Gold Bars in a Pile

Three robbers A, B, and C each place stolen gold bars in a common pile, their shares being 1/2, 1/3, and 1/6 of the total amount, respectively. Next, each man takes the bars from the pile until none remain. Now A returns 1/2 of what he took, B 1/3, and C 1/6. When the last pile of gold is divided equally by the three men, it turns out that each has the amount he had at the beginning.

What was the total number of gold bars? (look for the minimum number of gold bars to satisfy the conditions)

A Particular Square Number

Find a square number such that, when five is added or subtracted, the result is again a square number!

Rabbits and More Rabbits

A man bought a pair of rabbits. How many pairs of rabbits can be produced from the original pair, in a year, if it is assumed that every month each pair begets a new pair that can reproduce after 2 months?

Fashion Show

Three models - Miss Pink, Miss Green, and Miss Blue - are on the catwalk. Their dresses are solid pink, solid green, and solid blue.

"It's strange," Miss Blue remarks to the others. "We are named Pink, Green, and Blue, and our dresses are pink, green and blue, but none of us is wearing the dress which matches her name."

"That is a conicidence," says the woman in Green.

What color dress is each woman wearing?

The Mutilated Chessboard

Consider a regular chessboard and 32 dominoes. The size of the chessboard is such that one domino can cover 2 adjacent squares on the board. Therefore the 32 dominoes can cover all 64 of the chessboard squares.

Now, imagine that 2 diagonally opposite corners of the board are cut from the board and discarded. Is is possible to place 31 of the dominoes on the mutilated chessboard in a manner such that all of the remaining 62 squares are covered.

If so, explain; it not, prove it impossible.

Strange Signs

---------- To A -- To B -- To C -- To D

Sign A ---- X ----- 20 ---- 19 ----- 17

Sign B ---- 19 ----- X ---- 18 ----- 15

Sign C ---- 19 ---- 18 ----- X ----- 20

Sign D ---- 17 ---- 19 ---- 20 ----- X


The table above shows the distances (km) given on signposts at four villages A, B, C, and D to their three neighboring villages. For example, at village B the signpost gives a distance of 19km to village A. Each signpost has exactly three numbers on it. The trouble is, the signposts have been vandalized so that only sign gives exactly three correct distances, one gives precisely two correct, one has exactly one correct one correct, and one has no correct distances. When the signposts were correct, no distance between two villages was repeated between another pair of villages.

State the number of correct distances on each sign!

Mad Nomads

Every Saturday in the four-bedroomed Nomad house, the four occupants, one to each room, change bedrooms so that only one of them keeps the same room. On one particular Friday, Arnie occupied the front left bedroom, Barbara the front right one, Carrie the back left, and Denzil the back right. The next day, they changed rooms just before the landlord called for the rent. When he demanded his money, each made a statement about the location of the rent money.

1) "The bedroom to my right," said Arnie.

2) "The room in front of me," claimed Barbara.

3) "The room to my left," said Carrie.

4) The room diagonally to the right of mine." said Denzil.

The problem was, two of the tenants lied, while two told the truth. (Note: In a statement, a liar may refer to a room that does not exist, such as one "behind" or "to the left" of a back left room.)

Can you name the new occupant in each room and state who had the rent?

Alien Ages

NAME -------- RACE ----- PLANET -------- AGE

1) Bleep ------- Tartan ----- Parp ---------- 213

2) Ting -------- Polyp ------ Dorb ---------- 385

3) Hoot -------- Bunter -----Esther -------- 706

4) Eek --------- Crispy ----- Booper -------- 503

5) Peep ------- Winky ----- Grunt --------- 897

6) Doodah -----Fodder ---- Flip ------------- 32


Six galactic space people enterred the Funniest Space Face competition. The judges recorded the alien's name, race of origin, home planet, and age for the first six places in the competition. Due to a clerical error, although the info is in the right column, it is not assigned to the correct alien. There is one correct entry in each column. The following facts are true about the correct order:

1. Grunt is one place above Fodder.
2. Booper is three places below Eek, and two below 32.
3. Doodah is two places above Tartan and one below 385.
4. The 706-year old alien is three places above Ting.
5. Peep is two places below Bunter, and one above Parp.
6. Esther is one place above 213, and three above Polyp.

