OMCPLP 2021 Problem 1

Juca has decided to call all positive integers with 8 digits as $sextalternados$ if it is a multiple of 30 and its consecutive digits have different parity. At the same time, Carlos decided to classify all $sextalternados$ that are multiples of 12 as $super sextalternados$ .

a) Show that $super sextalternados$ numbers don't exist.

b) Find the smallest $sextalternado$ number.