Puzzle Definition and 595 Threads

Here is a sum from MATHCOUNTS: What are the last two digits in the sum of the factorials of the first 100 positive integers? From 1! to 4! you can add the units digits, since 5! to ... have 0 in their units place. From that I get 13, and I carry over the 1 over to the next column and...

Jane took several exams in math during the academic year with grades such as a,b,c,d,e,f and once she did quite badly. When repeating the poor exam, the teacher offered that instead of the two grades, say f and A, she can have the average of the two grades. Will it be disadvantagenous for...

A couple of years back, I came across a nice problem in a puzzle magazine. PROBLEM: Weedy Willie was getting too old to work the land alone so he decided to divide his cornfield between himself and his four sons in proportion to their five work rates. He knew that Rastus, Wig, Twig and Swig...

"One says that ten is divided into three parts, and if the small one is multiplied by itself and added to the middle one multiplied by itself, it equals the large one multiplied by itself, and when the small is multiplied by the large, it equals the middle multiplied by itself." This is a...

Determine all possible non-negative integer solutions to the equation: 3^x + 5^y = 7^z + 1 [ Comment: * I have only been able to derive (x,y,z) = (0,0,0); (1,1,1) as two of the solutions to the given problem. * It can be shown that each of x, y and z must be odd ( whenever x,y and...

(A) Determine all possible values of R that yields multiple solutions to the equation: 2^P – 3^Q = R; where P, Q and R are all positive integers. (B) Determine all possible values of R that yields multiple solutions to the equation: 2^P – 3^Q = R; where P, Q are positive...

Hi all, In a lighting storm,why do cows get killed more often than chickens?(i'm serious) Any help will be appreciated.

Consider all functions g from the positive integers to the positive integers such that: (a) For each positive integer p there exists an unique positive integer q such that g(q) = p; (b) For each positive integer q, we have g(q+1) as either 4g(q) -1; or; g(q) -1. Determine the set of...

My notes (from a physics course) justifies the following equality by invoking the convolution thm: \int_{-\infty}^{+\infty} \chi(\omega)\vec{E}_0(\omega)e^{-i\omega t}d\omega=\int_{-\infty}^{+\infty} \chi(\tau)\vec{E}_0(\tau-t)d\tau From a mathematical standpoint (i.e. without reference to...

Penrose: Before the Big Bang--Outrageous Solution to a Profound Cosmological Puzzle a video of a talk given at Perimeter Institute recently by Sir Roger Penrose Before the Big Bang: an Outrageous Solution to a Profound Cosmological Puzzle go here...

A train is moving parallel and adjaceent to a highway with a constant speed of 33 m/s, initially a car is 37 m behind the train, traveling in the same direction as the train at 47 m/s and accelerating at 5 m/s^2. What is the speed of the car just as it passes the train? Answer in units of m/s...

Puffy planet poses pretty puzzle http://news.bbc.co.uk/2/hi/science/nature/5346998.stm http://www.cfa.harvard.edu/press/pr0624.html http://arxiv.org/abs/astro-ph/0609369 http://www.cfa.harvard.edu/~gbakos/

Hi: I have two questions to answer and I,m not sure of the answers. I have looked in textbooks but that didn't help. The first one is: There is a brick hanging from the ceiling by a weak rope. there is another rope atached to the brick which a student is holding. If the second rope is pulled...

Consider an exponential tower of three thousand 7's. What is the remainder when you divide the tower by 11? Note that this notation means 7^(7^7) not (7^7)^7. So it's kinda like the Ackermann Function maybe? The final answer must be given as a single integer in the range 0-10. Anyone got...

Consider an exponential tower of three thousand 7's. What is the remainder when you divide the tower by 11? Note that this notation means 7^(7^7) not (7^7)^7. So it's kinda like the Ackermann Function maybe? The final answer must be given as a single integer in the range 0-10. Anyone got...

Recently reported observations of the Bullet Cluster of galaxies (see http://www.nasa.gov/centers/marshall/news/news/releases/2006/06-096.html ) claim proof that what I'll call Exotic Dark Matter (EDM) exists. Previously the most direct evidence for lots of some sort of Dark Matter (DM) was, as...

