Some Fruit Punch

There is a party tonight at the Puzzlaria Tavern and Ross asked me to get some orange juice and pineapple juice for the Fruit Punch he is preparing. Being already giddy with all the drinks I had had, I tried some mixing of my own. Grabbing the large orange juice jar (lets call it jar O), I added enough juice into the second jar containing pineapple juice (jar P) till its contents were doubled. Then, I poured some of the mixture back into jar O to double its contents.

Fairly sloshed now, I decide a good way to settle matters would be to again pour from Jar O into Jar P to double P’s contents and proceed to do so. At this point I realize there is an equal quantity of pineapple juice in each jar. If Jar P now has one more litre of orange juice than pineapple juice, can you tell this poor muddle-headed soul, how much more orange juice than pineapple juice there is in Jar O?

Help me! The party is in full swing and Ross is getting impatient !!

144

In what number bases does 144 represent a square number.

1111 - 22

Here's a fairly straightforward one:

Consider the sequence of numbers: 11-2, 1111-22, 111111-222,...
Show that they are perfect squares. What else do you notice?

If I lived here, I'd be home by now!

If I drive half-way to my house at 30 mph, how fast do I have to go for the rest of the way to make the average speed for the entire journey of 60 mph?

Prove that...

ok, here are some proving questions:

1) if H is the set to infinity of all positive integers, none of which have prime factors greater than 3, the PROVE THAT: the sum of the reciprocals of elements of H are smaller than 3

2) PROVE THAT any prime number (2^(2^n) + 1) cannot be represented as a difference of 2 fifth powers of integers.

NOTE: just for confirmation, this 2^2^n is the same like my last question, it is a continuation of it that i just found.

3) a₁ , a₂ , a₃ , ..... , a2009 are real numbers.

a₁ + a₂ + a₃ + ..... + a2009 >= 2009²

and, a₁² + a₂² + a₃² + ..... + a2009² <= 2009³ + 1

then, PROVE THAT 2008 <= a k <= 2010 for all values of k belonging to the set (1,2,3,4,.....,2009)

NOTE: here k is a subscript

Assorted questions

OK, these are just some assorted questions that I have, rather than putting many posts, I am putting them all in one as they aren't very difficult, but please post HOW you did it, I want more methods to solve them :)

1) p(x) is an expression. and it satisfies, 2p(x) + p(1/x) = x+1. find p(2)

2) Find the Sum of digits, and number of digits, of the number: (1000^20) -20

3) Find the last integer of the number (((2)^2)^n) + 1 and prove it. only for n>1(not using trials :P )

4) x = (-1 (+/-) rt(-3))/2 find the value of (x^1999 + x^2000) = ?

5)a+b+c = 0 ; (b^2 + a^2 + c^2) / (b^2 - ac) = ?

All of these are 10th grade problems, so should be easy.

100

Using only 16, 17, 23, 24, 39 and 40 and addition, make 100 with the minimum number of numbers. e.g. 40+39+21=100 uses only 3 numbers - unfortunately 21 isn't available. You may use a number more than once e.g. 23+23+... is ok. What are the numbers?

For the birds

There are two trees with birds in them. The birds in one tree say to the others, if one of you joined us, we'd be twice as many as you. The birds in the other tree say, if one of you came over here, then we'd have just as many as you.

How many birds are in each tree?

Divisible by 3?

As I haven't seen it be posted before: prove that if an integer is divisible by 3, that the sum of it's digits are as well.

Also show that the remainder after division by 3 of the sum of the digits is the same as the remainder after division by 3 of the original integer.

Number 9

In the past I have friends ask me why "mind reading" tricks work. A particular one led me to notice (and prove) that if you take any integer and subtract from it any anagram of it (subtracting the smaller number from the larger number) that the result is divisible by 9.

Now you prove it.

6174

Take any 4 digit number which has at least 2 digits that are different (e.g. 1112 is OK).

Rearrange the digits to produce the largest possible number and the smallest possible number. Subtract the smaller from the larger one. After at most seven steps, you'll end up with 6174, and then you'll only get 6174 after that. Prove it.

e.g. for 6174 you'd do 7641 - 1467 = 6174

Sadly, this one's easily to find on the Internet, so please don't cheat. I've only looked enough to confirm it's there.

