Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4

• Question 1 - Cutting

  What is the largest number of rectangles of size `2 times 5`  that can be cut from a `9 times 9` square?

  Topics:

  Geometry -> Area Calculation Proof and Example -> Constructing an Example / Counterexample Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry
  Additional sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 1

• Question 2 - Digit Sum - 9

  How many numbers in the range from 1 to 500 have a digit sum of 9?

  Topics:

  Number Theory Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• Question 3 - Gray Area

  In the figure is a rectangle composed of 5 squares of size `2 times 2 ` and a line that intersects it diagonally.
  Find the area of the shaded region.

  

  Topics:

  Geometry -> Area Calculation Geometry -> Plane Geometry -> Symmetry

• Question 4 - School Supplies

  An eraser and two pencils together cost 19 lira, a pencil and two notebooks together cost 23 lira, a notebook and two
  erasers together cost 18 lira. How much do an eraser, a pencil, and a notebook cost together?

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  Topics:

  Algebra -> Equations Algebra -> Word Problems

• Question 5 - Sum

  In the following problem, different digits have been replaced with different letters, and the sum is a three-digit number.
  What is the sum if the number "BA" is as small as possible?
  \(\begin{align} AB& \\ \underline{+\quad BA}& \\ ***& \end{align}\)

  Topics:

  Arithmetic Algebra

• Question 6 - Puzzle

  You have a puzzle where each piece looks like this:

  

  
  The following shape is made up of 12 pieces. What is its perimeter?

  

  Topics:

  Arithmetic Geometry -> Plane Geometry Geometry -> Area Calculation Algebra -> Word Problems