Quogmoth

It is the first anniversary of the formation of the Zircon Zargo team. Each player, being a clone, secretly buys all the other players a ticket to Quogmoth, a revolutionary Ballet of spheres except for the goalkeeper who, being forgetful, doesn't buy any. As a result 1,183 dinglies are spent.

How many men are there in a Zargo team and how much are the tickets ?

Telephone Dial

Speaking of numbers on the telephone dial, which of the digits 0 to 9 appears least and which appears most in the numbers from 1 to 100 inclusive ?

The Penny Farthing Bike

"My father was also a tireless man - an inventor," said Punnish, scarcely able to contain his amusement as Pembish tried to look disapproving. "His penny-farthing bike, if you pardon the term, had metal wheels of circumference 60 and 135 centimeters respectively."

How far would you have to push this machine forward before both the wheels were again in the same position relative to the road ?

A Short Career.

2 friends met up after a long time. One of them was a brilliant scholar and the other an engineer. They decided to have some coffee. During the course of their conversations, they began to talk about their days at college.
"So, I heard that you played for the state cricket team for a year after college" said the engineer.
"Yes" replied the scholar, and wanting to test his friend, he said, "In my total career as a state player, I played n games and made (n+1)(2^n+1 -n-2) / 4 runs totally, and in the kth math I made k.2^n+1-k runs"
"Oh!" said the engineer, "that was a short career."

Can you find how long did the 'short' career last?

The Waitress

"That reminds me," said the waitress, "of a time when I was giving three guests after dinner coffee and I called out from the kitchen to see how they wanted it. Back came the reply that two wanted it with cream, two with sugar, two with rum and none with all three.

For a moment I was at a loss to how to prepare those three cups. But not for long."

Now Johnny, You tell me how did I prepare them ?  

240 Cigarettes a Day

Colonel Plantpott-Smythe is about to doze off down at the old india club when he notices Cruddington settling down in a neighbouring armchair. Knowing that the man is trying to give up Smoking Cigarettes, he passes him a note on a napkin:

Cruddinton sighs, scrawls a reply on the back of the napkin and returns it. When old Plantpott reads the message, he is quite taken back, Holy Smokes,

240 Cigarettes !

Untill he realizes his mistake. what was his mistake ?

Time Stop

"Well, in that case, what time is it now?" asked the striker, noting that the wall clock said 2:00 PM.

"Time to be off," replied Chronos, picking up his cuckoo clock from the seat beside him and tucking it under his arm. "It's Thursday, and I have an appointment this afternoon in town. My seven-hour clock stopped this morning and I have to take it to the repair shop. Look it says 1:00 now." With this he swept out, making a timely exit.

When had the time stopped in his clock ?

What ?

ToM said he has joined 12345. Now some 123 in their 12533244 may say that it 12534 that he is lacking in 423424, because no 4532 153 would do that. We all knew that what ToM had was bigger than a 424512 and this news confirms the 4512.

If you are not all at 425 and the 534. comes to you, please congratulate him!

The One Question

I was walking on a road, on my way to Asgard, my hometown when I came across two robots, standing before the split of the road into two.
One of the roads lead to Asgard,
one of the roads lead to Fountain of Good Fortune, but I don't know which is which.
One of the robots always tell the truth,
one of the robots always tell the lie, but I don't know which is which.
One of the robots is coloured red,
one of the robots is coloured blue.

Confused where to go, I asked the robots, "Which road should I take?"
The red robot points to the road that's on the right,
the blue robot points to the road that's on the left.
Still confused, I asked the robots, "Which road leads to Asgard?"
The red robot points to the road that's on the left,
the blue robot points to the road that's on the right.

What one other question can I ask to determine which robot is telling the truth, and therefore knowing which road to take?

Copy Paste

Copy: You and I are twins and today is our birthday. If you multiply our ages together you get the same number that you would get if you added them instead and turned the result upside down.

Paste: Yes that's true enough, But it was also true several years ago, and you didn't think to mention it then.

How old are Copy Paste now ? How old were they then ?

Nothing Factor

There are many curious things about division.
One of the many mysteries is 0.
We all know that a/0=undefined.
But what if it was 0/0??
Or 0^0?
There are 3 possible answers for zero divided by zero.
Using the Properties of 0, Properties of Recipricals, Properties of Division,
Find all 3 possiblities of 0/0.

Mr. Tito

Mr. Tito while collecting data for census came across a peculiar house. The lady of the house replied just before closing the door "If you multiply together all the ages of all my children, the result is 60. Dividing that by the age of the eldest gives you the sum of ages of all three."

Can you help poor Mr. Tito ?

Johnny and the Waitress

When Johnny met the waitress the third time, He asked her what she did other than waiting table (part time), she replied with a smile that she was a

LATHEROSE CHOC

This puzzled him greatly until he learned what her first name was. What was her main occupation?

For the uninitiated here is another adventure of Johnny and the Waitress [^]

Heavenly Problem III

So, if you haven't looked at the first two 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.

So all the spirits from the "Down below" came up and went to the back of the hotel and filled in.
Since there's infinite number of hotel rooms, there should be infinite number of vacant hotel rooms in the back (starting with room number infinity, infinity-1, infinity-2....and so on(?)).

But once again, there was that "No Vacancy" sign up on the front gate of Heaven Hotel.
And on Earth, there was a major volcanic eruption at the Ring of Fire and a major tsunami at the Paficific Ocean and a terrorist attack in India Subcontinent and USA.
So a lot of people died and came to Heaven Hotel.
The manager angel started putting the dead from the side door, starting with infinity/2, infinity/2 + 1, infinity/2 - 1, and so on(?), splittig the group to two sides.
But as the dead started to pile into Heaven Hotel,
the manager angel realised that finally the Heaven Hotel had truly No Vacancy.

How is this possible if there's an infinite nummer of rooms??

Right digits

It's pretty easy to approximate the value of 125!.
It is about 1.8827 * 10^209. Or it maybe be written
as 1.8827E+209 as computed in Excel.

But to get the last 32 digits (right most digits)
it takes some extra work.

What are the right most 32 digits?

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).

Draw Blank

How can someone draw a blank?

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

The Trio Puzzle of the Deadly Mushrooms

There's a swamp.
There are 3 mushrooms that block the swamp's road.
Whenever a traveller comes by, they ask a trio of puzzles.

Puzzle 1)
There are five birds sitting upon a rail.
A hunter shoots down 2 of them.
The rest flies away.
How many birds are there left?

Puzzle 2)
There are 4 cats that can catch 4 mice in 4 minutes.
How many cats will there be needed to catch 10 mice in 10 minutes?

Puzzle 3)
There is a row of aeroplanes.
There are 4 in the front,
4 in the back,
and 3 in the middle.
How many are aeroplanes are there total?

If the traveller can't answer any one of them then the mushrooms eat him/her.

Can you solve the puzzles and get through the mushrooms?

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??

What is wrong with this equation?

What is wrong with this equation?

1^10 + 2^10 + 3^10.... + 10^10 = ((10*11)/2)^10

3 + 3 = 4

How can you make this possible ?

Weighty Problem

What is the minimum number of weights you need to weigh any number of pounds from one to forty ?

Meet Tom

Congratulations Deenen Jardstam for First Prize in the Draw Tom Contest.

Deenen gets a $50 Amazon Gift Card for her amazing illustration which makes Tom truly out of the world.

Here is the entry.



What emotions Tom(above) creates in you or What is Tom thinking ?

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