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.

Rolling All the Numbers

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

Number Logic

Two perfect logicians S and P are told that integers x and y are such that:
1 < x < y and that x + y < 100.

S and P are then given the values x+y and x*y respectively and privately. S and P know they have each been given the sum and product respectively. They then have the following conversation:

P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.

Given that they spoke the truth, what are the two numbers?

Dec 24, 5: 10 AM. I made a significant modification to the conditionals for x and y. The place I found this sneakily used computers in deriving the solution. Unfortunately, my modifications altered the situation too much and invalidated the conversation between S and P.

In fact x < 10 and y < 20; but S and P don't know that. Unfortunately, I doubt that extra info is going to usefully simplify the problem solution. So apologies in advance if this one has a high labour requirement.

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

Absolute maximum

Define the functions Abs(x) and Max(a,b) as:

Abs(x) = (x if x>=0) or (-x if x < 0) e.g. Abs(-2) = 2
Max(a,b) = (a if a >= b) or (b if b > a) e.g. Max (2,-3) = 2

You might think these functions are independent, but they're not, because it is possible to express one in terms of the other. What are the equivalence formulae?

Average but special numbers

481 = the average of 148, 184, 418, 481, 814 and 841.

What are all the other such 3 digit numbers?

Wine testing

The police commissioner hired a mathematician to help at a crime scene. At the scene there were between 100 and 200 glasses of wine, one of which had been poisoned. The mathematician was asked to determine which glass was the poisoned one, in the minimum number of tests. The mathematician counted exactly how many glasses there were and said "test one of the glasses at random". The commissioner asked, "wouldn't that waste a glass?". The mathematician said "no". How many glasses were there?

For each test you may mix the contents of as many glasses as you want, and then do a single test to determine if any of them was poisoned.

Insects on scale

There is a 100 cm long scale with 100 insects on it. At time t = 0, each starts moving either towards 0 or towards 100 at a speed of 1 cm/s. They fall off the scale when they reach any one of the ends.

You have to tell me this: what is the minimum time at which I can be sure that the scale has no insects left.

Spaceship Enterprise

Spaceship Enterprise starts at 3 am from planet Offensive to target planet Defensive.
It travels for one hour and then reduces its speed to 2/3rd for the next hour. The total distance at the end of the first hour is a four-digit square and at the end of the second hour a four-digit cube having no three digits identical. Defensive is informed by Informative about all this and it fires a missile Destroyer at 4 am itself. If the separation between the two planets is twice the initial speed of Speedster, at what speed must Destroyer travel to destroy Enterprise midway at 5 am?

* Speedster is the Enterprise

Boat Speed

Three boats, X, Y and Z are there to let the touristas tour a lake. They leave at different times and take 30 minutes to tour the lake. The time difference between X and Z is 20 minutes and that between Y and Z is 15 minutes. Given that the sum of time (in minutes) is 40 for all three to leave, after starting the countdown, at what time did each boat leave?

12 = M in a Y

OK that works out to MONTHS in a YEAR.

Now, all the polymaths out there solve the following

1) 54 = C in a P (with J)
2) 13 = P at the L S
3) 15 = M on a D M C
4) 29 = D in F in a L Y
5) 80 = F S
6) 10 = P B
7) 100 = N in B T
8) 28 = N of D in the L C
9) 5 = P on a P
10) 4 = R of P in the O T
11) D = 500 in A N
12) 13 = C in O S
13) 21 = P in a N D
14) 0.81818181 . . . = F
15) 26535 = The N five D of P.

* There’s also one trick one and one reverse one

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

Parallel Lines

How will you find the mid points of two parallel lines. You have a ruler without the scale. (Mid points of each of the lines)

Collatz Series

A strange series of numbers exists where the next number in the sequence depends on the previous one being either even or odd. If it was even, the next is one half of the previous, if odd the next one is 3 times the previous, plus one. The last number of the series is always one. The number of steps to get to one is sometimes called the halting point. (Even the next is N/2; if Odd the next is 3*N+1)

Example, Intital number is 6 then the steps are... 3,10,5,16,8,4,2,1
This has 8 steps and the high number is 16.

(If you plot the initial number vs. the high, you get a neat picture)

There once was a reward of $500.00 for solving various aspects of this series. See

http://en.wikipedia.org/wiki/Collatz_conjecture.

