MathDB

Problem 1

Part of 2007 Mongolian Mathematical Olympiad

Problems(2)

Prove that lines parallel in triangle

Source: Mongolian MO 2007 Grade 11 P1

4/8/2021
Let MM be the midpoint of the side BCBC of triangle ABCABC. The bisector of the exterior angle of point AA intersects the side BCBC in DD. Let the circumcircle of triangle ADMADM intersect the lines ABAB and ACAC in EE and FF respectively. If the midpoint of EFEF is NN, prove that MN∥ADMN\parallel AD.
geometry
# of subsets of 1,2,3,...,5n with 5|sum

Source: Mongolian MO 2007 Teachers P1

4/8/2021
Find the number of subsets of the set {1,2,3,...,5n}\{1,2,3,...,5n\} such that the sum of the elements in each subset are divisible by 55.
combinatorics