MathDB

1

Part of 1990 China Team Selection Test

Problems(2)

m people have exactly one common friend

Source: China TST 1990, problem 1

6/27/2005
In a wagon, every m≥3m \geq 3 people have exactly one common friend. (When AA is BB's friend, BB is also AA's friend. No one was considered as his own friend.) Find the number of friends of the person who has the most friends.
inductioncombinatorics unsolvedcombinatorics
Inequality for a triangle with C >= 60°

Source: China TST 1990, problem 5

6/27/2005
Given a triangle ABC ABC with angle C≥60∘ C \geq 60^{\circ}. Prove that: \left(a \plus{} b\right) \cdot \left(\frac {1}{a} \plus{} \frac {1}{b} \plus{} \frac {1}{c} \right) \geq 4 \plus{} \frac {1}{\sin\left(\frac {C}{2}\right)}.
inequalitiestrigonometrygeometry solvedgeometry