Young Mathematician Olympiad, 2019-2020, Final, Grades 5-6

• Question 1 - 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
  Additional sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 4

• Question 2 - We went on a trip

  Grade 4, consisting of 32 students, went on a trip. The students had to bring hats, sunglasses, and water bottles.
  No child forgot all of these things, but:

  • Among the students who brought hats, 9 forgot sunglasses,
  • Among the students who brought sunglasses, 7 forgot water bottles,
  • And among the students who brought water bottles, 10 forgot sunglasses.

  How many students in the class brought everything needed for the trip?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic Set Theory Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• Question 3 - Blue or Orange?

  In the diagram, there is a square ABCD and a parallelogram BCEF. Which area is larger: the blue or the orange?

  

  Topics:

  Geometry -> Plane Geometry Geometry -> Area Calculation

• Question 4 - Hunter in the Enchanted Forest

  In the enchanted forest lives a tribe of 150 people. Every day, the tribe members try to organize themselves to go hunting together,
  and each day, each person participates or does not participate according to their choice. Prove that during one week, there will certainly be two people who arrive on exactly the same days.
  Note: Even in the enchanted forest, a week has 7 days.

  Topics:

  Combinatorics -> Pigeonhole Principle

• Question 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
  Additional sources:
  • Young Mathematician Olympiad, 2019-2020, Final, Grades 3-4 Question 6

• Question 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