Mathematics as Problem Solving
I would like to start our discussion with the following stories.
Streetcar Story I
You enter a streetcar with six other passengers on the first stop of its
route. On the second stop, four people come in and two get off. On
the third stop, seven people come in and five get off. On the fourth
stop, eight people come in and three get off. On the fifth stop, thirteen
people come in and eight get off.
How old is the driver?
Did you start counting passengers in the streetcar? If you did, here
is your first lesson: Do not start solving a problem before you read it!
Sounds obvious? Perhaps you are right. But you should not un-
derestimate its importance. I for one underestimated some obvious
things in life, and had to learn the hard way lessons like, “Do not read
while you drive!”
The story above does not give us any information relevant to the
age of the driver. However, relevance of information is not always
obvious.
Streetcar Story II
The reunion of two friends in a streetcar sounded like this:
Streetcar Story I
You enter a streetcar with six other passengers on the first stop of its
route. On the second stop, four people come in and two get off. On
the third stop, seven people come in and five get off. On the fourth
stop, eight people come in and three get off. On the fifth stop, thirteen
people come in and eight get off.
How old is the driver?
Did you start counting passengers in the streetcar? If you did, here
is your first lesson: Do not start solving a problem before you read it!
Sounds obvious? Perhaps you are right. But you should not un-
derestimate its importance. I for one underestimated some obvious
things in life, and had to learn the hard way lessons like, “Do not read
while you drive!”
The story above does not give us any information relevant to the
age of the driver. However, relevance of information is not always
obvious.
Streetcar Story II
The reunion of two friends in a streetcar sounded like this:
— How are you? Thank you, I am fine.
— You just got married when we met last. Any children?
— I have three kids!
— Wow! How old are they?
— Well, if you multiply their ages, you would get 36; but if you
add them up, you’d get the number of passengers in this streetcar.
— Gotcha, but you did not tell me enough to figure out their ages.
— My oldest kid is a great sportsman.
— Aha! Now I know their ages!
Find the number of passengers in the streetcar and the ages of the
children.
Can the statement “my oldest kid is a great sportsman” have any
relevance? It can. In fact, it does! Moreover, the fact that without this
statement the second friend cannot figure out the ages of the children
carries valuable information, too!
— You just got married when we met last. Any children?
— I have three kids!
— Wow! How old are they?
— Well, if you multiply their ages, you would get 36; but if you
add them up, you’d get the number of passengers in this streetcar.
— Gotcha, but you did not tell me enough to figure out their ages.
— My oldest kid is a great sportsman.
— Aha! Now I know their ages!
Find the number of passengers in the streetcar and the ages of the
children.
Can the statement “my oldest kid is a great sportsman” have any
relevance? It can. In fact, it does! Moreover, the fact that without this
statement the second friend cannot figure out the ages of the children
carries valuable information, too!
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