2008 Nordic

Part of Nordic

Subcontests

(4)

1

Nordic MC 2008 Q3

ABC

be a triangle and

D,E

BC,CA

AD,BE

are angle bisectors of

\triangle ABC

F,G

be points on the circumcircle of

\triangle ABC

AF||DE

FG||BC

\frac{AG}{BG}= \frac{AB+AC}{AB+BC}

1

Nordic MC 2008 Q1

A,B,C

such that there exists a real function

f

f(x+f(y))= Ax+By+C

x,y

1

Nordic MC 2008 Q2

n\ge 3

people with different names sit around a round table. We call any unordered pair of them, say

M,N

, dominating if 1) they do not sit in adjacent seats 2) on one or both arcs connecting

M,N

along the table, all people have names coming alphabetically after

M,N

.
Determine the minimal number of dominating pairs.

1

Nordic MC 2008 Q4

The difference between the cubes of two consecutive positive integers is equal to

n^2

for a positive integer

n

n

is the sum of two squares.