stress for a metal with an average grain diameter of 0.045mm, if the yield stress for a metal changed from 650Nmm^-2 to 720Nmm^-2 when the average grain diameter decreases from 0.054mm to 0.037mm. I cannot figure this out, I've been trying...

I just thought of this. I think I know the answer to it now, but it took me a little bit of thinking. Maybe someone who teaches high school physics might find it useful. - - - - - I have a battery-powered toy car. I turn it on and it accelerates from speed 0 to speed 1. (I'm leaving...

Game Theory a problem which is a bit similar to the "Impossible Puzzle" From numbers 1 to 10, two integers X, and Y (not necessarily distinct) are chosen by a referee . The referee informs secretly to Joe the integer U where U = X + Y . The referee informs secretly to Bob the integer V where V...

I found this puzzle in some other forums. I found it to be very difficult. Maybe somebody would like to that a crack at it :smile: Anyway, here it is: The human race spread out to the stars, eventually terraforming and colonizing thousands of planets. On one planet, P3, they decided to...

Why is it possible that an object can be found in the same place in different times but can not be found at the same time in different places?

ok, so here's the problem: given a 3 x 3 x 3 cubic system of vertices, a starting vertex, and an end vertex, how many paths that pass through all vertices ONLY ONCE and start and end at the given vertices(for example let's say the starting and end vertices are two opposite corner vertices) can...

Homework Statement A puck of mass 30g slides across rough ice, experiencing a frictional force of 0.2N. If it was moving at 10km/h when it hit the ice patch, how long did it take to stop? How long was the ice patch? Homework Equations The Attempt at a Solution I don't think this question is...

What's going to happen?

on a sheet of paper, you have 100 statements written down. the first says, "at most 0 of these 100 statements are true." the second says, "at most 1 of these 100 statements are true." ... the nth says, "at most (n-1) of these 100 statements are true. ... the 100th says, "at most 99 of these...

http://www.cut-the-knot.org/Curriculum/Games/Skyscrapers.shtml I wonder of they could make it more like sudoku where there's a 9x9 latin square made out of 3x3 subsquares where only certain numbers of skyscrapers are visible in each rown & column of each subsquare. & beware the creepy eyes...

Homework Statement Largest known prime is the no... P = 2216091-1 consisting of 65050 digits. Show that there exists another prime that ends in the same 65050 digits as P.Homework Equations none The Attempt at a Solution Sorry, but I have totally no ideas for this one. Comes from a Math...

http://blogs.nationalgeographic.com/blogs/news/breakingorbit/2010/11/new-dark-matter-map-hubble.html?source=link_tw20101112hubble" i found this article interesting , so shared here

Homework Statement N is divisible by 4. N! has exactly 50 zeros. Find N. Homework Equations In case anyone younger doesn't know, Y!=Yx(Y-1)x(Y-2)x(Y-3)x...x3x2x1 The Attempt at a Solution No idea.

Here's a little puzzle that I thought of earlier. I gave it to my roommate and he wasn't able to solve it without a pretty good hint, but I'm sure somebody here will get it. |A|+|B| = 2 |A+B| = √(2) What are A and B? (The bars are absolute value signs, and the " √(2) " is the square...

Homework Statement The 70kg student in the figure balances a 1200kg elephant on a hydraulic lift. A second 70kg student joins the first student. How high do they lift the elephant? diameter of the piston elephant is on = 2.0m diameter of the piston student is on = 0.48m The liquid inside...

We know the temperature of a BH is related to the area of it's event horizon. So we can imagine if we are in a very cold universe with a very nice detector measuring the temperature of a black hole and being able to infer it's radius. Great. Now, I want to explain the difference between...

Here is a brain teaser I came across recently. Ten prisoners are arranged single file in a line. They are sorted so that the shortest prisoner (prisoner #1) is in the front, and the tallest prisoner (prisoner #10) is in the back. The are all looking forward (in the direction of #1). They...

Homework Statement Suppose that two people are dividing two cakes using the following rules: 1. The first person divides the first cake into two pieces in any fashion. 2. The second person then chooses which of the two cakes they will get to choose the first piece from. 3. The first person...

I was wondering what would be the largest possible value for a determinant, for a 3 by 3 matrix whose entries can only be 0 or 1. My solution is the following: 1 0 1 1 1 0 0 1 1 With a determinant of 2. Can anyone go any higher, or better yet is there an algebraic algorithm to...

Homework Statement Two farmers have no more than 15 cows. They get as many dollars for each cow as they have cows. For example, if they have 3 cows then they get 3 dollars per cow so a total of 9 dollars. After taking this money they bought as many sheep as possible at $10 a sheep. The...

1. A force acts on a 2 kg mass and gives it an acceleration of 3 m/s^2. What acceleration is produced by the same force when acting on a mass of (a) 1 kg? (b) 4 kg? (c) How large is the force? Answers: (a) 6 m/s^2 (b) 1.5 m/s^2 (c) 6 N 2. - 3. I can't figure out what formula to...

