4

Part of 2009 May Olympiad

Problems(2)

red or blue on cells of 5x5

Source: XV May Olympiad (Olimpiada de Mayo) 2009 L2 P4

Each square of a

5 \times 5

board is painted red or blue, in such a way that the following condition is fulfilled: “For any two rows and two columns, of the

4

squares that are in their intersections, there are

4

2

0

painted red.” How many ways can the board be painted?

combinatoricsColoring

areas inside 3 circles (May Olympiad 2009 L1 - Olimpiada de Mayo)

Source:

Three circumferences are tangent to each other, as shown in the figure. The region of the outer circle that is not covered by the two inner circles has an area equal to

2 \pi

. Determine the length of the

PQ

segment . https://cdn.artofproblemsolving.com/attachments/a/e/65c08c47d4d20a05222a9b6cf65e84a25283b7.png

geometryArea of a circle