Missing Digit

Find the missing digit!

4,?,9,3,7

- Francois Joubert

Last Digit

What is the last digit of 24784337^38383822458 ?

- Shpilo

Evens and Square Numbers

Prove that adding up even numbers starting with 0 cannot addup to a square number
Ex. 0+2+4+6+8+...


OR


Show the square number it adds up to and its root

- Jordan McMichael

Four Quarters

Start with a square. Divide it into four equal square quarters. In the top left corner, draw the largest possible circle. Shade it in. Divide the three remaining quarters into four quarters. In the top left corner of each of those, draw the largest possible circle. Shade it in. Continue this process of division into quarters, and shading the top left incircle. What fraction of the square will be shaded? What is the significance of this number?

-Shpilo

World Travelling

For fans of QI, you'll know this....

What is the shortest time to theoretically get to anywhere on the planet? And how would you do it?
Whilst you may assume it would only take but a moment to move to just over there..... how long would it take to get to the furtherst point on the globe? The answer is fascinating, and impossible, hence theoretical, but could be done on the moon.... Bonus points if you know how long it would take on the moon....

- Karl Sharman

Sons or daughters?

While walking in a park you encounter an old friend from times gone by. He invites you immediately to dinner to do some catching up.

Between courses you need to use the bathroom, and you enter the hallway upstairs. The door you thought was the bathroom seems to be something else: Completely pink, dollhouses, toys etc. Some girls bedroom.
The next door you try was correct. On your return to the dinner, you notice an envelope lying on the doormat. You recognize it as a letter sent to parents of at least one boy, to advertise some summer camp.


Back at the table, your friend shares that he has in fact three children.

The question is: is it more likely that he has two boys and one girl, or two girls and one boy? Can you figure out the exact probabilities?

Practical Problem

There's a long movie on TV this weekend and we want to tape it. The movie is well over two hours, but we only have a T-120 VHS cassette to use.

Here's the plan: we can record the boring beginning of the movie at slow speed (EP), and AT A CERTAIN POINT IN TIME we then switch over to the higher quality faster recording speed of SP. That way the whole movie will exactly fit onto one VHS cassette.

The problem is to find the algebraic expression that tells us exactly where that CERTAIN POINT is when we are to switch the recording speed.

- MikeO

Man and Horse

There is a man and his horse. The man leaves town on Sunday, spends one night in a different town, he wakes up and returned home on Sunday .

How is this possible ?

- chw 1980

Charming Inscription

This charming inscription is carved into a stone tablet, and sits above my throne (euphemism for toilet)

What does it say?

NUFSURO
RSETSYT
AERHETS
ETEAHEI
LOWTCAH

- Karl Sharman

Simple Maths

Baileyville, IL – Dolton, IL = 588 = Blackfoot, ID – ?

- Matt Stephans

A Double Century

When will the beginning of a century fall on a Sunday? (Note to pedants: for this question, I define the centuries as beginning with the year ending in 00, not 01.)



To help you in your quest…



There are no agreed-upon leap year rules with timescales longer than 400 years, so what we have is one fixed pattern that repeats itself exactly every 400 years. No, I'm not telling you what the pattern is.... look it up on wikipedia at your peril!



Now keep in mind that a fair amount of tinkering with the calendar occurs now and again. Our current (Modern Gregorian) calendar was instituted on Friday, 15 October 1582, and took a couple hundred years to be generally adopted. Prior to this, the year 1100 had started on a Sunday, but timekeeping was so generally screwed up back then that when the Gregorian system was adopted, a bunch of days had to be removed to get the dates to synch up correctly with the seasons. (In the U.S., the missing days were September 3 through 13, 1752.)



Next question…There is already talk (premature in my opinion) that to get the current calendar to remain accurate, we'll need to eliminate one extra leap day every 4,000 years. Bearing this in mind, and the extra leap day is eliminated, when will the beginning of a Century then fall on a Sunday?

- Karl Sharman

Hmmm ... what is it?

Things it's not:

liquid
gas
solid
animal
plant
mineral

Things it is:

transparent, but visible
always in motion
man's best friend or worst enemy

Additional hint:

it has no gender, but reproduces itself

What is it?

Complete the Words

Fill in the missing letters with a 2 word phrase which completes a 4 letter word in each column:
(you will place one word of the 2 word phrase in row 1, and the second word in row 4)

---- ? ---- ? ----- ? ---- ? ---- ? ---- ?

---- S ---- E ---- O --- A ---- L --- O

---- E ---- A ---- T --- C ---- S --- E

---- ? ----- ? ---- ? ---- ? ---- ? ---- ?

