Young Mathematician Olympiad, 2020-2021, Stage A, Grades 3-4

• Question 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

• Question 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

• Question 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

• Question 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

• Question 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

• Question 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