MathDB

3

Part of 2009 Balkan MO

Problems(1)

Broken line with a centre of symmetry in a rectangle

Source: BMO 2009 Problem 3

4/30/2009
A 9×12 9 \times 12 rectangle is partitioned into unit squares. The centers of all the unit squares, except for the four corner squares and eight squares sharing a common side with one of them, are coloured red. Is it possible to label these red centres C1,C2,…,C96 C_1,C_2,\ldots ,C_{96} in such way that the following to conditions are both fulfilled i) the distances C1C2,…,C95C96,C96C1C_1C_2,\ldots ,C_{95}C_{96}, C_{96}C_{1} are all equal to 13 \sqrt {13}, ii) the closed broken line C1C2…C96C1 C_1C_2\ldots C_{96}C_1 has a centre of symmetry?
Bulgaria
symmetrygeometryrectanglecombinatorics proposedcombinatorics