What Does It Mean?

The following each represent a different word or phrase, and they have a common theme.

1. + am

2. jojojof

3. $a$r$d$

4. in ... not out

What are the 4 words or phrases, and what is the common theme?

Spiral Problem

Start with a square with a side length of one.
Divide it in half (left from right).
Divide the right half in half (top and bottom).
Divide the top half in half (left and right).
Divide the left half in half (top and bottom).
Divide the bottom half in half (left and right).
So on and so forth.
It creates a spiral.
The centre of each subsequent division is approaching a limit.
What are the coordinates of the point the spiral is moving towards?

-- Shaul

Family Members

Four male members of the Smith family went racing one afternoon at a local track. The racetrack was short and each one them had a go at breaking the record time of 19 seconds for one lap. None of them managed it but on a positive note none of them embarrassed themselves by taking longer than a minute to complete a lap. When the Stewart collection the lap times (to the nearest second) he revealed that there was at least five seconds gap between each racer. He also gave out a series of clues to see if they could guess their lap times:

He told Bill that he his time was exactly two thirds of Alex’s.

He told Calvin that two racers were precisely 20 seconds apart and that the 45-year old was not one of them

He told Derek that one of the family members older than him was exactly 30 seconds quicker than him.

He told the only member of the family who was not old enough yet to buy an alcoholic drink, that his time was double his age.

He told the 30 year old, that his lap time was not a prime number but one of the other three racers lap time was.

He told the 25 year old that he does not share either digit of his number (i.e. lap time) with another family member.

Can you work out which family member had which time?

-- Antn'y Jacobs

Painting a Fence - The Next Job

Chris and Zaux have decided to take on another fence paining job, as they did so well on the last job. They realise that they need some help, so they recruit Knightmare. How long would it take them to finish the job if Zaux can do it alone in 6 hours more, Chris 2 hours more and Knightmare in twice the time. I'm paying by the hour... minimum wage, mind...

- Karl Sharman

Paint a Fence

it takes Chris three hours to paint a fence. it takes Zaux 6 hours to do the same job. How long would it take both of them together to finish the job?

-Knightmare

bag n balls

You have a bag with n balls. 50% are black, 50% white (n is even).

How many different ways can you pull out all the balls?

E.g.
n = 2 -> {BW, WB} = 2 ways.
n = 4 -> {BBWW, BWBW, BWWB, WBBW, WBWB, WWBB} = 6 ways

- steve brick

The Robbery

There are 4 suspects in a robbery: A, B, C , and D. Each makes a statement, but only one speaks the truth:

A. B did it.

B. C did it.

C. I did it.

D. Either A or C is the guilty one.

Who is the robber?

Three Primes

Find three different two-digit prime numbers where the average of any two is a prime , and the average of all three is a prime.

Odd Streak of Heads

On average, how many times do you need to flip a fair coin before you have seen a run of an odd number of heads, followed by a tail?

Losing at Dice

When six dice are rolled, the number of different numbers which can appear range from 1 to 6. Suppose that once every minute the 6 dice are rolled and you bet $1, at even odds, that the number of different numbers to appear will be exactly 4.

If you start with $10, roughly how long will it be on average before you are wiped out?

Summing to 15

Alice and Bob alternately choose numbers, one at a time, from the set:

1, 2, 3, 4, 5, 6, 7, 8, 9

The first to select 3 numbers whose sum is 15, wins the game.

If Alice goes first, it there a strategy which insures her win?

First Odd Number in an Alphabetical list

Each number from 1 to 10^10 is written out in formal English (e.g. , "two hundred eleven", "one thousand forty-two") and then listed in alphabetical order (as in a dictionary, where spaces and hyphens are ignored).

What's the first odd number in the list?

Uses of Fuses

You are presented with two fuses (lengths of string), each of which will burn for exactly one minute, but not uniformly along its length.

How can you use them to measure 45 seconds?

Rolling All the Numbers

On average, how many times do you need to roll a die before all six numbers have turned up?

The Gambler's Ruin

At the beginning of play, gamblers A and B have m and n chips, respectively. Let their probabilities of winning be p for A, and q=1-p for B. After each play, the winner gets a chip from the loser, and play continues until one of the players is ruined.

What is the probability of A being ruined?

The Wrong Letter

An individual has written k letters to each of k different friends, and addressed the k corresponding envelopes.

How many different ways are there to place every letter into a wrong envelope?

