No child under the age of five years shall be admitted to any public school, except such as may be provided pursuant to law for children of his age.
No board of education shall be required to accept by transfer from public or private school any pupil who was not eligible by reason of age for admission on October 1 of that school year, but the board may in its discretion admit any such pupil if he or she meets such entrance requirements as may be established by rules or regulations of the board.