Young Mathematician Olympiad, 2018-2019, Stage A, Grades 5-6

• Question 1 - Cutting

  What is the largest number of rectangles of size `2 times 5`  that can be cut from a `9 times 9` square?

  Topics:

  Geometry -> Area Calculation Proof and Example -> Constructing an Example / Counterexample Combinatorics -> Combinatorial Geometry -> Cut a Shape / Dissection Problems Combinatorics -> Combinatorial Geometry -> Grid Paper Geometry / Lattice Geometry
  Additional sources:
  • Young Mathematician Olympiad, 2018-2019, Stage A, Grades 3-4 Question 1

• Question 2

  The numbers with a digit sum of 28 are written on the board in ascending order. What is the 24th number among them?

  Topics:

  Arithmetic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• Question 3 - Another Gray Area

  In the figure, a rectangle of size `3 times 5` and a line that crosses it diagonally. Find the shaded area.

  

  Topics:

  Geometry -> Plane Geometry Geometry -> Area Calculation

• Question 4 - Volume of a Rectangular Prism

  Given a rectangular prism whose face areas are 6, 10, and 15. Find its volume.

  

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  Topics:

  Geometry -> Solid Geometry / Geometry in Space Algebra -> Algebraic Techniques -> Roots / Radicals

• Question 5

  Find the smallest two-digit number `☺` that satisfies:

  `☺times☺ - ☺ = 600`

  Topics:

  Number Theory Arithmetic Algebra -> Equations

• Question 6 - Number Network

  In the diagram, the numbers on the edges indicate the differences between the numbers inside the circles. Place positive numbers inside the circles and discover what the number in the bottom circle is.

  

  Topics:

  Arithmetic Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures