Paraguayan Mathematical Olympiad 2014

Consider a square of side length $12$ centimeters. Irina draws another square that has $8$ centimeters more of perimeter than the original ...

  1. Consider a square of side length $12$ centimeters. Irina draws another square that has $8$ centimeters more of perimeter than the original square. What is the area of the square drawn by Irina?
  2. Clau writes all four-digit natural numbers where $3$ and $7$ are always together. How many digits does she write in total?
  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 $52,713$. What can the sum of the five digits of the original number be?
  4. Nair and Yuli play the following game:
    - There is a coin to be moved along a horizontal array with $203$ cells.
    - At the beginning, the coin is at the first cell, counting from left to right.
    - Nair plays first.
    - Each of the players, in their turns, can move the coin $1$, $2$, or $3$ cells to the right.
    - 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?
  5. Let $ABC$ be a triangle with area $92$ square centimeters. Calculate the area of another triangle whose sides have the same lengths as the medians of triangle $ABC$.



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MATHEMATICAL OLYMPIAD PROBLEMS: Paraguayan Mathematical Olympiad 2014
Paraguayan Mathematical Olympiad 2014
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