MathDB

4

Part of 2009 Bundeswettbewerb Mathematik

Problems(2)

decimal palindrome

Source: Germany Federal - Bundeswettbewerb Mathematik 2009, round 1, p4

4/9/2020
A positive integer is called decimal palindrome if its decimal representation zn...z0z_n...z_0 with zn≠0z_n\ne 0 is mirror symmetric, i.e. if zk=zn−kz_k = z_{n-k} applies to all k=0,...,nk= 0, ..., n. Show that each integer that is not divisible by 1010 has a positive multiple, which is a decimal palindrome.
number theorypalindromesmultiple
no of diagonals inside a 2009-gon, every diagonals cuts at most another

Source: Germany Federal - Bundeswettbewerb Mathematik 2009, round 2, p4

4/9/2020
How many diagonals can you draw in a convex 20092009-gon if in the finished drawing, every drawn diagonal inside the 20092009-gon may cut at most another drawn diagonal?
combinatorial geometrycombinatoricsdiagonals