Opgaver til kursusgang 1.
ancient Sicilian legend says that the barber in a remote town who can
be reached only by travelling a dangerous mountain road shaves those
people, and only those people who do not shave themselves. Can there be
such a barber.
Use a direct proof to show that every odd integer is the difference of two squares.
Show that at least 10 of any 64 days chosen must fall on the same day of the week.
Prove that at least one of the real numbers a1, a2, ... , an is greater that or equal to the average of these numbers.
What kind of proof did you use?
Exercise 39 to show that if the first 10 positive integers are placed
around a circle, in any order, there exist three integers in
consecutive locations around the circle that have a sum greater than or
equal to 17.
Opgave til afsnit 1.6: Vis at log2(3) er irrational.
(19/12 bliver dog anvendt som en approximation. Se eventuelt appendix A-2 om logaritme funktioner).