5
Part of 2000 May Olympiad
Problems(2)
Rectangle can be divided
Source: May Olympiad(Olimpiada de Mayo) 2000
2/21/2018
A rectangle with area with positive integer, can be divided in squares(this squares are equal) and the rectangle also can be divided in squares (the squares are equal). Find the sides of this rectangle
geometrycombinatoricsrectangle
12 cards of three kinds in a row
Source: VI May Olympiad (Olimpiada de Mayo) 2000 L1 P5
9/22/2022
In a row there are cards that can be of three kinds: with both white faces, with both black faces or with one white face and the other black. Initially there are cards with the black side facing up. The first six cards from the left are turned over, leaving cards with the black face up. The six cards on the left are then turned over, leaving cards with the black face up. Finally, six cards are turned over: the first three on the left and the last three on the right, leaving cards with the black face up. Decide if with this information it is possible to know with certainty how many cards of each kind are in the row
combinatorics