2. DEAR MR. MAILMAN, PLEASE SEE THE NOTE.
Please put
the
envelopes in
the desk’s
pigeon holes.
If possible,
put each
envelope in a
separate
pigeon hole.
3. THE MAILMAN SAYS,
I’ll do my best. I have 9 letters and
there are only 8 pigeon holes in this
desk.
5. WE CAN GUARANTEE THAT
at least one of the pigeon holes will
have more than one envelope in it.
The mailman could have
thought, well, since it is not
possible, I will put all 9
envelopes into just one
pigeon hole. Also, he could
have decided to split them
into two pigeon holes, maybe
4 in one and 5 in the other (in
which case 2 holes would
have more than one
envelope).
6. PIGEONHOLE PRINCIPLE
If we have n objects that have to fit into m
holes or slots, and if n>m, then we can
guarantee that at least one of the slots
has more than one object in it.
What is another example of using this
principle?
7. WE CAN USE DATES AS PIGEON HOLES!
How many days are in a non-leap year?
Suppose I have 366 people in my class.
Using the pigeonhole principle, pretending
each day on the calendar is a pigeon
hole, what can you guarantee about the
birthdays of my students?
At least 1 day of the year is a birthday for
more than 1 of my students.
In other words, at least 2 of my students
share a birthday.
8. WE CAN USE NATURAL NUMBERS AS SLOTS!
I’ll read the example on pages 53-54.
9. PIGEONHOLE PRINCIPLE AND NATURE
Find something outside in nature with little parts to it.
Count how many little parts are on a small area. Over-
estimate. Count how many small areas are on it. Over-
estimate. Multiply to get an over-estimate for how many
little parts could possibly be on one of your things.
Then pretend you have a hypothetical garden or farm with
many of these plants on it. Using the pigeonhole
principle, what can you say?
For example, if I have 1201 of these plants in my garden,
then I can guarantee that at least 2of them have the exact
same number of little bids on them. I can say that
because 1201 is larger than 1200, and I calculated that the
highest possible number of little buds that can be on one
flower is 1200. Here is how I came up with that
estimation….
