Young Mathematician Olympiad, 2019-2020

• Question from sources: Stage B, Grades 3-4(2), Stage B, Grades 5-6(2) - The Bakery

  In the morning, a bakery's storage room contained 135 kilograms of flour and 92 kilograms of sugar.
  To bake one cake, the baker uses one kilogram of flour and one kilogram of sugar.
  At the end of the workday, the amount of flour remaining for the baker was twice as large as the amount of sugar remaining.
  How many cakes did the baker make during the workday?

  Topics:

  Algebra -> Equations Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 3-4 Question 5
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 2

• Question from sources: Stage B, Grades 5-6(3) - SLV LVS BLS

  In the following expression, different letters represent different digits, and identical letters represent identical digits:

  SLV = LVS + BLS

  Find the number SLV.

  Topics:

  Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rule by 11 Algebra -> Equations Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 3

• Question from sources: Stage B, Grades 3-4(4), Stage B, Grades 5-6(4) - The Number

  Given a positive integer less than 2000.
  If it is not divisible by 43, then it is divisible by 41,
  If it is not divisible by 53, then it is divisible by 43,
  If it is not divisible by 41, then it is divisible by 53.
  Find the number.

  Topics:

  Number Theory -> Prime Numbers Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules Logic -> Reasoning / Logic Number Theory -> Greatest Common Divisor (GCD) and Least Common Multiple (LCM) Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Number Theory -> Division
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 3-4 Question 6
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 4

• Question from sources: Stage B, Grades 5-6(5) - Drawing Board

  A painter has a `10 times 10` grid. Each time, the painter chooses a row or column and paints it entirely with a color of their choice.
  If they pass over a square that has already been painted with a new color, the new color completely covers the old color,
  that is, the color of the square changes.
  What is the largest number of colors we can see on this board?

  Topics:

  Combinatorics -> Pigeonhole Principle Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Combinatorics -> Colorings
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 5

• Question from sources: Stage B, Grades 5-6(6) - How Many Triangles - 2?

  How many triangles are in the picture?

  

  Topics:

  Geometry -> Area Calculation Geometry -> Plane Geometry -> Triangles Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Stage B, Grades 5-6 Question 6

• Question from sources: Final, Grades 3-4(1) - 5 Lines, 8 Intersections

  Draw 5 lines such that there are exactly 8 points of intersection between them.

  Topics:

  Combinatorics -> Combinatorial Geometry Geometry -> Plane Geometry Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 1

• Question from sources: Final, Grades 3-4(2) - Who Likes Cola?

  Shmuel has 4 children: Ohad, Benny, Guy, and Dor. Each of them has one drink that he likes (no two people share a favorite drink): water, cola, grape juice, and orange juice.
  In addition, each of them also has a favorite subject (and no two have the same one): mathematics, physics, computer science, and chemistry.

  Hints:

  1. 1. Ohad likes computer science
  2. 2. The one who likes mathematics does not drink orange juice
  3. 3. Dor does not like physics
  4. 4. Benny drinks water
  5. 5. Guy does not drink grape juice
  6. 6. The child who likes chemistry drinks grape juice
  7. 7. Benny does not like mathematics

  Question: Who likes cola?

  Topics:

  Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 2

• Question from sources: Final, Grades 3-4(3) - Dissect into four parts

  Geometric shapes are called congruent if they coincide when superimposed. Cut the following shape into four congruent parts:

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries)
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 3

• Question from sources: Final, Grades 3-4(4), Final, Grades 5-6(4) - Compose a Sum

  Compose three numbers from the digits `1,2,3,4,5,6,7,8,9` such that one of them is the sum of the other two.
  Each digit must be used exactly once.

  Topics:

  Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 4
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6 Question 1

• Question from sources: Final, Grades 3-4(5) - How Many Sums Are Possible?

  What is the number of possible results of addition exercises of the form `A + B`
  where A and B are two distinct positive single-digit numbers?

  Topics:

  Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 5