Riddles I haven't had the time to write up nicely:

Prove: For every natural number n there exists a natural number s such that
s * n results in a number with only 7 and 0 as digits (example: 707007)

I'm looking for a 10 digit number that fits into the following statement.
note the first number is the number to the far left, example- the first
digit of this number is 526897413 is 5)
The first digit represents the number of 0's in the number
The second digit represents the number of 1's in the number
The third digit represents the number of 2's in the number
The forth digit represents the number of 3's in the number
The fifth digit represents the number of 4's in the number
The sixth digit represents the number of 5's in the number
The seventh digit represents the number of 6's in the number
The eight digit represents the number of 7's in the number
The ninth digit represents the number of 8's in the number
The tenth digit represents the number of 9's in the number
 

HOW MANY BANANAS CAN CORI TAKE TO THE MARKET?
1.THE MARKET IS 1,000 MILES AWAY.
2.CORI CAN CARRY 1,000 BANANAS AT A TIME.
3.CORI EATS ONE BANANA EVERY MILE. ( IT DOES NOT MATTER IF SHE RUNS OR
WALKS BACKWARDS, SHE STILL EATS A BANANA EVERY MILE).
4. CORI WALKS;, SHE DOES NOT FLY OR HAVE ANY HELPERS.
(What is the fewest number of bananas needed to move a certain number of bananas?)

A king decides to release all his prisoners on Christmas eve, he has 1000
jail cells of them. He has his jailer unlock all the cell doors. He
thinks this is too many to release at once, so he has him go back and
starting with door # 2 he tells him to turn the key in lock and do this
every second door. He then tells him to insert the key and turn the lock
on door # 3 and to do it in every third door. Then starting with door
number 4 and every fourth door. This continues the same pattern through
all 1000 cell doors. How many prisoners are released and how many are
still locked up? Explain your answer.

What do the numbers 3, 7, 8, 40, 50, 60 have in common that no other
numbers have? -- Not a math riddle, more a language riddle

If I'd have 60 apples, and i would like to sell 30 in one spot at 3
apples for 1 dollar = 3/1.00 and in another spot,the other 30 at 2
apples for 1 dollar = 2/1.00 I'd make 10 dlls, in the first one, and 15
dlls, in the second one, right? So that would be 25 dlls total earned.
Well if i just forget, about putting two different spots, and i'd choose
to sell my apples at 5 apples for 2 dlls = 5/2.00 , why in the world i
get 24 dlls????

Frank is three times as old as his son was when Frank was twice as old
as his son will be two years form now. What is Franks age now.

Three cards are in a hat. One is red on both sides,
one is white on both sides, and one is red on one side
and white on the other. I draw a card from the hat, and
place it on the table. The upward-facing side is red.
What are the odds that the downward-facing side is also
red?

This is an old problem with anew twist. A poor farmer is going tomarket
with his faithful but hungry dog, two plump geese to seell, and three
bags of corn. The farmer knows that unless he is right there, the dog
will eat a goose or a goosewill eat some of the corn. Travelling
carefully, he avoids trouble until he comes to small river which
he must ferry across. The ferry (actually a creaky old rowboat) is in
such bad shape, he decides it will only hold him and any two of the six
things he has with him. How can he get all of his possessions to market
safely, and uneaten?

A farmer is taking her eggs to market in her cart, but she hits a pothole,
which knocks over all the containers of eggs. Though she herself is not
hurt, every egg is broken. So she goes to her insurance agent, who asks her
how many eggs she had. She says she doesn't know, but she remembers some
things from the various ways she tried packing the eggs. She knows that when
she put the eggs in groups of two, there was one left over. When she put them
in groups of three , there was also one egg left over. The same thing
happened when she put them in groups of four, groups of five, or groups of
six. But when she put them in groups of seven, she ended up with complete
groups of seven with no eggs left over.
 

