2010 Junior Balkan Team Selection Tests - Romania

Part of JBMO TST - Romania

Subcontests

(5)

1

bw distinct points in the plane

n

be a non-zero natural number,

n \ge 5

n

distinct points in the plane, each colored or white, or black. For each natural

k

, a move of type

k, 1 \le k <\frac {n} {2}

, means selecting exactly

k

points and changing their color. Determine the values of

n

for which, whatever

k

and regardless of the initial coloring, there is a finite sequence of

k

type moves, at the end of which all points have the same color.

5

4

5

5