Your question is this. There are six different initial numbers between 3 and 100
that end with these nine steps... 40,20,10,5,16,8,4,2,1 ... what are the six initial numbers?

As a hint, each of these six initial number has 17 steps to reach 1.
So as you can see the first 8 steps vary, but the step nine is 40.

Please give as many of the six you can solve.

Trio is Back

Tom, Dick and Harry went fishing, having agreed to share the catch equally. After a successful day, they put the catch on the boat deck to be divided up later, had a big party, and went to sleep. In the middle of the night the Tom wakes up, feeling ill, and decides to go home with his share. But he sees that the catch can't be divided evenly into three because there is one fish too many. So he throws the extra fish into the lake, takes his share, and goes home. A little later the Dick wakes up, also feeling sick, and decides to go home with his share. Not realizing that Tom has already left, he also sees that the catch can't be divided equally because of an extra fish. He throws the extra fish into the water and departs. Finally Harry wakes up, ill as well, and unaware that his friends have gone, counts the fish, finds one extra, throws it away and takes his share.

The question is, What is the smallest number of fish that the fishermen could have caught during the day?

Circular Coverage

Consider a disk with a radius of one unit. We need to cover the disk’s surface with some smaller disks so that none of the larger disk can be seen. These smaller disks have a diameter of one unit. How many (the least number) will it take to completely cover the surface?

Six and Seven

How do you proof, for the fact that if any set of integers is repeated six times to form another integer it must be divisible by seven? (eg. 111111)

Sum Problem

In a group of 10 people, each one is asked to write sum of the ages of the other 9. The sums form the 9 element-set (82, 83, 84, 85, 87, 89, 90, 91, 92). Find the ages of the youngest and the oldest in the group and the ages of the two persons with the same age.

X Factor

What is the product of the following series?

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

-Knightmare

a! * b! = c!

Find three numbers where a is less than b and b is less than c
where a! * b! = c!

Urgent Letter

A military car carrying an important letter must cross a desert. There is no petrol station in the desert, and the car's fuel tank is just enough to take it half way across. There are other cars with the same fuel capacity that can transfer their petrol to one another. There are no canisters or rope to tow the cars.

How can the letter be delivered?

soaking it up

A wet sponge weighs 1kg and 99% of its weight is water. Squeeze it till 98% of its weight is water. How much does it weigh now?

Feeding frenzy

If it takes 6 cows 3 days to eat a field of grass and it takes 3 cows 7 days to do the same, how many days would it take 1 cow to do it?

The Traveller

A truck travels down the hill at 72 mph, on the level at 63 mph, and up the hill at only 56 mph. The truck takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes. What’s the distance between the two towns?

Ace, King and Queen

Place a Ace (A), a Queen (Q) and a King (K) on three slots in a row like AQK (A on extreme left, K on extreme right). Reverse the position of the cards (ie, KQA) in the least possible number of moves. In a valid move, a card can be moved either left or right into an empty slot or placed onto a card of a higher rank. (eg, a Q can be placed on a K, but not vice-versa). Also, only the top card of the stack can be moved. Now, what is the least number of moves required if:
(a) there are only three slots?
(b) there is an empty slot to the left of the Ace?
(c) there is an empty slot to the right of the King?

The Rope Problem

Assume, we lay a rope tightly around the Planet and then elongate this rope by just 1 meter and then evenly distribute this additional length around the whole equator.

What is the extra length of the Rope required ?

A flipping fortune

You begin flipping a coin. Each time it comes up heads you double your money . You stop when the coin lands tails up. How much money do you expect to make before you throw a tails? You start with $1. I've no idea where the money is coming from.


Addendum, 10/10/09. The expected value is the same as the average value. To measure it, you would have to observe an infinite number of trials.

You cannot lose in this game. If you threw 10 heads, then a tail, you'd walk away with $1024. The probability of doing that is 1/2048. If you threw a tail on your first flip, you'd still have $1. The probability of doing that is 1/2.

Marbleous 2

You have a collection of bags of marbles. Some of the bags contain marbles of weight 10 g, the other bags contain marbles of weight 11 g. Your mission is to determine which bags are which in one weighing. You have a suitably accurate weighing machine. I won't state the other assumption, in case I give too much away.

