Young Mathematician Olympiad, 2018-2019, Final
Grades 3-4 Grades 5-6-
Question from sources: Grades 5-6(4) - Consecutive Numbers
a. Avi wants to find 10 consecutive numbers whose sum is divisible by 90. Will he succeed?
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b. Benny wants to find 11 consecutive numbers such that their sum is divisible by 90. Will he succeed? -
Question from sources: Grades 3-4(5), Grades 5-6(5) - 6 on the Board
The number 6 is written on the board. At each step, you can add the digit 6 to the end of the number (so that it is the units digit,) or replace the number with the sum of its digits.
Which numbers can be obtained in this way? Describe the entire set of numbers and explain why there are no moreSources:Topics:Arithmetic Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 3 and 9 Combinatorics -> Induction (Mathematical Induction) Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd) Algebra -> Sequences Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures -
Question from sources: Grades 5-6(6) - Numbers on the Board
The following numbers are written on the board:`1/3,1/2,1,2,3`. In each step, you are allowed to choose any two numbers written on the board and replace each of them with their product.
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Can you reach a quintet of numbers in this way whose sum is `4 1/4`? -
Question from sources: Grades 5-6(7) - The Parallelogram
In the drawing, there is a parallelogram with its diagonals drawn and the midpoints of two of its sides connected to opposite vertices.
Which area is larger: the shaded or the striped?
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