MathDB

3

Part of 2016 Junior Regional Olympiad - FBH

Problems(3)

Junior Regional Olympiad - FBH 2016 Grade 6 Problem 3

Source:

9/29/2018
From three boys and three girls, every boy knows exactly two girls and every girl knows exactly two boys. Prove that we can arrange boys and girls in pairs such that in every pair people know each other
combinatorics
Junior Regional Olympiad - FBH 2016 Grade 7 Problem 3

Source:

9/29/2018
Prove that when dividing a prime number with 3030, remainder is always not a composite number
number theoryprime numbers
Junior Regional Olympiad - FBH 2016 Grade 8 Problem 3

Source:

9/29/2018
In trapezoid ABCDABCD holds AD∣∣BCAD \mid \mid BC, ∠ABC=30∘\angle ABC = 30^{\circ}, ∠BCD=60∘\angle BCD = 60^{\circ} and BC=7BC=7. Let EE, MM, FF and NN be midpoints of sides ABAB, BCBC, CDCD and DADA, respectively. If MN=3MN=3, find EFEF
geometrytrapezoid