Young Mathematician Olympiad, 2019-2020, Final

Grades 3-4 Grades 5-6

• Question from sources: Grades 3-4(5), Grades 5-6(5) - Cards with Digits

  Rachel has three cards with different digits, all of which are greater than 0. Rachel formed all possible three-digit numbers from these cards and calculated their sum.
  Prove that the sum is divisible by 3

  Topics:

  Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 3 and 9 Logic -> Reasoning / Logic Proof and Example
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 6
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6 Question 5

• Question from sources: Grades 5-6(6) - Cut a Boat in Half

  Geometric shapes are called congruent if they coincide when placed on top of each other. Cut the shape into two congruent parts

  

  Topics:

  Geometry -> Plane Geometry -> Symmetry Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems
  Sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6 Question 6