Brain
Teasers
1.
The Missing Dollar Three students checked into a hotel and paid
the clerk $30 for a room ($10 each). When the hotel manager
returned, he noticed that the clerk had incorrectly charged
$30 instead of $25 for the room. The manager told the clerk
to return $5 to the students. The clerk, knowing that the students
would not be able to divide $5 evenly, decided to keep $2 and
to give them only $3.
The students were very happy because they paid only $27 for
the room ($9 each). However, if they paid $27 and the clerk
kept $2, that adds up to $29. What happened to the other Dollar?
(see answers at the bottom of page)
2.
You have to measure exactly 4 liters of water, but you only
have a 3-liter bottle and a 5-liter bottle. How do you do it?
3.
The Mysterious Square
When we
rearrange the pieces of the upper picture to form the lower
picture we have a missing square. The pieces in both pictures
are identical. Can you explain why the square is missing? You
will need your knowledge of geometry to solve this problem.
Answer 1
There is a saying that you cannot add apples and oranges. If
you have 3 apples and 2 oranges do you have 5 apples? No. Do
you have 5 oranges? No. You have five fruits, but the number
of apples and oranges has not changed. Similarly, you cannot
add real money and "what they think they paid". When we count
only real money, the students have $3, the clerk has $2, and
the manager has $25. That is $30 total.
Answer
2
Fill the 3-liter bottle and pour it into the empty 5-liter bottle.
Fill the 3-liter bottle again, and pour enough to fill 5-liter
bottle. This leaves exactly 1 liter in the 3-liter bottle.
Empty the 5-liter bottle; pour the remaining 1 liter from the
3-liter bottle into the 5-liter bottle.
Fill the 3-liter bottle and pour it into the 5-liter bottle.
The 5-liter bottle now has exactly 4 liters
Answer 3
The area of a right triangle is computed by multiplying the
base times the height and dividing by two. The pieces of the
puzzle have an area of 32 square units. Although they can be
assembled to form what appears to be a 13×5 right triangle,
they actually form quadrilaterals that are slightly smaller
or slightly bigger than a 13×5 right triangle.
The top figure has an area of 32 square units. The bottom figure,
including the empty square, has an area of 33 square units.
A real 13×5 right triangle would have an area of 32.5 square
units.
The distortion is difficult to see because one square of the
picture is approximately 3% of the area. The distortion can
be seen more clearly when the empty square constitutes a larger
percentage of the area, as in the figure below where 1 square
represents 13% of the area.
