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# PSPFun Datafile
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# Name    : Riddles with some Math/Logic
# Author  : MK2k
# Language: EN
# Type    : Riddle
# NOTE    : Max. 58 Characters per Line
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#0000r
You are a bug sitting in one corner of a cubic room. You 
wish to walk from A to F. Describe the shortest path 
that you can walk. Imagine the Cube being:
      G-----F
     /     /.
    D-----C .
    .     . E
    .     ./
    A-----B  
#0000s
Shortest Path is A->B/C (middle point of the B-C edge.
Then B/C -> F.

#0001r
A windowless room contains three identical light 
fixtures, each containing an identical light bulb. Each 
light is connected to one of three switches outside of 
the room. Each bulb is switched off at present. You are 
outside the room, and the door is closed. You have one , 
and only one, opportunity to flip any of the external 
switches. After this, you can go into the room and look 
at the lights, but you may not touch the switches again. 
How can you tell which switch goes to which light?
#0001s
Switch on switch number 1, wait a few minutes, switch off 
switch number 1 and switch on switch number 2. Enter the 
room and which ever bulb is on is connected to switch 
number 2, which ever bulb is hot is connected to switch 
number 1, and the remaining bulb is connected to switch 
number 3. 

#0002r
You are to open a safe without knowing the combination. 
Beginning with the dial set at zero, the dial must be 
turned counter-clockwise to the first combination number, 
(then clockwise back to zero), and clockwise to the 
second combination number, (then counter-clockwise back 
to zero), and counter-clockwise again to the third and 
final number, where upon the door shall immediately 
spring open. There are 40 numbers on the dial, including 
the zero. Without knowing the combination numbers, what 
is the maximum number of trials required to open the safe 
(one trial equals one attempt to dial a full three-number 
combination)?
#0002s
40 x 40 = 1600
The key word here is 'immediately.' The implication of 
this is that you do not have to try 40 times at the last 
number for each combination of the first number two 
numbers.

#0003r
Inside of a dark closet are five hats: three blue and two 
red. Knowing this, three smart men go into the closet, 
and each selects a hat in the dark and places it unseen 
upon his head. Once outside the closet, no man can see 
his own hat. The first man looks at the other two, 
thinks, and says, "I cannot tell what color my hat is."
The second man hears this, looks at the other two, and 
says, "I cannot tell what color my hat is either." The 
third man is blind. The blind man says, "Well, I know 
what color my hat is." What color is his hat?
#0003s
We will call the people A, B and C in the story's order.
A does not know what colour hat he is wearing. A would
only know what colour hat he was wearing if he could see
that B and C were both wearing red hats. This is not the
case so either:
B and C are both wearing blue hats OR one of B and C is
wearing red and the other is wearing blue.
When B speaks we obviously assume he has thought of all of
this. When B looks at C, if C were wearing red then he
would know that he must be wearing blue as they can't both
be wearing red. But this does not happen so C must be
wearing blue, meaning that B doesn't know if he is wearing
red or blue:
The third person must be wearing a BLUE hat.

#0004r
You have a chessboard (8x8) plus a big box of dominoes 
(each 2x1). I use a marker pen to put an "X" in the 
squares at coordinates (1, 1) and (8, 8) - a pair of 
diagonally opposing corners. Is it possible to cover the 
remaining 62 squares using the dominoes without any of 
them sticking out over the edge of the board and without 
any of them overlapping? You cannot let the dominoes 
stand on their ends
#0004s
Firstly the answer to this question is NO you can't cover 
the board. There is a trick here. If you think about a 
Domino placed any where on the board it will necessarily 
cover a black square and a white square. We have in our 
example a 32 black squares and 30 white squares to cover. 
So it just can't be done.

#0005r
You have a string-like fuse that burns in exactly one 
minute. The fuse is inhomogeneous, and it may burn slowly 
at first, then quickly, then slowly, and so on. You have 
a match, and no watch. How do you measure exactly 30 
seconds?
#0005s
Light the fuse at both ends!

#0006r
Can the mean of any two consecutive prime numbers ever be 
prime?
#0006s
By definition of mean the result must be between the two 
source numbers. By definition of consecutive there can't 
be a prime number in between two consecutive prime 
numbers. There also can't be any apples in between two 
consecutive apples, shame on you if you had to think 
about this.

#0007r
How many consecutive zeros are there at the end of 100! 
(100 factorial).
#0007s
24 Zeros!

#0008r
A man is in a rowing boat floating on a lake, in the boat 
he has a brick. He throws the brick over the side of the 
boat so as it lands in the water. The brick sinks 
quickly. The question is, as a result of this does the 
water level in the lake go up or down?
#0008s
The Water Level Goes Down!
The brick in the boat dispenses it's own weight.
The brick in the water just dispenses it's own volume.

#0009r
You have a 3 and a 5 litre water container, each 
container has no markings except for that which gives you 
it's total volume. You also have a running tap. The 5 
litre container does not fit under the tap. You must use 
the containers and the tap in such away as to exactly 
measure out 4 litres of water. How is this done?
#0009s
Fill the 3 litre can from the tap.
Empty the contents of the 3 litre can into the 5 litre can.
Fill the 3 litre can from the tap.
Empty the contents of the 3 litre can into the 5 litre 
can.  - Leaving the 5 litre can full and 1 litre in the 3 
litre can.
Poor away the contents of the 5 litre can
Poor the 1 litre from the 3 litre can into the 5 litre can.
Fill the 3 litre can from the tap.
Empty the contents of the 3 litre can into the 5 litre can.
Leaving 4 litres in the 5 litre can.

#0010r
I have three envelopes, into one of them I put a 20 Dollar
note. I lay the envelopes out on a table in front of me 
and allow you to pick one envelope. You hold but do not 
open this envelope. I then take one of the envelopes from 
the table, demonstrate to you that it was empty, screw it 
up and throw it away. The question is would you rather 
stick with the envelope you have selected or exchange it 
for the one on the table. Why? What would be the expected 
value to you of the exchange?
#0010s
Initially there was a 1/3 chance that you were holding the
envelope with the note in it and a 2/3 chance that the
note was on the table. This is still the case after one of
the envelopes on the table has been removed, there is
still a 1/3 chance that you have the note and a 2/3 chance
of it being on the table. Simply before the exchange you
have 1/3 of 20 Dollars and afterwards you will have 2/3 of
20 Dollars, i.e. the advantage to you is about 6.66
Dollars.
#END