5

Part of 2013 May Olympiad

Problems(2)

May Olympiad 2013, Level 2, Problem 5

Source:

600

200

of them having written the number

5

200

2

, and the other

200

1

, a student wants to create groups of cards such that the sum of the card numbers in each group is

9

. What is the maximum amount of groups that the student may create?

erase lengths on 8x8 board May Olympiad (Olimpiada de Mayo) 2013 L1 P5

Source:

8\times 8

square is drawn on the board divided into

64

1\times1

squares by lines parallel to the sides. Gustavo erases some segments of length

1

1\times 1

square he erases

0, 1

2

sides. Gustavo states that he erased

6

segments of length

1

from the edge of the

8\times 8

square and that the amount of

1\times 1

squares that have exactly

1

side erased is equal to

5

. Decide if what Gustavo said it may be true.