It's a riddle of sorts: given a list of numbers $\alpha_1 \dots \alpha_n$ and operators $o_1 \dots o_{n-1}$ which can be only $\times\, \mbox{or}\, + $ if the above is a specific algebraic expression in the form $\alpha_1 o_1 \alpha_2 \dots \alpha_{n-1} o_{n-1} \alpha_n$ which configuration of brackets would maximize the value of the expression given that $\forall i \,\alpha_i \geq 1 \in \mathbb{N}$ ?
Is it sufficient to only place brackets over the $+$ series in the expression? I've checked this rule with $a_1 + a_2 \cdot a_3 $ and $a_1 + a_2 \cdot a_3 +a_4 $ but couldn't find a counter example.