1

Part of 1991 Cono Sur Olympiad

Problems(2)

Prove parallelism

Source: Cono Sur 1991-problem 1

A, B

C

be three non-collinear points and

E

\ne B

) an arbitrary point not in the straight line

AC

. Construct the parallelograms

ABCD

AECF

BE \parallel DF

geometryparallelogramgeometry unsolved

Is this possible?

Source: Cono Sur 1991-problem 4

A game consists in

9

coins (blacks or whites) arrenged in the following position (see picture 1). If you choose

1

coin on the border of the square, this coin and it's neighbours change their color. If you choose the coin at the centre, it doesn't change it's color, but the other

8

coins do. Here is an example of

9

white coins, and the changes of their colors, choosing the coin said: (see picture 2). Is it possible, starting with

9

white coins, to have

9

combinatorics unsolvedcombinatorics