MathDB

3

Part of 2011 Saint Petersburg Mathematical Olympiad

Problems(2)

Building from bricks

Source: St Petersburg Olympiad 2011, Grade 11, P3

9/15/2017
Can we build parallelepiped 6×7×76 \times 7 \times 7 from 1×1×21 \times 1 \times 2 bricks, such that we have same amount bricks of one of 33 directions ?
combinatorics
Point in triangle

Source: St Petersburg Olympiad 2011, Grade 9, P3

9/15/2017
Point DD is inside △ABC\triangle ABC and AD=DCAD=DC. BDBD intersect ACAC in EE. BDBE=AEEC\frac{BD}{BE}=\frac{AE}{EC}. Prove, that BE=BCBE=BC
geometry