Old Arthur owned a perfectly square piece of land in each of
whose corners was an inexhaustible well (a, b, c ,d).
Shortly before he died, Arthur had four identical houses
built in a row, as shown in the drawing (A, B, C, D)
It was his wish that each of his sons be left one of the houses,
and a quarter of the land, with one of the wells on it.
In his will, Arthur stipulated that the four pieces of land should
have not only the same area but also exactly the same shape.
How must Arthur's land be divided up in order
for his wishes to be carried out?

Answer:

A bag contains fifty blue and fifty green marbles.
Two marbles at a time are randomly selected.
If they are both green, they are placed in box A;
if both blue, in box B;
if one is green and the other blue, in box C.
After all marbles are drawn,
what is the probability that the number of
marbles in box A and box B is the same?
Answer:  1 (or 100%)

How many miles per hour is a car traveling
if the wheels have a diameter of 3 feet
and are turning 600 times a minute?
Answer:  64.26 miles per hour

A swimming pool whose surface forms a rectangle measures 25 m long by 15 m wide.
The pool is 2 m deep at the shallow end, and the depth increases
at a constant rate to 4 m deep at the other end.
How many liters of water will the pool hold?
Answer:  1,125,000 liters

Find the total score in this figure
if triangles count 3, quadrilaterals count 4,
pentagons count 5, and hexagons count 6

Answer:  54
 

If the reciprocal of (x+1) is (x-1),
determine x.
Answer:  + or - square root of 2

A rectangular field is twice as long as it is wide.
Express the area A of the rectangle as a function
of its perimeter P.
Answer:  P²/18

If an arc of 45 degrees on circle A has the same length
as an arc of 30 degrees on circle B,
find the ratio of the area of circle A to the area of circle B.
Answer:  4/9

Take any three-digit number and write it down twice
to make a six-digit number.
Show that this number is exactly divisible by 7 or 11 or 13.
Answer:  If a number is divisible by 7, 11 and 13
then it must have factors of 7, 11 and 13.
So your number must be a multiple of 7*11*13, or 1001.
1001 times any three-digit number will result in the three digits
being written down twice -- (1000+1)*abc = abc000+abc = abcabc.

A clock chimes on the hour a number of times equal to
the hour and also chimes once every quarter hour.
If the face of the clock cannot be seen
and the clock has just chimed once,
what is the longest time you might have to wait
to be sure of knowing the time?
Answer:  105 minutes
[If you interpreted the question to ask for the longest amount of time AFTER
hearing that first one-chime, then your answer would be 90 minutes.]

If m and n are whole numbers,
49 < n < 101 and 19 < m < 51,
then what is the greatest value for (n + m) / n?
Answer:  2

 A circular sheet of paper of radius 6 cm is cut into three equal sectors,
and each sector is formed into a cone with no overlap.
What is the height in centimeters of each cone?
Answer:  4√2 cm

A basketball player is on the line to shoot a one-and-one free throw,
wherein a second shot is allowed only if the first shot is successful.
If the player's free-throw-shooting average is 0.750,
what is the probability that she will score exactly one basket?
Express the answer as a common fraction.
Answer:  3/16

What are the four smallest natural numbers
that are both perfect squares and perfect cubes?
Answer:  1, 64, 729, 4096

Find the degree measure of an angle
whose complement is 25 percent
of its supplement.
Answer:  60º

Find the exact area of the circle that passes through
the centers of four unit squares as shown.

Answer:  (1/2)π

When Paul crossed the finish line of a 60 meter race,
he was ahead of Robert by 10 meters and
ahead of Sam by 20 meters.
Suppose Robert and Sam continue to race to the
finish line without changing their rates of speed.
By how many meters will Robert beat Sam?
Answer:  12 meters

Does the parabola 3y = x² - 17
pass through any lattice points?
Answer:  No

Find the smallest positive integer n such that the product
of n and 999 does not contain the digit 9.
Answer:  112

Upon solving the system of equations x⁵y¹⁷ = r and x²y⁷ = s for x and y,
the answers turn out to be of the form
x = r^a/s^b and y = s^c/r^d, where a, b, c, and d are positive integers.
Calculate the sum a + b + c + d.
Answer: 31

You and your 5 friends decide to order a large pizza, but when you call in your
order, the pizza man asks you how many cuts across the pizza you want him to make.
Although stunned at this question you tell him 6 because there are 6 of you.
Then the pizza man responds back ...
"I'll tell you what -- when your pizza arrives, if you can tell the driver the maximum
number of pizza pieces you would have with 6 cuts, he will take $1 off the bill.
And, if you can tell him the maximum number of pieces you would have in general
with "n" cuts, he will give you the pizza for free."
What would your answer have to be to get the free pizza?
Answer:  (1/2)n² + (1/2)n + 1

Suppose that a, b, and c are positive integers such that a/3 = b/4 = c/5
and abc = 1620.  Find b.
Answer:  b = 12

In the target shown below, the circles have radius = 1, 2, and 3, respectively.
If you throw three darts and you are assured all three will hit the target,
what is the probability that your score will be exactly 150 points?

Answer:  34/243

A certain examination of 12 questions was graded by giving 10 points for each
correct answer and then deducting 5 points for each incorrect answer.
David attempted all 12 questions leaving no question unanswered,
and scored a total of 75 points.
How many wrong answers did he have?
(Answer:  3)

In a new version of the dating game, two of the three bachelors always lie while the
other tells the truth.  A woman asks questions of the men from behind a partition.
She asks each man, "Which of you is the tallest?"
Bachelor 1 replies, "Not me."  Bachelor 2 replies, "I am."
Bachelor 3 replies, "Not Bachelor 2."
Who is the tallest?
(Answer: bachelor #1)

An integer n in base eight is 3175.
What is the integer immediately following n
written in base 830?
(Answer:  22(base 830))

A bank has been charging a monthly service fee of $2.00 plus $0.10 a check
for a personal checking account.  To attract more customers it is advertising a new
reduced plan with a monthly service charge of $3.00 plus only $0.05 a check.
How many checks must you write each month for the new plan to save you money?
(Answer:  21 checks)

A piece of wire 64 centimeters in length is cut into two parts.
Each part is then bent to form a square.
The total area of the two squares is 130 square centimeters.
How much longer is a side of the larger square than a side of the smaller square?
(Answer:  2 cm.)

Six students stood under an umbrella.
Two left and then three more came.
Finally six more students came.
No students got wet.
How can this be?
(Answer:  It wasn't raining.)

It is given that the five-digit number 2xy89 is the square of an integer (in base ten).
Find the two-digit number xy.
(Answer:  xy = 78)

If  log_A27 = 0.75, what is A?
(Answer: A=81)

For the set of numbers {30, 80, 50, 40, x}, the
mean, mode, and median are all equal.
Find x.
(Answer: x = 50)

Find a function f(x) such that f(f(x)) = x
but f(x) does not equal x.
(Answer:  f(x) = 1/x, or more generally, f(x) = a + 1/(x-a)
where a is a constant and a does not equal x)

Separate 1000 into two parts so that one part is a multiple of 19
and the other is a multiple of 47.
(Answer:  1000 = 18(19) + 14(47))

A three-digit number is selected at random from all three-digit numbers 100 through 999.
What is the probability that the number selected is a perfect square?
(Answer:  22/900)