My God..... It's full of stars

There are 4 men, Zaux, Wizard of Oz, Cam and Rajesh Lal, all buried up to their necks in the ground. They cannot move so can only look forward. Between Zaux and the Wizard of Oz is a brick wall which cannot be seen through. They all know that between them they are wearing 4 hats, 2 x black and 2 x white, but they do not know what colour they are wearing. In order to avoid being shot one of them must call out to the executioner the colour of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out.
There are no outside influences nor other ways of communicating. They cannot move and are buried in a straight line. So Zaux and the Wizard of Oz can only see their respective sides of the wall, Cam can see the Wizard of Oz, and Rajesh Lal can see the Wizard of Oz and Cam.

After 1 minute, one of them calls out.

Question: Which one of them calls out?
Question: Why is he 100% certain of the colour of his hat?

- Karl Sharman

A Christmas Puzzle

How long does Santa take to deliver his presents to all the children under the age of 12yrs on Christmas Day.

- Karl

Marching Cadets & the Trotting Dog

A square formation of Army cadets, 50 feet on a side, is marching forward at a constant pace. The company mascot, a small terrier, was standing at the center of the rear line of cadets when the march began. Also when the march began, the mascot began running, at a constant pace, along the perimeter of the square identified by the cadets. (For the sake of argument, we will define the dog's path as always directly on the line of the square identified by the cadets... and also that he loses no time in making a turn). When the mascot reaches the point of the formation, where he originally started, the Cadets halt their march.

The formation has moved 50 feet ... how far did the terrier run?

- Zaux

How many Children

"I heard some children playing in your backyard," said Jones. "Are they all yours?"

"Heavens no," exclaimed Smith. "My children are playing with friends from three other families in the neighborhood, although our family happens to be the largest. The Browns have a smaller number of children ... the Greens have a still smaller number ... and the Blacks family is the smallest of all."

"How many children are there all together?" asked Jones.

"Let me put it this way," said Smith. "There a fewer than eighteen children, and the product of the number of children in each of the four families
happens to be my house number ... which you saw when you arrived."

Jones began figuring on his notepad ... he then said, "I need more info ... is there more than one child in the Black family?"

As soon as Smith responded, Jones smiled and then stated the number of children in each family.

How many children were in each family?


- Zaux

Big Cross Out Swindle

Cross out 9 letters in such a way that the remaining letters spell a single word:

N A I S N I E N L G E L T E T W E O R R S D

- Zaux

Liquid Assets

At the reading of their father's will, 3 sons of a wine merchant learn their father left them:

7 full barrels of wine
7 half barrels of wine
7 empty barrels

The will stipulates that each son receive the same number of full barrels, half full barrels, and empty barrels.
The lawyer, reading the will, exclaims "Oh my goodness ... how is this possible?"

- Zaux

Letter Words

Q1: Nine letter word for Confirm that ends with "in".

Q2: Ten letter word for "Take pains beyond limit" that ends with "in".

- nitin

3D Object

* Draw Square 1 with sides of length x. Draw a smaller square, inside square 1, with sides of length x/2. Align the smaller square such that one of it's sides lies on top of, and in the center of, the lower side of square 1. (lower side of square 1 refers to the side closest to the bottom edge of the paper upon which you are drawing)

* Repeat the above instructions and label the second drawing as Square 2

* Square 1 and Square 2 are identical.

* Square 1 is a plan view (top view) of a 3 dimensional object.

* Square 2 is the elevation (front view) of the same object.

* Draw a 3 dimensional representation of the object.

* DESCRIBE the OBJECT.

-- Zaux

X Factor

What is the product of the following series?

(x-a)x(x-b)x(x-c)x(x-d)....(x-z)

-Knightmare

Super Women

What does a woman do everyday, that if a man does once, he dies?

-- Greets from Germany

Ordered Pairs

Find all ordered pairs (A,B) such that:

A! = 1680 * (B!)

where "!" denotes the factorial function. For those unfamiliar, the factorial function is defined as the product of all integers less than or equal to the argument and greater than zero. For example, 6! = 6 * 5 * 4 * 3 * 2 * 1. In addition, the argument must be a non-negative integer (i.e. (6.5)! does not exist).

-- Brian Furtado

Three Laws of Robotics

The Three Laws of Robotics
1. A robot may not injure a human being or, through inaction, allow a human being to come to harm.
2. A robot must obey the orders given it by human beings except where such orders would conflict with the First Law.
3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.


There were 2 Mathematicians on board a spacecraft Travelling to attend a Mathematical conference. “Dr. Humbug is one of the top three mathematicians, by long-established repute, in the galaxy and has been working for the past 27 decades in this feild. Dr. Drake, on the other hand, is quite young, not yet fifty, but he has already established himself as the most remarkable new talent in the most abstruse branches of mathematics.”