This is probably another familiar golden oldie.

Cash cows

Two men have equal shares in a herd of N cows. They sell all the cows for $N each. The money they get is in $10 bills plus less than ten $1 bills. One at a time they take a $10 bill. The man who takes the first $10 bill also takes the last one. The second man then takes all the $1 bills. How much does the first man owe the second?

Warren Buffet and Bill Gates

There is a round table conference. Warren Buffet is the richest person while Bill Gates sitting on his right has one dollar less then him. And the person on Bill’s right has two dollars less than Warren. And so on. Warren feels game and gives 1 dollar to Bill. He in turn gives 2 dollars to the person on his right. And so on.

But at one stage some one says, "Now I don’t have 1 dollar extra to give to the person on my right." However, he also says that he has 101 dollar more than him. How many dollars did Warren have initially and how many people were there?

Elementary Arithmetic

In the introduction to an early literary work on elementary arithmetic, the author looking back over his life, muses: "I was once x years old in the year x cube. I am now x square years of age and in another x years my only son will be y years of age in the year y square."

In what year was the author of the manuscript born?

Heads or Tails?

A box contains two coins. One coin is heads on both sides and the other is heads on one side and tails on the other. One coin is selected from the box at random and the face of one side is observed. If the face is heads what is the probability that the other side is heads?

17 (camels)

A father dies leaving instructions that his 17 camels are to be split up between his 3 sons as follows:
Half the camels are to go to the eldest son
a third of the camels are to go to the middle son
and a ninth of the camels are to go to the youngest son

Failing to think of a way of carrying out split, they sought help from their wise but poor uncle. Their uncle arrived on his tatty old camel. He said, "I'll lend you my camel, then you'll have 18, and you should be able to divide them up without difficulty." So the eldest son chose his 9 camels, the middle son chose his 6, and the youngest chose his 2 camels. The uncle then got back on his camel (which no-one wanted) and went home.

DUH!! and DUH!! ... or is it? ^^

You're kidding!

A and B have the following conversation:

A: How old are your three kids?
B: The product of their ages is 36.
A: I still don't know their ages.
B: The sum of their ages is the same as your house number.
A: I still don't know their ages.
B: The oldest one has red hair.
A: Ah, now I know their ages.

How old are the kids?

Assume the kids ages are an exact number of years.

Beady Eyed

If you drill a diametrical hole of final length L through a sphere, the volume of the remainder is the same as the volume of a sphere of diameter L. How come?

The best thing since...

Three men are about to eat. Fred has five small loaves, Tom has three small loaves and Ed only has $8. Fred and Tom agree to share their loaves equally in exchange for the cash. So Ed gives Fred $5 and Tom $3. Fred and Tom, being smarter than Ed start laughing. Why?

Life of a Battery

The users guide of my scientific calculator says its battery life is “approximately 9000 hours continuous display of flashing cursor OR approximately three years when left with power turned off.” I use the calculator on an average of 30 minutes daily. Approximately how long will the battery last?

Short changed

Three men go to a hotel. They pay for a $30 room to share, each giving $10. Later the manager realizes that the room was only $25 and so gives $5 to the bellboy to return to the men. The bellboy takes the $5 to the men. They give the bellboy $2 as a tip. Just after the bellboy left, one of the men says, "We each spent $9 just now, since we each got back $1, and we gave the bellboy $2, that's $29". Where's the missing $1?

This must have been a long time ago.

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.

NEVER is prime

NEVER is prime,
NOW is too!
SHE is not,
Unlike YOU!

Where are we?

Needle Mileage

A phonograph record has a total diameter of 12 inches. The recording itself leaves an outer margin of an inch; the diameter of the unused center of the record is 4 inches. There are an average of 90 grooves to the inch. How far the needle travel when the record is played ?

Treasure hunt

A man has a treasure map. It shows an island with a gallows, an elm tree and an oak tree. The map has instructions. They say go to the gallows and walk to the elm tree, counting your paces. Then turn 90 degrees right and walk the same number of paces as you had just counted. Mark that spot. Go back to the gallows. Now walk to the oak tree, counting your paces. Turn 90 degrees left and walk the same number of paces as you had just counted. Mark that spot. The treasure is buried halfway between the two marked spots.

