Puzzle - 1:
A
car has to carry an important person across the desert.
There
is no petrol station in the desert and the car has space only for enough petrol
to get it half way across the desert.
There
are also other identical cars that can transfer their petrol into one another.
How
can we get this important person across the desert?
Answer: We need 4 cars
(including the car with the important person).
All
4 cars start full.
At
1/6th of the way, all cars are 2/3rds full. One car sacrifices itself and fills
up two of the other cars. Two cars are now full, one is 2/3rds full. (An empty
car is left behind.)
At
2/6th of the way, two cars are 2/3rds full. One car is one third full, and
sacrifices itself to fill up one of the other cars. One car is now full, one is
2/3rds full. (An empty car is left behind.)
At
half way, one car is 2/3rds full. One car is one third full, and sacrifices
itself to fill the other car, which is now full and can make the other half of
the journey.
Puzzle - 2:
Joey
leaves his house in the morning to go to day camp.
Just
as he is leaving his house he looks at an analog clock reflected in the mirror.
There
are no numbers on the clock, so Joey makes an error in reading the time since
it is a mirror image. Joey assumes there is something wrong with the clock and
rides his bike to day camp.
He
gets there in 20 minutes and finds that just as he gets there the day camp
clock has a time that is 2 1/2 hours (2 hours and 30 minutes) later than the
time that he saw in the mirror image of his clock at home.
What
time was it when he got to day camp?
(The
clock at camp and the clock at home were both set to the correct time.)
Answer: First subtract 20
minutes from 2 1/2 hours to compensate for his 20 minute bike ride to give a
difference of 2 hours and 10 minutes.
To
be a "Mirror Effect" it must be mirrored around 12 o'clock (when the
hands are straight up), or around 6 o'clock (when the hands are pointing up and
down), as we know he left in the morning, it must be 6 o'clock.
So,
divide that 2 hours and 10 minutes by 2 and this will give you the center-point
(65 minutes) for compensating for the mirror.
By
adding that 65 minutes to 6 o'clock you get the time he left home (7:05), and
the time he saw in the mirror (4:55).
Furthermore,
by re-adding the 20 minutes from when he left (7:05), you get what time he got
to camp (7:25).
Puzzle - 3:
In
front of you are several long fuses.
You
know they burn for exactly one hour after you light them at one end.
But
the entire fuse does not burn at a constant speed. For example, it might take
five minutes to burn through half the fuse and fifty-five minutes to burn the
other half.
With
your lighter and using these fuses, how can you measure exactly three-quarters
of an hour of time?
Answer: Light both ends
of one fuse.
At
the same time light one end of a second fuse.
The
first fuse will finish in half an hour.
At
that point the second fuse will be half done (in time, not necessarily in
distance) and you immediately light its other end. The second half hour will now
take only quarter of an hour.
Total
time: half an hour plus quarter of an hour equals three-quarters of an hour.
Puzzle - 4:
You
have two straight lengths of wood.
How
can you cut one of them so that one of the three pieces is the average length
of the other two?
Answer: Put the two
pieces end to end in a straight line
Then
the average length of the three cut pieces has to be one third of this total
length.
So we simply cut one third of the way along the longer piece.
Puzzle - 5:
A
girl, a boy, and a dog start walking down a road.
They
start at the same time, from the same point, in the same direction.
The
boy walks at 5 km/h, the girl at 6 km/h.
The
dog runs from boy to girl and back again with a constant speed of 10 km/h. The
dog does not slow down on the turn.
How
far does the dog travel in 1 hour?
Answer: 10km. Because the dog's speed is 10 km/h.