“Dr. Humbug tells the story clearly. Shortly before he boarded the starship, he had an insight into a possible method for analyzing neural pathways from changes in microwave absorption patterns of local cortical areas. The insight was a purely mathematical technique of extraordinary subtlety. These do not, however, matter. Dr. Humbug considered the matter and was more convinced each hour that he had something revolutionary on hand, something that would dwarf all his previous accomplishments in mathematics. Then he discovered that Dr. Drake was on board.”
The two had met at professional meetings before and knew each other thoroughly by reputation. Humboldt went into it with Drake in great detail. Drake backed Humbug’s analysis completely and was unstinting in his praise of the importance of the discovery and of the ingenuity of the discoverer. Heartened and reassured by this, Humbug prepared a paper outlining, in summary, his work and, two days later, prepared to have it forwarded subetherically to the co-chairmen of the conference, in order that he might officially establish his priority and arrange for possible discussion before the sessions were closed. To his surprise, he found that Drake was ready with a paper of his own, essentially the same as Humbug's and Drake was also preparing to have it subetherized.”
“Except for the mirror-image exchange of names. According to Drake, it was he who had the insight, and he who consulted Humbug; it was Humbug who agreed with the analysis and praised it. But there are 2 Robots who witnessed it all. The personal servants of Dr humbug and Dr Drake But both of the robots confirm the stories of their masters(Robots cant lie according to the 3 laws unless to save the life of a human Being). So They are both Interrogated The transcript Follows”




“Greetings, R. Idda.”
“Greetings, sir,” said R. Idda,
“You are the personal servant of Gennao Drake, are you not?”
“I am sir.”
“For how long, boy?”
“For twenty-two years, sir.”
“And your master’s reputation is valuable to you?”
“Yes, sir.”
“Would you consider it of importance to protect that reputation?”
“Yes, sir.”
“As important to protect his reputation as his physical life?”
“No, sir.”
“As important to protect his reputation as the reputation of another.”
R. Idda hesitated. He said, “Such cases must be decided on their individual merit, sir. There is no way of establishing a general rule.”


He said, “If you decided that the reputation of your master were more important than that of another, say, that of Alfred Barr Humbug, would you lie to protect your master’s reputation?”
“I would, sir.”
“Did you lie in your testimony concerning your master in his controversy with Dr. Humbug?”
“No, sir.”
“But if you were lying, you would deny you were lying in order to protect that lie, wouldn’t you?”
“Yes, sir.”
“Well, then, let’s consider this. Your master, Gennao Drake, is a young man of great reputation in mathematics, but he is a young man. If, in this controversy with Dr. Humbug, he had succumbed to temptation and had acted unethically, he would suffer a certain eclipse of reputation, but he is young and would have ample time to recover. He would have many intellectual triumphs ahead of him and men would eventually look upon this plagiaristic attempt as the mistake of a hot-blooded youth, deficient in judgment. It would be something that would be made up for in the future.
“If, on the other hand, it were Dr. Humbug who succumbed to temptation, the matter would be much more serious. He is an old man whose great deeds have spread over centuries. His reputation has been unblemished hitherto. All of that, however, would be forgotten in the light of this one crime of his later years, and he would have no opportunity to make up for it in the comparatively short time remaining to him. There would be little more that he could accomplish. There would be so many more years of work ruined in Humbug’s case than in that of your master and so much less opportunity to win back his position. You see, don’t you, that Humbug faces the worse situation and deserves the greater consideration?”
There was a long pause. Then R. Idda said, with unmoved voice, “My evidence was a lie. It was Dr. Humbug whose work it was, and my master has attempted, wrongfully, to appropriate the credit.”

“Good. Now for the other.”
“But is there any point to that in view of what R. Idda has confessed?”
“Of course there is. R. Idda’s confession means nothing.”
“Nothing?”
“Nothing at all. I pointed out that Dr. Humbug's position was the worse. Naturally, if he were lying to protect Drake, he would switch to the truth as, in fact, he claimed to have done. On the other hand, if he were telling the truth, he would switch to a lie to protect Humbug. It’s still mirror-image and we haven’t gained anything.”
“But then what will we gain by questioning R. Preston?”
“Nothing, if the minor-image were perfect--but it is not. After all, one of the robots is telling the truth to begin with, and one is lying to begin with, and that is a point of asymmetry. Let me see R. Preston


“Greetings, R. Preston.”

