4
Part of 2011 May Olympiad
Problems(2)
Some points in a circle with 0 and 1 write on them
Source: Mayo Olympiad 2011
10/13/2020
Given points in a circle, Arnaldo write 0 or 1 in all the points. Bernado can do a operation, he can chosse some point and change its number and the numbers of the points on the right and left side of it. Arnaldo wins if Bernado can´t change all the numbers in the circle to 0, and Bernado wins if he cana) Show that Bernado can win if
b) Show that Arnaldo wins if
combinatorics
no of cubes to assemble large cube May Olympiad (Olimpiada de Mayo) 2011 L1 P4
Source:
9/28/2021
Using several white edge cubes of side , Guille builds a large cube. Then he chooses faces of the big cube and paints them red. Finally, he takes apart the large cube and observe that the cubes with at least a face painted red is . Find the number of cubes that he used to assemble the large cube.
Analyze all the possibilities.
combinatorial geometrycombinatorics