Please assist the judges. Find the correct name, race, planet, and age for each position.

Alphabet l

Group 1: A - T - Y - M - U - W

What do the letters in group 1 have in common?

Group 2: C - B - K - D - E

What do the letters in group 2 have in common?

Inscribed Polygons

Imagine a circle with a radius of one unit. Inside the circle, inscribe the largest possible equilateral triangle. In the triangle, inscribe a circle. In the circle goes a square ... in the square a circle...in the circle a regular pentagon ... in the pentagon a circle ... etc. Each consecutive polygon has one more side ... alternating with circles. The circles get smaller and smaller.

Can you make a rough guess as to how small the circle will eventually become?

Hexagon In-Out

Imagine a hexagon with a circle inside it. Six points, on the circle, each lie on the center of a different side of the hexagon ... thus it is the largest circle which will fit inside the hexagon. Now imagine another hexagon inside the circle ... each vertex of the hexagon lies on the circle ... making it the largest hexagon which will fit inside the circle.

The inner hexagon has an area of three square units.

What is the area of the outer hexagon?

Fair's Fair

Bill Fair's gaming booth at the state fair had an interesting game. On the counter in front of him were four overturned cups. Each concealed the same number of balls. On each cup was a statement about the number of balls underneath. From left to right the statements were:

one or four
two or four
two or three
one or two

Only one of the statements was correct.

Could you win a prize at Bill Fair's booth? How many balls were under each cup, and which statement was true?

Settling the Account

A man ordered dinner at an expensive restaurant. When the meal was brought to him, he looked at it, wrote the following note for the waiter, and left the restaurant:

1 0 2 0 0 4 1 8 0

The waiter took the note to the cashier, who understood its meaning and placed it in the cash register.

Can you determine what the note meant?

Red Hair

Two Russian mathematicians end up on the same plane.

"If I remember correctly, you have three sons," says Ivan. "What are their ages?"

"The product of their ages is thirty-six," says Igor, "and the sum of their ages is exactly today's date."

"I'm sorry," Ivan says after a minute, "but that doesn't tell me the ages of your boys."

"Oh, I forgot to tell you, my youngest son has red hair."

"Ah, now it's clear," says Ivan. "I now know exactly how old your three sons are."

What are the ages ... and how did Ivan determine them?

Probably relatively prime

What is the probability that two randomly chosen positive integers are relatively prime?

Two numbers are relatively prime if they have no common factors.

Balls Big and Small

If 4" diameter steel balls are packed into a cubic yard container, and 2" diameter steel balls are packed into another cubic yard container, which full container weighs more?

Paint paradox

Consider the curve y = 1/x, over the region x = 1 to infinity. The volume of revolution about the x-axis is Pi, but the surface area is infinite.

So you can fill the cone shape with paint, but you can't paint it. Explain!

Ice bound

A glass of water has an ice cube floating in it. When the ice melts, will the water level rise, fall or remain the same?

Please ignore evaporation and other such sophistication.

Bouncing ball

I've just found this. I haven't got an official answer, but here goes:

A ball is dropped from a height of 1 m on to a surface. During the bounce, the ball loses half of it's energy. How long does the ball bounce for?

Assume everything else is ideal.

(I know Ragknot will have a field day with this.)

Piggy Banks

Three nickels and three dimes are distributed among three piggy banks such that each holds two coins:

one bank is labeled 10 cents
one bank is labeled 15 cents
one bank is labeled 20 cents

The banks are mislabeled according to the coin distribution ... is it possible to accurately re-label the banks by shaking only one of them until a single coin falls out? If so, explain!

Under the Band

Imagine you are on a perfectly smooth sphere as big as our sun. A steel band is stretched tightly around the equator.

One yard of steel is added to the length of the band so that it is raised from the sphere's surface the same distance all the way around.

Will the distance between the steel band and the sphere be enough to:

1) slip a playing card between?

