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National and Regional Contests
Paraguay Contests
Paraguay Mathematical Olympiad
2014 Paraguay Mathematical Olympiad
2014 Paraguay Mathematical Olympiad
Part of
Paraguay Mathematical Olympiad
Subcontests
(5)
5
1
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2014 Paraguayan Mathematical Olympiad: Problem 5
Let
A
B
C
ABC
A
BC
be a triangle with area
92
92
92
square centimeters. Calculate the area of another triangle whose sides have the same lengths as the medians of triangle
A
B
C
ABC
A
BC
.
4
1
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2014 Paraguayan Mathematical Olympiad: Problem 4
Nair and Yuli play the following game:
1.
1.
1.
There is a coin to be moved along a horizontal array with
203
203
203
cells.
2.
2.
2.
At the beginning, the coin is at the first cell, counting from left to right.
3.
3.
3.
Nair plays first.
4.
4.
4.
Each of the players, in their turns, can move the coin
1
1
1
,
2
2
2
, or
3
3
3
cells to the right.
5.
5.
5.
The winner is the one who reaches the last cell first. What strategy does Nair need to use in order to always win the game?
3
1
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2014 Paraguayan Mathematical Olympiad: Problem 3
Juan chooses a five-digit positive integer. Maria erases the ones digit and gets a four-digit number. The sum of this four-digit number and the original five-digit number is
52
,
713
52,713
52
,
713
. What can the sum of the five digits of the original number be?
2
1
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2014 Paraguayan Mathematical Olympiad: Problem 2
Clau writes all four-digit natural numbers where
3
3
3
and
7
7
7
are always together. How many digits does she write in total?
1
1
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2014 Paraguayan Mathematical Olympiad: Problem 1
Consider a square of side length
12
12
12
centimeters. Irina draws another square that has
8
8
8
centimeters more of perimeter than the original square. What is the area of the square drawn by Irina?