When he got to the island, he could find the trees, but not the gallows. How can he find the treasure?

There are quite a few ways to answer this problem. One is partly outside the box. It is a famous problem.

Miller's Fee

In a Tennessee mountain community the miller retains as his fee one-tenth of the corn the mountaineer farmers deliver for grinding. How much corn must a farmer deliver to get 100 pounds of cornmeal back provided there is no loss ?

Reversing a Number

You can get a reverse of number only by multiplying the number by X or Y ? Find X, Y ?
Assume the number is not a palindrome.

if you are wondering, reverse of ABC = CBA

Do you Know Gambling

With two dice getting a total of X is more likely than Y.
Can you tell for what value of X and Y this is true ?

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.

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!!!!

Time Turn

At this moment the time is 9:00 PM. Can you tell me what time it will turn, 23999 999 992 hours later ?

Rectangle Tangle

A rectangle is cut out from another bigger rectangle. How can you divide the remaining portion into two equal parts ? Of-course, you don't have the measuring tape, where the heck these things are when you need them the most ?

Smallest Integer

If the largest of X consecutive integers is M, what is the smallest ?

Pentagon Problem

How will you inscribe a pentagon in a circle

Compass Problem

How can you draw an Oval on the paper using a compass ?

Minus One

What is the square root of '-1'?

- Josh Mudie

Largest Number - II

What is the largest number you can create using four 2's ?

Five 2's

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

- Kevin Caron

Largest Number

What is the largest number formed by four 1's ?

Line Name

What is the name of the line referred to when you say "Cut a circle in two points" ?

The Rhetorical Question

"If it takes 1 & 1/2 men, 1 & 1/2 days," says Punnish strutting about in imitation of his master, "to pot 1 & 1/2 geraniums in 1 & 1/2 pots, how many will 2 & 1/2 men pot in 6 days?"

He is rather shocked to hear Pembish answering this rhetorical question from with in the greenhouse.

What, incidentally, is the answer ?

Socks Story

John Bayleaf often wears odd socks, and this afternoon was no exception. He tells me that he keeps all his socks in a bottom drawer and that when he dresses he removes a pair at random.

If he has four pairs of socks: one black, one white, one red and one blue. How many days per week on average will he be found wearing a matching pair?

The White and the Snakeshead

There are two types of Zirconian fritillary: the White and the Snakeshead. Both grow to a height of 45 zonks. The White, however, grows at a rate of one zonk in the first tink, two zonks in the second tink, three zonks in the third zink, etc. The Snakeshead variety is more interesting, it grows in such a way that its height increases by three zonks in first two tinks, by six zonks in second two tinks, nine zonks in the third tinks, etc. The both germinate(from zero height) at the same time.

Which of the two will be fully grown first?

Chances of Smoking

Mr. Striker is walking home across the parks. It is a walk which takes exactly two cigarettes. In his cigarette case he has two craven Doodahs and a pair of El-Rashids(which he prefers).

What are the chances of his smoking two El-Rashids in such a walk if he randomly withdraws cigarettes from the case.

Cuckoo Clock

At this moment the conversation was interrupted by a loud "Cuckoo" Dr. Chronos had just entered with a large cuckoo clock under his arm.

"Your clock is not exactly right," said Stars.

"Well It's not exactly wrong either," said Chronos, sitting next to Mr. Striker, who was puffing away on a cigarette. "You see, this is a very special clock: the hands shows the right time, but the cuckoo only emerges when the hands on the clock coincides."

If the bird was on time and the time was roughly 2:00 PM, what time was it exactly ?

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 ?

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 ?  

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 ?

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

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 ?

Tom, Dick and Harry

Tom, Dick and Harry are in prison. One of them has been randomly selected to die in the morning, and the other two will be set free. Their guard knows which one will die, but none of the prisoners does. The guard is under strict instructions not to divulge the identity of the doomed man.

Tom is desperate for any information beyond the fact that his probability of death is one in three. He begs the guard to throw him an informational bone. Finally, to shut him up, the guard agrees to reveal only the following: the name of one of Tom's fellow prisoners who will be set free rather than killed. The guard then says that Dick will be set free.

After receiving this information from the guard, what is the most accurate calculation Tom can make of the probability that he is the doomed man?