1. What is the average force exerted by a shot-putter on a 7.0 kilogram shot if the shot is moved through a distance of 2.8 meters and is released with a speed of 13 m/s? 2. F=ma, x = vo t + 1/2 at^2, v=vo at 3. I think you get time by using D = vt, but when I use this time and...

The drawing shows two thermally insulated tanks. drawing: http://www.webassign.net/CJ/14_26.gif They are connected by a valve that is initially closed. Each tank contains neon gas at the pressure, temperature, and volume indicated in the drawing. When the valve is opened, the contents of the...

I got this from Brainteaser Physics. [PLAIN]http://img820.imageshack.us/img820/4614/lostenergy.jpg

On average, how many times do you need to roll six dice together to see all six different numbers turn up within a single such group roll?

I'm reading Ince on ODEs, and I'm in the section (in Chapter 5) where he talks about the Wronskian. There are quite a few things here that I don't quite understand or follow. I'm not going to get into all the details, but briefly, suppose we have the Wronskian of k functions: W =...

Hi, I'm a new learner of CM and I was stuck at the very beginning. TT The transformation equation is ri=ri(q1,q2,...,qn,t) I wonder why t should be in the bracket. Aren't r determined by these independent coordinates？ Isn't t already contained in them?

Look at the attached 2 pictures. Tell me in which structure Pipe C will have more water pressure and I can get more water from pipe C. Some info :– Pipe A – Bigger in size, Pipe B – 1” pipe (1 inch), Pipe B – 3/4” pipe (3/4 inch)

Hello, I'm studying for a final exam and I'm having trouble with this particular question. I attached the data required to solve the problem. I am required to fill in the missing information in the data. I've defined the acronyms below: SSE = Sum of Square Errors MSE = Mean Square of...

Homework Statement If A is an acute angle and sinA = cosA Find the value of 2 tan2 A+ sin2 A-1 Homework Equations The Attempt at a Solution I well tried this way >> 2 (sin 2 A/cos 2A) +sin 2 A-1 = 1+ cos 2 A But I am unable to get the 'value' the answer given in the book...

I just realized I don't even have to do this problem, but I've thought too much about it, and at times like this I tend to be a bit OCD. If someone could just get me started on the right track of thought that would be great! Q: In figure...

Homework Statement Ali is making solids out of cubes . Each cube has a volume of 27 cm^3. The diagram shows one solid Ali made . It has 10 faces and a volume of 108 cm^3. Ali made a solid out of the cubes that has 9 faces.What is the smallest volume in cm^3 the solid could have? Homework...

I have designed a spring launcher for my class and it works really well using the range equation...x=sqrt(Rmg/KSin2(Theta)). So I have made a contraption that displaces the spring by x metres. I even have re-arranged and have it working using angles of launch and determining the range (R)...

Homework Statement A fire-hose must be able to shoot water to the top of a building 35.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m³.s¯¹ and shoots out of a round nozzle. (a) What is the maximum diameter that this nozzle can have? (b) If the only...

Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero. ABCD*EF=GHJB*KE, and: (EH)2 + (KC)2 = (KH)2

My friend is moving in my inertial frame and receives light in the two directions parallel to her movement: from behind and from ahead. The photons that reach her travel at c in my frame, so I presume they will approach my friend at different speeds (as I view it): faster from ahead and slower...

Hello, my name is Eugene, i am glad i found a forum for people who love math. I was reading a book on mathematical puzzles recently, and there was one which i couldn't solve, mostly because i am not a very clever guy. Perhaps you will have some ideas? The area of the puzzle is non...

Determine all possible value(s) of a 8-digit base 10 positive integer having the form ABCDEFGH, where each of the capital letters denotes a different digit from 1 to 9, that satisfy each of the following conditions: (I) AB is divisible by 2, and: (II) BC is divisible by 6, and: (III) CD...

If you think of a bow (as in bow and arrow) placed in space in the proximity of a massive object. This bow for arguments sake is 100 km from tip to tip. Now replace the bow (wooden part and string) with what might be considered waypoints. The curved wooden part represents a straight line in...

the top and bottom margins of a poster are 2cm and the side margins are each 4cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area. so the area l*w = 382 and the perimiter = 2(l-4)+2(w-8) but if i...

There is in the past significant very rapid rises and falls of sea level. As there is no mechanism to rapidly melt and reform ice sheets to explain the sea level rise and fall based on mass balance (more or less water in the ocean) specifically what is causing the rapid changes in sea level is...

\sum^k_{n=1}e^{-n\sum^k_{n=2}...e^{-n\sum^k_{n=k-1}e^{-n}}} Can anyone help me find out if this converges and if so how to calculate the sum? I don't have an idea on how to even start. This is not homework

Question 1. Homework Statement The question shows a circle labeled as follows -A at the uppermost point -B at the most-right point -C at the lowest point -D at the most-left point so, the length along the circle from A to B (and B to C, C to D, D to A) is one quarter of the...

Is the value of this expression 49? The andwers in my book say that it should be 9! (2 + 5)2