“Greetings, sir,” said R. Preston.
“You are the personal servant of Alfred Ban Humbug are you not?”
“I am, sir.”
“For how long, boy?”
“For twenty-two years, sir.”
“And your master’s reputation is valuable to you?”
“Yes, sir.”
“Would you consider it of importance to protect that reputation?”
“Yes, sir.”
“As important to protect his reputation as his physical life?”
“No, sir.”
“As important to protect his reputation as the reputation of another?”
R. Preston hesitated. He said, “Such cases must be decided on their individual merit, sir. There is no way of establishing a general rule.”
“If you decided that the reputation of your master were more important than that of another, say, that of Gennao Drake, would you lie to protect your master’s reputation?”
“I would, sir.”
“Did you lie in your testimony concerning your master in his controversy with Dr. Drake?”
“No, sir.”
“But if you were lying, you would deny you were lying, in order to protect that lie, wouldn’t you?”
“Yes, sir.”
“Well, then, let’s consider this. Your master, Alfred Barr Humbug, is an old man of great reputation in mathematics, but he is an old man. If, in this controversy with Dr. Drake, he had succumbed to temptation and had acted unethically, he would suffer a certain eclipse of reputation, but his great age and his centuries of accomplishments would stand against that and would win out. Men would look upon this plagiaristic attempt as the mistake of a perhaps-sick old man, no longer certain in judgment.
“If, on the other hand, it were Dr. Drake who had succumbed to temptation, the matter would be much more serious. He is a young man, with a far less secure reputation. He would ordinarily have centuries ahead of him in which he might accumulate knowledge and achieve great things. This will be closed to him, now, obscured by one mistake of his youth. He has a much longer future to lose than your master has. You see, don’t you, that Drake faces the worse situation and deserves the greater consideration?”
There was a long pause. Then R. Preston said, with unmoved voice, “My evidence was as I--”
At that point, he broke off and said nothing more.
“Please continue, R. Preston.”
There was no response.
“I am afraid, that R. Preston is in stasis. He is out of commission.”
“Well, then, we have finally produced an asymmetry. From this, we can see who the guilty person is.”


So who is the guilty Person... ?

-- Jyani vishav

What is X?

What is X?

14 | 19
---|---
8 | 22

1 | 50
---|---
22 | 41


22 | 4
---|---
30 | 8

10 | 34
---|---
28 | X

Consider these as sequence of 4 groups
- Rajeev Nair

Two trouble

Prove that 2/10=2 !

- Kushal chandel

Three Gods

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god.

The gods understand English, but will answer in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

- hamujemy

Isn't it marbleous!

You have 10 bags of marbles. Each bag contains 25 marbles. 9 of the bags have marbles that weigh 10 gm. The other bag has marbles that weigh 11 gm. The bags aren't labelled. You have a weighing machine that displays in grams, and is sensitive enough to reliably read to the nearest gram. Using only one weighing, how can you find which bag has the 11 gm marbles?

Mixing it

You have jugs A and B that contain the same amount of differing liquids. Take a small sample from A and mix it into B. Then take the same size sample from the A+B mix and mix it into A. What is the relative concentration of A in B to B in A?

There's more than one way of solving this.

xth root of x

Just how big can x^(1/x) be? Assume x is real number.

Who squares?

How many squares are there on a chessboard?

Assume a simple chess board with no margin.

Just making a point

Prove that the three perpendicular bisectors of a triangle always meet at a point.

Here's a link so you can see what I'm blathering on about:
http://www.analyzemath.com/Geometry/Circumcircle/Circumcircle.html

On that page, click the "click here to start button". Ignore the circle that you see. Drag the triangle around and see what happens.

Classical geometry on allows the use of a straightedge and compass. Rulers and protractors are not allowed. Trigonometry is not allowed.

However for this problem any reasonable proofs are OK with me.

Happy Birthday

I expect everyone knows this one, but it's better than nothing.

In a random group of 23 people, there is a slightly better than a 50% chance that at least two of them share the same birthday. How is that possible?

How big would the group need to be to get the chance of a shared birthday up to at least 95%?

Discard all leap year complications. Assume each birthday is equally likely. Only consider the day and month, not the year of birth. It is not a trick problem.

Graham's Number

Not a problem. Just for interest.
If you thought you knew what a big number is, then you may be in
for a surprise and a headache. Follow this link:
http://en.wikipedia.org/wiki/Graham%27s_number

The bare facts of the naked truth

I hope this one isn't too well known.

A man died and went to heaven. When he got there he found that everyone was naked. A man and a woman walked over to greet him. The (newly dead) man said to them, "Hello Adam, hello Eve".

