5

Part of 2002 May Olympiad

Problems(2)

Source: May Olympiad(Olimpiada de Mayo) 2002

x

y

be positive integers we have a table

x\times y

(x + 1)(y + 1)

points are red(the points are the vertices of the squares). Initially there is one ant in each red point, in a moment the ants walk by the lines of the table with same speed, each turn that an ant arrive in a red point the ant moves

90º

to some direction. Determine all values of

x

y

where is possible that the ants move indefinitely where can't be in any moment two ants in the same red point.

combinatoricscombinatorics unsolved

max no of 3x5x7 boxes in 11x35x39

Source: VIII May Olympiad (Olimpiada de Mayo) 2002 L1 P5

Find the maximum number of

3 \times 5\times 7

boxes that can be placed inside a

11\times 35\times 39

box. For the number found, indicate how you would place that number of boxes inside the box.

combinatoricstiles