Section 51 - Filling vacancies by open competitive examination1. Upon the written request of the appointing officer stating his reasons therefor, or on its own initiative, the state civil service department or appropriate municipal commission may determine to conduct an open competitive examination for filling a vacancy or vacancies instead of a promotion examination.2. Except where the state civil service department or appropriate municipal commission finds that there are less than three persons eligible for promotion in the promotion unit where the vacancy exists, or in the department, if such vacancy is not in a separate promotion unit, and except where the department or municipal commission determines to conduct an open competitive and a promotion examination simultaneously, a notice of intention to conduct such open competitive examination or a copy of the appointing officer's request for open competitive examination, as the case may be, shall be publicly and conspicuously posted in the offices of both the appointing officer and the state civil service department or appropriate municipal commission and such request shall not be acted upon until said notice has been posted as aforesaid for a period of not less than fifteen days.3. Any employee who believes that a promotion examination should be held for filling such vacancy may submit to the state civil service department or appropriate municipal commission his request, in writing, for a promotion examination rather than an open competitive examination, stating the reasons why he believes it to be practicable and in the public interest to fill the vacancy by promotion examination.