2) slip your hand between?

3) slip a baseball between?

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

The Bicycles and the Fly

Two boys on bicycles, 20 miles apart, began racing directly toward each other. The instant they started, a fly on the handle bar of one bicycle started flying straight toward the other cyclist. As soon as it reached the other handle bar, it turned and started back. The fly flew back and forth in this way, from handle bar to handle bar, until the two bicycles met.

If each bicycle had a constant speed of 10 miles an hour, and the fly flew at a constant speed of 15 miles an hour, how far did the fly fly?

Crossing the Desert

An unlimited supply of gasoline is available at the edge of a desert 800 miles wide, but there is no gasoline in the desert. A truck can carry enough gasoline to go 500 miles (this amount will be called one load), and it can build up its own refueling stations at any point along the way. These caches can be any size and it is given that there will be no evaporation loss.

What is the minimum amount (in loads) of gasoline the truck will require in order to cross the desert? Is there a limit to the size of a desert the truck can cross?

Water and Wine

Consider 2 beakers ... one with 10 ounces of water ... and the other with 10 ounces of wine. Begin by transferring 3 ounces of wine into the beaker with water. Alternating back and forth, and stirring thoroughly after each transfer of 3 ounces, how many transfers are necessary for the percentage of wine in each beaker to be equivalent?

A Christmas Gift

It's Christmas, all merry and joyful
In me, the goodies are plentiful
If you know what's in me,
you'll get three,
with another for free
A third is yellow, with spikes for protection,
A third is red, with its seeds like perspiration,
A third is purle, with bitter peels as protection,
They're for Jesus' favourites, they say
But they're even on gingerbread house roofs that play
They're all sweet and tasty
But they might give you cavities, ouchy
They come from country of islands
near the most populous land
So go ahead and guess
or all you'll get is a mess!!!

So, what goodies are inside me??

(Merry Christmas
and a Happy New Year
to everyone ^^)

Flags, ropes, roofs - oh my!

This is a riddle of two flags on flagpoles on houseroofs
You have a rope to assist you
You are only human so there're no poofs
You can't tie the rope on flage poles and pull across
Because then you would surely fall
You can't reach across roofs
Because you're just not that tall
You can't swing on the rope
Because then you will meet your death
You can't be on the ground
Because then you will be in enemy's grasp
If you can make a road
Then you'll cross without a yelp
Mind that glue gun in your pocket
Because it will come to help
Oh and with infinite amount of rope
How would you get to the other flag?
But don't worry if you have no hope
Because it won't cost you an arm nor leg
Try this, if you can, without your glue.

(sorry, I'm not really a poet)

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

Nearly one

Prove that 0.9999999999..... = 1.

Bright idea

In your basement you have three light switches. They are in the off position. The lights can't be seen from the basement. Using only one visit to the lights, how can you determine which switch controls which light?

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

Hole in the Sphere

A cylindrical hole six inches long has been drilled straight through the center of a solid sphere. What is the volume of the solid material remaining in the sphere?

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

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?

Chess Squares

What is the probability to randomly chose any 3 squares on a chess board, and they would form a continuous diagonal?

You don't hold a chess board in your hands to solve this one. simply think.

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

Deer Dilemma

In Kisatchie National Forest in Louisiana, where there are thousands of deer, one out of 10 on an average is a blackbuck (endangered species). If you happen to shoot at random 10 deer in this forest, what is the chance that you will have hit at least one blackbuck? And how many deer do you need to shoot to be sure with a confidence of 90 percent that a blackbuck has been shot?

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.

Bicycle Pedal

A wire is tied to a cycle pedal that is stationary at the bottom of its arc. If someone pulls this wire backwards (while another person lightly holds the seat to keep the bike balanced), will the cycle move forward, backward or not at all?

Give reasons !

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.

About Arrows

What makes arrows fly straight ?

Body Parts

HEAD, HEART, EYES, TONGUE, LIPS, JAWS, HANDS, FINGERS, LEGS, FOOT, TOES, BLOOD, BONE, GUTS

these words are connected to each other in a very unique other than being body parts can you find that out ?

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