There's a variety of NP-Complete problems like the Clique problem, the Hamiltonian cycle problem, Satisfiability, etc. Recently i discovered a simple puzzle problem that is NP-Complete (the proof involves a straightforward reduction of the Clique problem). Anyway, i built the actual puzzle...

I am trying to solve a puzzle. How do I find an algorithm (or a formula) behind a series of six two-digit numbers? (The numbers are as follows: 14, 21, 33, 41, 56, 68.) The two-digit numbers, although different from one another, are always the same ones given. Each time they are rearranged...

Hi all, The minute hand of a church clock is twice as long as the hour hand. At what time after mid-night does the end of the minute hand move away from the end of the hour hand at the fastest rate? I totally dun have a clue on how to do this any hints?? By thw way what is linear speed?

Hey there all of you. I am doing some studying for my final for physics and i have come across this question. I thought it was easy but it is not working that way. The question is. A 4kg block (held by a block) is accelerating down at 3 m/s/s, what is the tension of the rope? So I am...

Puzzle question... I am developing an interactive combination lock that involves utilizing a total of 9 buttons to open a door. I am wondering how many combinations there are if the answer requires a certain three to be pushed on? I am not sure how to calculate this, but I am trying to...

Here my problem to solve: (Could anyone share some insight?) You have seven hexagonal-shaped mats in a line. These mats all have to be turned over, but you can only turn over exactly three at a time. You can choose the three from anywhere in the line. A mat may be turned over on one move...

In black hole thermo the famous entropy is that of the event horizon viewed from the outside. does the standpoint of the observer make any difference to the entropy? and in particular does it make any difference to the entropy of the horizon if the observer falls in and is now viewing the...

To determine the pressure of water, you would use Force/Area. With a column of water. For example a 4 inch diameter column of water with 24 pounds of water in it. Equation would be 24/12.56637061. Would equal 1.909 psi. But if at the bottom of the column there was a 1 inch diameter tube. Would...

According to Google, the puzzles require skill, intellect, and perseverance. Google promises that should anyone answer all 24 puzzles correctly, they will have a chance of winning "untold riches." (oooh) The Google webquests run over a span of 24 days ending May 11th 2006. One new puzzle of the...

A converging lens has a focal length of 25cm. A 1.00cm tall object is placed 15.0cm in front of the lens. Find the image location and size, and describe it. Draw a ray diagram. Ok so I get 1/p + 1/q = 1/f rearranged for q=pf/p-f which equals -37.5, so the object is 37.5cm behind the...

:cool: o.k wats missing from the LINE UP... 9,36,225,256,400, _ ,1225,1600 . damm, u got all the others instantly.. hope it isn't the case for this ...its a 3 step solution ...sorta ,nothing too ridiculous ,,and its slightly lateral and mensa ' ry...

a number puzzle... tell me a the lowest number for which the number just below it is divisible by 2 ,the one below that 3, below that 4 ,and below that 5 ,and below that 6 .

u have a certasin number of aliens in a room they each have the same number of hands and fingers ,,the total number of fingers in the room is just under 300...clue is that there is an answer with logic behind it. question how many aliens were there? (a specific number)

Ok, I know this is not too much of a teaser but maybe you guys could come up with something cool and original. I'm getting a tattoo and part of it has my birthdate in it. Except I don't want it to be obvious...I want some type of complicated equation with lots of mathmatical symbols etc so if...

Ok here is what the problem states in the book "A ladybug settled onto the tip of a clock's minute hand. The minute hand is 12ft long. How far does the ladybug travel from 3:00pm to 3:20pm?" I figured there are 30 degrees to every hour (divide 360 by 12). Then the 20 minutes would...

Well, i have been doing some fluids problems, and i came upon this. It has me stuck A T-shaped tube with a constriction is inserted in a vessel containing a liquid. What happens if air is blown through the tub from the left? A) The liquid level in the tube rises above the surface of the...

i reackon youv'e seen it already, the problem is to rearrange the next numbers in the fixed order: 1 2 3 4 5 6 7 8 9 11 10 when you have at the last entry a vacant place you need to put it in order. this is from the text of edwin h. connell, and i think it's impossible (after a lot...

