Young Mathematician Olympiad, 2020-2021

Stage A Stage B Final

• Question from sources: Stage A, Grades 3-4(1) - The missing number

  Find a number such that if we write it in each of the blue squares, the sums in all `3times3` squares in the table will be equal to each other.

  

  Topics:

  Combinatorics -> Number Tables
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 1

• Question from sources: Stage A, Grades 3-4(2) - Five-Digit Palindromic Numbers

  A number is called palindromic if its digits can be read in reverse order, and the result will not change. For example, the number 4407667044 is a palindromic number, and so is 92329.
  How many five-digit palindromic numbers are there in total?

  Topics:

  Arithmetic Combinatorics
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 2

• Question from sources: Stage A, Grades 3-4(3)

  In the following addition problem, different shapes replace different digits, and identical shapes replace identical digits:

  `triangle square triangle square triangle+ square triangle square triangle square = o+ triangle triangle triangle triangle o+`

  What is the result of the addition?

  Topics:

  Arithmetic Algebra -> Equations Logic -> Reasoning / Logic Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 3

• Question from sources: Stage A, Grades 3-4(4) - The Elevator

  Avi works in a multi-story building, on the top floor. His friends Benny and Gil also work in the same building. Every day, in the morning and evening, Avi goes to greet them.
  In the morning Avi enters the building,

  • goes up 21 floors in the elevator to Benny's office,
  • walks down to Gil's office,
  • goes up 17 floors in the elevator to his office.

  After work,

  • Avi goes down 9 floors in the elevator to Benny's office,
  • walks down to Gil's office,
  • goes down 13 floors in the elevator and exits the building.

  How many floors are in the building? (Reminder - the ground floor is also a floor)

  Topics:

  Arithmetic Algebra -> Word Problems
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 4

• Question from sources: Stage A, Grades 3-4(5) - Largest Perimeter

  A polygon with an area of 12 is drawn on grid paper, with all its sides passing through the grid lines. What is the largest possible perimeter of this polygon?

  Topics:

  Geometry -> Area Calculation Minimum and Maximum Problems / Optimization Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 5

• Question from sources: Stage A, Grades 3-4(6) - Colorful Street

  Along the street are 16 houses, in red, blue, and green. There is at least one house of each color. No two adjacent houses are of the same color.
  Between any two blue houses there is a red house. Between any two green houses there is a blue house and a red house.
  What is the largest possible number of green houses?
  Note: The street is straight, all houses are located on one side of the street.

  Topics:

  Combinatorics -> Pigeonhole Principle Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4 Question 6

• Question from sources: Stage A, Grades 5-6(1) - Average of Averages

  Consider the following diagram:

  

  Each number in the diagram, connected to 4 other numbers, must be equal to their average:
  What is the number in the circle marked with a question mark?
  Note: The average of four numbers is their sum divided by 4.

  Topics:

  Algebra -> Equations Algebra -> Inequalities -> Averages / Means
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 1

• Question from sources: Stage A, Grades 5-6(2) - The Truth-Teller and Liar Survey

  13 truth-tellers and 12 liars participated in a survey. In the survey, each participant was asked about every other participant (including themselves) whether they were a truth-teller. How many "yes" answers were received in the survey in total?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Logic -> Truth-tellers and Liars Problems
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 2

• Question from sources: Stage A, Grades 5-6(3) - The Orange Path

  In the illustration, there is an orange path surrounding a blue square. The area of the path is 44% of the area of the square.
  What is the width of the orange path as a percentage relative to the side length of the blue square?

  

  Topics:

  Geometry -> Plane Geometry Geometry -> Area Calculation Algebra -> Word Problems Arithmetic -> Percentages
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 3

• Question from sources: Stage A, Grades 5-6(4) - Pairwise Relatively Prime Composite Numbers

  Yossi writes two-digit composite numbers on the board. He wants all the numbers written on the board to be pairwise relatively prime.
  What is the maximum number of integers Yossi can write on the board?
  Note: Integers are called relatively prime if they have no common factors other than 1.

  Topics:

  Logic -> Reasoning / Logic Number Theory -> Prime Numbers -> Prime Factorization Number Theory -> Greatest Common Divisor (GCD) and Least Common Multiple (LCM)
  Sources:
  • Young Mathematician Olympiad, 2020-2021, Stage A, Grades 5-6 Question 4