Thanks for your time
-- Josh Mudie

Through the Playing Card

Bill Gates wagers Warren Buffet 1 million dollars that he can cut a hole in an ordinary playing card and step right through it. As Warren's financial advisor, would you suggest him to bet ? Or What explanation can you give him ?

Bill Gates and Warren's old adventure here

Triangle Trick

How can this be true ?


Shared by Ardelean Ciprian with the following note

"u're the best, best site ever, like those games on PSP and NintendoSD...the logics that keeps the mind alive. I love it.. So,,,,I wait for some answers for my problem that i copied from internet... Still I didn't found an answer ,...."

Temperature Twist

"What's the temperature in Fahrenheit, required for the chemical reaction?" asked the student.

"Its a two digit number in Celsius and if you switch the place you get the temperature in Fahrenheit" explained the professor.

"That is still ambiguous !" said the student.

"You are smart ! Choose the pair with more evens !"

Beer Barrel

A dealer used to sell local beer using a cylindrical barrel of radius 10" and length 40". One day the barrel got broken. He found another barrel of similar dimension, radius was 40" and length 10".

"Wow ! what a coincidence I don't have to buy a new barrel now. I can use this one without changing anything," He thought.

Can he?

Clock Work

When Sylar opened a clock to service, he saw that the big wheel has 21 teeth and the small one 7 teeth. He immediately knew how many times it takes for small wheel to rotate to circle around the big wheel. Do you ?

* Can you believe there is a standard formula for this !

Square Sum

Do you know that no natural numbers having more than one digit is equal to the sum of the squares of its digits. But there are natural numbers which are equal to the square of the sum of its digits.

Can you think of one, which is greater than 9 ?

Fifty Cents

A drink machine has three options Coke, Pepsi and Random. Each drink is fifty cents. A friend tells you that the machine is faulty and that the buttons are never correct.

How much money would you need to spend to know which buttons deliver which drinks?

Shortest Time

A man is on an island which is 4 miles from the nearest point on a straight shoreline. He wishes to go to a house which is 12 miles from this nearest point. If he rows at 3 miles per hour and runs at 5 miles per hour, find the shortest time to reach the house.

If the quickest time is achieved when x =3, how much time does he waste if he lands at x =2 or x =4?

Square Root till Infinity

SQRT(x + SQRT(x+SQRT(x+SQRT(x+...)))) = x

What is x ?

Black Friday

Shopaholic Sofie, who was born in a leap year, was very superstitious about her shopping and always insisted on odd number of items. While shopping for her boyfriend, she saw a deal of Waistcoat and Trousers for $30, A deal of Jacket and Trousers at $40 and a Waistcoat and Jacket bundle for $ 32.

How much she will pay for the three piece suit ?

Breakfast Blues

I got an egg for breakfast and I know that it takes 9 minutes to boil the egg. There is a small problem though. I only have a 4 minute egg timer and a seven minute egg timer.

If only I could be as smart as Pythagreous ! Can you help me do the egg ?

Pensioner

John is an old pensioner. Reversing the digits of his age this year and doubling the answer gives his age next year. How old is John ?

Fair Enough

Bill Gates bets Warren Buffet 100 million dollars, that if Buffet gives Bill 200 million dollars, Bill will give 300 million dollars back. Every one knows that Warren has got 62 billion and Bill Gates 58 billion dollars.

Should Buffet make the transaction ? and who is going to gain and by how much ?

Going in Circles

Bob: ToM Puzzles are not so difficult now a days
Alice: Are you guys able to solve it all
Ted: Except the one when I am too busy
Alice: I have heard that before, you are not busy now

The Circle have three distinct points P,Q, and R. Question is to find another point "S" in the circle so that another circle can be inscribed in the Quadrilateral obtained.

You only have a scale and a compass.

Number Cruncher

So the number X is of three digits and it is divisible by 11. With one more condition that X/11 is equal to sum of the squares of the digits of X.

What is X, won't be a surprise question will it ?

Bathtub misery

Hercule Poirot knows that his bath fills in three minutes if the cold tap only is turned on full, and in four minutes if the hot tap only is turned on full. With the plug out, the bath empties in two minutes.
One day he find o his horror that Mrs Lemon has mislaid the plug, but he is intelligent enough to realize that he can still manage to fill the bath with both taps on full.