How did he know who they were?

Beam me up

You have two *square-section beams of wood. One has a density greater than half that of water, the other less than half that of water. You throw them in a pond. What do you notice about the orientation of the floating beams?

*In the original posting, I unintentionally wrote "rectangular".

You're so special

Numbers like pi and e are usually regarded as being special.
Are there any numbers that are not special?
Prove your assertion.

one for all ...

What is 1/(1 + 1/(1 + 1/(1+ ..... ?

pie eyed

Just a sick and quilly.

What is e^(pi/2 e^(pi/2 e^(pi/2 e^(pi/2 e^(pi/2 e^(pi/2 e^(pi/2 e^(pi/2 e^(pi/2 e^(pi/2 e^(....e ^(pi/2 i)))...))) ?

Can I say "annulus"?

Draw two concentric circles with different radii. Draw a chord
in the larger circle that is also a tangent to the smaller circle.
If the chord length is d, what is the area of the annulus (the
washer shape) between the two circles?

To enable consistent communication, use O for the centre of
the circle, T for the point at which the tangent touches the
inner circle, A and B for the ends of the chord and R and r for
the larger and smaller radii respectively.

aye aye

If i is the usual unit imaginary number (Sqrt(-1)), what is i^i ?

Take the pole into the room

The pole from the previous flatland post, is now going
into a large room off a hallway. The walls are 6 inches thick,
the door is 30 inches wide. The pole is 24 feet long.
The hall is not very wide. How wide would it have to be for
the 4 inch diameter pole to be taken into the room without bending it?

Proof that 1 = -1

I hope this hasn't been posted before

1 = sqrt(1)
=> 1 = sqrt( (-1) * (-1) )
=> 1 = sqrt(-1) * sqrt(-1)
=> 1 = (sqrt(-1))^2
=> 1 = -1

What!!!!

Algebra Trig ?

I have a problem I can solve but I need a better solution.

The equation is

y = r - r * COS( d / r )

Given d and y find r.

r= ?

I don't think a picture will make the equation solvable, but here's a picture.

http://1.bp.blogspot.com/_gQkeSWqb63Q/SoS1r1bjrCI/AAAAAAAAAFY/_aQzlEhMJY4/s1600-h/tom-Capture.JPG

Black Holes and the Big Bounce

Big Bounce is a theory uniting two other theories, Big Bang and the Big Crunch.
The theory is that after the Big Bang, there will be a Big Crunch,
then after the Big Crunch, there will be another Big Bang and so on...

A Black Hole is what's left from a Supernova, an infinately small object with a giant mass of a supergiant that was massive enough to be a Supernova.

If a Black Hole is just a vast amount of mass all crushed together into an infinately tiny space,
then wouldn't the Big Crunch create a super, super, super....super, super massive Black Hole and also isn't the Big Bang a reverse of the Big Crunch, therefore "unwinding" the tiny volume of the supermassive Black Hole?

CAN THIS LEAD TO A NEW THEORY FOR THE CREATION AND DEATH OF THE UNIVERSE???? (sorry....got excited....don't answer this....just answer what I wrote above....)

Palindromic Fun

1. Mischievous children of celebrities.

2. What did I see ? was it a rodent ?

3. Mother is as self - sacrificing as myself

4. All inhabitants of ancient Rome were smart ; not stupid

5. All chieftains moan

Card Staircase

If you take a pack of cards, you can slide them over to make
a kind staircase. What is the maximum horizontal distance the
top card can be from the bottom card?

The staircase will not have a constant slope. Use obvious
idealisations, this isn't a real engineering problem. You can
use as many cards as you want.

- Photino

Trigonometry

Tan20.Tan40.Tan60.Tan80=?

This seems like a textbook question, but i want able to find it in the 6 books that I own.

Word Fun

Find me a word that contains 7 times as many consonants as it does vowels.

- Xavier

Another Odd Rafting Trip

There are 8 people that need to cross the river on a raft.
Only 2 can be on the raft at a time.
There is a Red Indian Chief and his two daughters. A Cowboy with his two sons. A policeman with a criminal.
The Red Indian Chief cannot be with any of the Cowboy's sons or he will kill them, unless the Cowboy is present.
The Cowboy cannot be with any of the Chief's daughters or he will kill them, unless the Chief is present.
The policeman must be with the criminal at all times or the criminal will escape.
Only the Policeman, Chief and Cowboy know how to operate the raft.
Try getting everyone across.

