Young Mathematician Olympiad, 2019-2020, Stage A

Grades 3-4 Grades 5-6

• Question from sources: Grades 5-6(4) - Five Numbers

  Given five distinct positive integers. The sum of these numbers is 27. Additionally, it is known that the product of these five numbers is odd. Calculate this product.

  Topics:

  Arithmetic Number Theory -> Division -> Parity (Even/Odd)
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 4

• Question from sources: Grades 5-6(5) - Angles

  Calculate the sum of the marked angles:

  

  Topics:

  Geometry -> Plane Geometry -> Triangles Geometry -> Plane Geometry -> Angle Calculation
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 5

• Question from sources: Grades 5-6(6) - More Game Cubes

  Aviv has game cubes, where two opposite faces of each are painted red and the rest are blue.
  Aviv glued together a `3 xx 3 xx 3` cube from the game cubes. Then his friend Kfir came and calculated the total red area on the surface of the large cube.
  What is the largest result Kfir can get?

  Topics:

  Geometry -> Solid Geometry / Geometry in Space Combinatorics -> Combinatorial Geometry Minimum and Maximum Problems / Optimization Problems Combinatorics -> Colorings
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 6

• Question from sources: Grades 5-6(7) - More Numbers with Ascending Digits

  Miri writes down all the numbers whose decimal representation contains only the digits `1, 2, 3, 4, 5, 6`.
  (Not all digits must appear) and all the digits that appear are written in ascending order (e.g., 1356 or 124 or 5 but not 162 and not 1223).
  How many numbers will Miri write down?

  Topics:

  Combinatorics -> Product Rule / Rule of Product Set Theory
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 7