Young Mathematician Olympiad, 2019-2020, Stage A

Grades 3-4 Grades 5-6

• Question from sources: Grades 3-4(1) - Difference of Square Areas

  Two squares are given as depicted in the drawing. The side length of the larger square is 9,
  the side length of the smaller square is 8. What is the difference between the area of the orange region and the area of the blue region?

  

  Topics:

  Arithmetic Geometry -> Area Calculation
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 1

• Question from sources: Grades 3-4(2) - Sun Minus Five

  In the following arithmetic problems, different letters replace different digits, and identical letters replace
  identical digits.
  `5 = ש + מ + ח`
  `9 = ש + מ + ש`
  Calculate the value of the expression: `ח + ש`

  Topics:

  Arithmetic Algebra -> Equations Puzzles and Rebuses
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 2

• Question from sources: Grades 3-4(3), Grades 5-6(3) - Ten-Digit Number

  Yael writes ten-digit numbers in whose decimal representation each of the digits `0, 1, 2, 3, 4, 5, 6, 7, 8, 9` appears exactly once.
  In the numbers that Yael writes, the difference between any two adjacent digits is at least 2. What is the smallest number Yael can write?
   

  Topics:

  Number Theory Proof and Example -> Constructing an Example / Counterexample Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 3
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 1

• Question from sources: Grades 3-4(4) - Four Numbers

  Given four distinct positive integers. The sum of these numbers is equal to 18.
  Additionally, it is known that the product of these four numbers is odd. Calculate this product.

  Topics:

  Arithmetic Number Theory -> Division -> Parity (Even/Odd)
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 4

• Question from sources: Grades 3-4(5) - Zionism Street

  On Zionism Street live Benjamin, Chaim, Judah, and Max. Benjamin left his house, walked 169 meters, and arrived at Chaim's house.
  After a short rest, he walked 196 meters and arrived at Judah's house. Then he walked 171 meters and arrived at Max's house.
  Finally, after walking another 144 meters, he returned to his house. What is the distance from Benjamin's house to Judah's house?

  Topics:

  Arithmetic Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 5

• Question from sources: Grades 3-4(6) - Game Cubes

  Aviv has game cubes, where on each of them two opposite faces are painted red and the rest are blue.
  Aviv glued a `2 times 2 times 2` cube from the game cubes. Then his friend Kfir arrived and calculated all the
  red area on the surface of the large cube. What is the largest result Kfir can get?

  Topics:

  Geometry -> Solid Geometry / Geometry in Space
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 6

• Question from sources: Grades 3-4(7) - Numbers with Ascending Digits

  Miri writes down all the numbers in whose decimal representation only the digits `1, 2, 3, 4, 5` appear.
  (Not all digits have to appear) and all the digits that appear are written in ascending order (e.g., 135 or 1234 or 5 but not 153 and not 1223).
  How many numbers will Miri write down?

  Topics:

  Combinatorics
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 7

• Question from sources: Grades 3-4(1), Grades 5-6(1) - Ten-Digit Number

  Yael writes ten-digit numbers in whose decimal representation each of the digits `0, 1, 2, 3, 4, 5, 6, 7, 8, 9` appears exactly once.
  In the numbers that Yael writes, the difference between any two adjacent digits is at least 2. What is the smallest number Yael can write?
   

  Topics:

  Number Theory Proof and Example -> Constructing an Example / Counterexample Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 3-4 Question 3
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 1

• Question from sources: Grades 5-6(2) - How Much is Happy?

  In the following arithmetic exercises, different letters replace different digits, and identical letters replace identical digits.
  `19 = ט + מ + ח + ש`
  `10 = ק + ח + ש + מ`
  Calculate the value of the expression: `ח + מ + ש`

  Topics:

  Arithmetic Algebra -> Equations Puzzles and Rebuses
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 2

• Question from sources: Grades 5-6(3) - Orange Star of David

  The area of the blue triangle is equal to 1. Calculate the area of the orange Star of David:

  

  Topics:

  Geometry -> Area Calculation Geometry -> Plane Geometry -> Triangles Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage A, Grades 5-6 Question 3