SideNotes:
The Red Indian Chief and Cowboy will not kill each other. Well you can say they know they are evenly matched so fighting is pointless.
And when I mean they cannot be together, it means either together on shore or on the raft.

Well it will take a while but it is possible. Have fun. :D

~MadiLLusionist

The Odd Rafting Trip

There are 8 people that need to cross a river on a raft. Only 2 people can be on the raft at a time. There is the Mom, Dad, two sons, two daughters, a policeman, and a criminal. The Mom can't be left alone with any of the sons, for she beats them (its just the rules, go with it), and the Dad can't be left alone with any of the daughters (same reason). The criminal can't be left alone without the officer or else he hurts everyone. Only the Officer, the Mom, and the Dad know how to operate the raft. Get Everyone Across.

- Bren

House Of Night

A woman walked to her apartment door. When she entered there were two men laying on the floor dead. They both had bullet wounds in their chests. And there were 53 bicycles sitting around them. What happened?

- House Of Night

How many planes ?

If there are 66 people in each plane, there are 10 full planes and there are 630 passengers

Is this possible?

- matthew hinds

How did he survive?

A man watched a horror movie in which there was a big pile of dead bodies, he had a drink and he noticed that there was something else in the cup besides the drink, he thought it was nothing. but when he went outside, he fell unconsious, he found himself on top of a big mountain, he fell off and died, he woke up in hospital a day later

how did he survive?

- matthew hinds

A zebra?? and water??!!

There are five houses.

The Ukrainian drinks tea.

The green house is immediately to the right of the ivory house.

The Spaniard owns the dog.

Coffee is drunk in the green house.

An Englishman lives in the red house.

Kools are smoked in the yellow house.

The Old Gold smoker owns snails.

Milk is drunk in the middle house.

An Englishman lives in the red house.

The Norwegian lives in the first house.

Kools are smoked in the house next to the house where the horse is kept.

The man who smokes Chesterfields lives in the house next to the man with the fox.

Kools are smoked in the yellow house.

The Japanese smokes Parliaments.

The Norwegian lives next to the blue house.

The Lucky Strike smoker drinks orange juice.

Now, if it is given that a resident drinks water and the same OR another has a zebra, which one is it?(or which ones are they)

PS: I hope this is good enough... the standard has gone down a little.

Equation

What is one thing you would do to make this question right?

81 X 9 = 801

-- Teddy Kumar

Cheesy

What Cheese is made backwards?

- Amber Lewis

Minus One

What is the square root of '-1'?

- Josh Mudie

No Kill

A woman shoots her husband. Then she holds him underwater for five minutes. Then finally she hangs him. Later they go out and enjoy a wonderful evening together. How is this possible?

- Ryan Lane

T Shape Number Grid

if you have a ten by ten grid and you get a t shape of numbers out like this:

1-2-3
--12--
--22--

The t number is the number of the bottom of the t (22)
The t total is all the nubers in the t added together (1+2+3+12+22=40)

find the nth term (to get the t total when you are given the t number)

then do the same with a 9 by 9 and/or 11 by 11 grid and try to find the nth term to get the t total from the t number from any grid.

-- matthew hinds

Next Number

Solve for the next number in the series:

1 = 7
2 = 16
3 = 27
4 = 40
5 = 55
6 = 72
7= ?

- Bobby Braun

Free Fall

Brad stared through the dirty soot-smeared window on the 22nd floor of the office tower. Overcome with depression he slid the window open and jumped through it. It was a sheer drop outside the building to the ground. Miraculously after he landed he was completely unhurt. Since there was nothing to cushion his fall or slow his descent, how could he have survived the fall?

- Chris Azarian

Snow and Bang

A man is looking out the windows of his home he see's that everything outside is covered with snow. He goes out of the room to tend to something more important. After a while he hears a loud bang, runs to the window and see's that all the snow has melted. What happened?

- Edward Novyk

Murder Mystery

There was a bang at the front door, a man opens it but no one is there, he closes the door.
There was another bang after he closed it, he opened the door again but before he did, he noticed two holes in the door, he opens the door and dies, how did he die?

- matthew hinds

Five 2's

By using five 2's can you create all the digits from 0-9

- Kevin Caron

Ten Letter Word

What ten letter word starts with G-A-S?

- Cris Azarian

Magic and luck

What number is magic times luck?

- matthew hinds

Phone Fun

There is a phone hooked up to ten computers. Bob calls his friend mike's computer but angelina replys. how can this be?

- Chris Azarian

Head on a Tail

What has a head an a tail, but can never see it's tail?

- Chris Azarian

Band

What band does not act sing or act? 

