Let there be many numbers $a_1,a_2,a_3,\dots,a_n$.
I want to find the first digit of their product, i.e. of $A=a_1\times a_2\times a_3\times a_4\times \dots\times a_n$.
These numbers are huge and multiplying all of them exceeds the time limit.
Is there any shortcut to find the most significant digit of $A$ (first digit from the left)?