Young Mathematician Olympiad, 2018-2019

Stage A Stage B Final

• Question from sources: Stage A, Grades 3-4(1), Stage A, Grades 5-6(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
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4 Question 1
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 1

• Question from sources: Stage A, Grades 3-4(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
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4 Question 2

• Question from sources: Stage A, Grades 3-4(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
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4 Question 3

• Question from sources: Stage A, Grades 3-4(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
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4 Question 4

• Question from sources: Stage A, Grades 3-4(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
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4 Question 5

• Question from sources: Stage A, Grades 3-4(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
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4 Question 6

• Question from sources: Stage A, Grades 3-4(1), Stage A, Grades 5-6(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
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4 Question 1
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 1

• Question from sources: Stage A, Grades 5-6(2)

  The numbers with a digit sum of 28 are written on the board in ascending order. What is the 24th number among them?

  Topics:

  Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 2

• Question from sources: Stage A, Grades 5-6(3) - Another Gray Area

  In the figure, a rectangle of size `3 times 5` and a line that crosses it diagonally. Find the shaded area.

  

  Topics:

  Geometry -> Plane Geometry Geometry -> Area Calculation
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 3

• Question from sources: Stage A, Grades 5-6(4) - Volume of a Rectangular Prism

  Given a rectangular prism whose face areas are 6, 10, and 15. Find its volume.

  

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  Topics:

  Geometry -> Solid Geometry / Geometry in Space Algebra -> Algebraic Techniques -> Roots / Radicals
  Sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6 Question 4