This is a list of small mathematical puzzles I've written which I find fun --- it's a work in progress though :)
Problem 1. Consider three numbers α , β , γ ∈ [ 0 , π ] such that for any x , y , z ∈ ℝ we have x 2 + y 2 + z 2 + 2 x y cos α + 2 x z cos β + 2 y z cos γ ≥ 0 Then α + β + γ ≤ 2 π .