3
Part of 2009 Portugal MO
Problems(2)
Giant square - Portuguese MO, Problem 3, 2009
Source:
8/29/2010
Duarte wants to draw a square whose side's length is cm and which is divided in squares whose side's length is cm and whose sides are parallel to the original square's one, without taking the pencil out of the paper. Starting on one of the vertex of the giant square, what is the length of the shortest line that allows him to make this drawing?
combinatorics proposedcombinatorics
Explorers, Traps and Stones - Portuguese MO, Problem 6, 2009
Source:
8/29/2010
Two players play the following game on a circular board with 2009 houses. The two plays put, alternatively, on an empty house, one of three pieces, called explorer (E), trap (T) or stone (S). A treasure is a sequence of three consecutive filled houses such that the first one (on any direction) has an explorer and the middle one doesn't have a trap. For example, STE is not a treasure, while TEE is a treasure. The first player forming a treasure wins. Can any of the players guarantee the victory? And, in affirmative case, who?
combinatorics proposedcombinatorics