2020 IMO Shortlist A4

Let $a, b, c, d$ be four real numbers such that $a \geq b \geq c \geq d>0$ and $a+b+c+d=1$. Prove that $$(a+2 b+3 c+4 d) a^{a} b^{b} c^{c} d^{d}<1$$ (Belgium)

令 $a, b, c, d$ 为四个实数，使得 $a \geq b \geq c \geq d>0$ 且 $a+b+c+d=1$。证明 $$(a+2 b+3 c+4 d) a^{a} b^{b} c^{c} d^{d}<1$$(比利时)