If you have a circle and you are only given three lines to divide it in
seven equal pieces, how can this be accomplished

5, 5, 5, 1 = 24
You must use all digits.
You can use: +, -, x, / (divided by) several times
You cannot use sqaure root
How do I get 24?

Mr. Miller, I've been stumped with this riddle for 3 weeks. Here it
goes: You have $100.00 and you must buy 100 animals and they must
include cows, pigs and chickens. Cows sell for $10.00 each, pigs - $3.00
each, and chickens 50 cents a piece. You must spend all of the $100.00
and you must buy 100 animals.
 

1
1 1
2 1
1 2 1 1
3 1 1 2
1 3 2 1 1 2
3 1 1 3 2 2
what is the next line there is a pattern?

There are 1000 light bulbs all switched off.
Starting with number 1, going up to 1000 by jumps of one
(i.e. 1,2,3, etc.), you will turn ON each light bulb
that is off, and each light bulb that is on will be
turned OFF, then you start again going up this time by
jumps of two (i.e.2, 4,6,etc.) Start all over again with
jumps of 3(i.e.3, 6,9,etc.), jumps of 4,5,6 etc. until
you reach Jumps of 1000. Here is the question: how many
light bulbs will be left on by the time you reach jumps
of 1000? Remember on each jump you will turn ON each
light bulb that is off, and each light bulb that is on
will be turned OFF.
 

A warden in a prinson decides to give a certain prisoner a chance at
freedom. THe warden brings the prinsoner to the two doors as shown and
explains that, behind the doors, no room is empty. If gold is behind the
door that the prisoner chooses, he/she gets to keep it, as well as gets
to go free. But, if the prisoner chooses a door with a tiger behind it,
the tiger will have its dinner for the night. The warden tells the
prisoner that either both signs are true or both are false. If you were
the prisoner, which door would you choose to get the gold and obtain your
freedom? Explain why.

Alfred is vacationing on a south seas island when he encounters two
tribes. The members of one tribe always thell the truth, and the members
of the other tribe always tell falsehoods. Alfred comes to a fork in the
road and wants to know which of the two forking paths leads to the
village. There is a member of one of the tribes at the intersection, and
alfred has the opportunity to ask one yes/ no question. What question
can Alfred ask and the answer to which will tell him which of the forking
paths leads to the village?

Using numbers 1,2,3,4,5,6,7,8,9 (each exactly once) to form three fractions
(numerators 1 digit, denominators 2 digits) such that the three sum to 1.
Example: 1/23 + 4/56 + 7/89, but of course this doesn't work).

Problem: construct a sequence of real numbers a_i such that Sum_i a_i converges
but Sum_i a_i^3 diverges.

Five real numbers between 0 and 1 are chosen at random, with uniform
probability distribution. The player is shown each number in turn and
asked whether he believes it to be the largest of the five.
If the player guesses wrong, the game ends (player loses). If the
player guesses correctly that the current number IS the largest, the
player wins. If the player guesses correctly that the current number
is NOT the largest, then the player is shown the next number and the
game continues.

What are the next numbers? 4 4 4 4 2 1 1 1 1 1 1 2 1 1 1 3 1 2 ? ? ? ? ? ? ? ? ? ?
Hint: this is a language riddle as well as a number riddle (passed on by Steve Hampton,
Australia).

How do you cut a 16x9 units rectagle into two evenly sized and shaped
pieces that may be rearranged to make a square? The square has the same
area, so it is 12x12 units. (passed on by Brooke)
 

You have 9 coins and an equal arm balance scale, one coin weighs
slightly more. Can you find it in two weighs????

You have two pieces of string each burns in one hour but they burn
irregularlly in terms of how many inches burn per minute anywhere along the
string, can you use the strings to time 45 minutes????

City A is 9000 miles from city B, City A is also 9000 miles from City
C. (Appproximately) what are the odds that city B is closer to city C than
it is to city A... ... [from Jeff Miller]