Just in case you have some time that isn't yet wasted. Has anyone else tried this puzzle? I took just over 20 minutes to do level 12, then it seems to get exponentially more difficult. It's much more fun replaying level 10 or 11. http://www.planarity.net Every now and then you find a...

You have twelve coins, eleven identical and one different. You do not know whether the "odd" coin is lighter or heavier than the others. Someone gives you a balance and three chances to use it. The question is: How can you make just three weighings on the balance and find out not only which coin...

There is a full story that comes along with this puzzle but I will just stick to the puzzle itself. There are four men. Three of them are friends and the fourth has approached them with a proposition for a bet which they have taken him up on. We'll call the three friends Bob, Tom, and Jim...

Hi, please help me with this. Find the cost per meal if you serve 120000 meals, spend $46000 in food purchases and $1250 worth of food was removed from the inventory. How should i proceed with this problem. Please let me know,thanks.

this is a puzzle from highiqsociety.org i've been looking at this for a very long time, can anyone break this? http://www.geocities.com/invinbotmail1/hd3

Imagine that we have two masses m1 & m2 connected by a "rigid" but lightweight bar. The masses are attracting each other in essentially a Newtonian way (the masses are not so large as to need GR to calculate the force). Picture: m1 | |<... bar of length d, cross sectional area A |...

from a website I've seen wat does this sequence represent- 11111121113122223222 enjoy

Please refer to page 6 of http://www.physics.usyd.edu.au/ugrad/jphys/jphys_webct/jp_exams/1902_exam_2004.pdf I'm quoting from the solution guide: http://www.physics.usyd.edu.au/ugrad/jphys/jphys_webct/jp_exams/1902_exam_solutions_2004.pdf P_1 = P_A + \rho g y_1 and P_2 = P_A +...

I got this question from my teacher to be completed by the beginning of Dec. It goes like this. sheep eat grass at a fixed rate grass grows at a fixed rate 1 sheep in a pen eats grass forever 8 sheep eat grass in 5 days then starve 9 sheep eat grass in 4 days then starve I figure...

Spring Question! A 250g block is dropped onto a relaxed vertical spring that has a spring constant of 2.5N/cm. The block becomes attached to the spring compresses the spring 12 cm before momentarily stoppoing. While the spring is being compressed, what work is done on the block by (a)The...

Hi, I encountered this problem while I was studying for a Physics test, and this is how far I got, hopefully someone can point me in the RIIGHT direction. The proof goes like this, a guy is sitting on the top of an ice hemisphere, and someone pushes him off, and so he slides down the...

I've come up with a partial solution (a correct answer in fact) to this puzzle but am not completely satisfied in that I don't fully see how it works. the problem is: I and my wife invite 10 couples to a party. At the end I ask everyone except for myself how many people they have shaken hands...

formula Help! i got this question but i don;t know which formula to use Q - A 1m plank of Mass 1.0kg is placed on two scales which are at either end of the plank. Masses are hung underneath the plank. Mass A = 5.0kg at a distance of 0.30m from the left of the plank Mass B = 5.0kg at a...

hi, i have another question i can't get, the problem is: We want to boil one liter of water in a light thin-walled vessel. For this purpose, we start to heat water by an electric heater, with the label "500W. Made in Wonderland". However, after the temperature becomes 60*C, it stops...

This is a fun little puzzle a friend sent me a while back. It's all abbreviations for recognizable quantities of things, for instance, # 0 is 24 hours in a day. At one point my friend and I worked them all out but there's a few I may have forgotten. Anyway, I thought you might enjoy these...

I know two distinct secret numbers: call them X and Y, and assume that X < Y, without loss of generality. You have no clue how I came up with them. They could be anything (positive, negative, rational, irrational, etc). They could come from any probability distribution (discrete or continuous)...

A farmer uses a pump to lift water from a river to a arable land who lies 5.0m higher than the river. The pump exhaust an electrical effect of 1.0kW but only 65% is used to do the lifting. ok A) I have resolved the lifting work is 0,65*60 = 39kJ But B) is harder,,,, how much water is pumped...