- Chris Azarian

The Black Dog

A black dog stands in the middle of an intersecton in a town painted black. None of the street lights are working due to a power failure caused by a storm. A car with two broken headlights drives towards the dog but turns in time to avoid hitting him. How could the driver have seen the dog in time?

- Chris Azarian

More You Take

What is it the more you take, the more you leave behind?

Chris Azarian

2 @ a Time

A man is swimming in a pool. At the same time he is flying an airplane. How can this be?

- Chris Azarian

The Stone and The Water

A stone falls into the water and water drops are splashed. Why do the water drops fly upwards? Does the maximal height reached by the drops depend (primarily) on the size of the stone or on its speed? What is the maximal height?

Cube-Roots

The mathmaticians agreed that every number has 3 cube roots.
But like 8, or 216, it seems that there's only 1 cube root.
But there is still 3, unless it is a perfect cube, in the form of

a³+3a²b+3ab²+b³,

where the roots can overlap, or be the same number. Now, having that said, find all 3 cube roots of 27 (and no, it is not a perfect cube so it has 3 cube roots).

Heavenly Problem II

So, if you haven't looked at the first Heavenly Problem then please do so.
That way I don't have to repeat the components about Heaven Hotel.

So the spirit earns a room as the manager hotel solved it by telling every guest to move over 1 room. 1st room to 2nd room, 2nd room to 3rd room and so on.
And because there are infinite amount of rooms,
the first room should be vacant so the spirit goes in there.

But one day, when the "No Vacancy" sign was up once more,
every spirit and soul from down below (starts with an H, if you dare say it...)
was granted to move into Heaven Hotel.

Now how is the manager angel going to give each & every spirit and soul a room.
(by the way there are uncountably many spirits that has to move in)

Irrational Roots

If

P(x) = x⁴ - 2x³ - x² - 9x + 2 has only irrational roots, of which their real roots are between -1 and 3.

How does one find x?


-- abdeali kothari

Heavenly Problem

I know this is very religious.
If you don't believe in Heaven, then just pretend for this problem.

There is a hotel in Heaven called Heaven Hotel.
It has an infinite amount of rooms.
But one day, the manager angel lost count of how many rooms are occupied so puts up a sign that says, "No Vacancy" on the front gate.
That same day the manager angel put up the sign, a spirit flies over to Heaven.

"What! No vacancy! But I have travelled so far and suffered so much.
I want to get into Heaven! Please let me in!!" the spirit cried.

Being an angel, a merciful angel, the manager angel tries to make a room for the spirit.

How will the manager angel do it?

Positive or Negative ?

We all know that the value of tan 270 is - infinity.
But also there is a formula stating that for any value for A between 0 and 90 tan (180+A) = tan A So tan (270) = tan (180+9) = tan 90 = infinity


So what is wrong in this as tan cannot be infinity AND - infinity.

-- abdeali kothari

0.99999 = 1

When, can 0.99999 recurring EQUAL 1?

JMudie

Lying Taxi Driver

A man got into a taxi fare.
The driver asked where he was going and he told the driver his destination.
The driver started to drive.
The man immediately started to talk about his day and what happened.
After many red lights and many blocks past by, the man was still talking.
As time passed on, the driver realized that the man won't shut up.
So, irritated, he said, "I'm sorry, sir, I cannot hear anything you're saying because I have a very bad ear and I need my ear aid. But I forgot it today and I'm pretty much deaf without my ear aid." just to shut him up.
So then the man kept quiet for the rest of the ride.
When they arrived at the man's destination, the man paid for the fare and got off.
But after few minutes, he realized that the driver was lying to him about his ear and that the driver could hear him all along.

How did he know??

What happened?

A famous mathmetician sent a letter containing a riddle to one of his best friends.
It read:
"My friend, help me.
If x=1, y=1,
then it's must be true that x-y=0.
Then 5(x^2-y^2)=0 must be correct.
And also 2(x-y)=0 must be correct.
Because they both equal 0, then 5(x^2-y^2)=2(x-y) must be correct.
But then if you divide both sides by x-y,
you end up with 5(x+y)=2.
But 5(2)=2, 10=2 is not correct.
What happened during this process?
Dear friend, I hope you can be even sharper than I."


Can you see what went wrong??

Set of Four Letters

How many set of 4 letters that can be changed in order ( so something like b-o-o-k and k-o-b-o) are there if they are used to fill in the blanks and made a sentence that make sense?

A _o_a_l_ doctor had _o_a_l_ and therefore was _o_a_l to operate.

-James Yu