Rabbi Tzadok and his son Rabbi Eleazar were close to Rabban Gamliel, and frequently visited him. For example, R' Eleazar stated "Many times I entered after my father to the house of Rabban Gamliel, and they did not sweep the room of the beds on Yom Tov, but rather, they would sweep them on the eve of Yom Tov, and stretch sheets over them; the next day when guests arrived they would remove the sheets, and thus the house was swept on its own."Beitzah 22b Similarly, R' Eleazar stated, Rabban Gamliel found a way to circumvent the prohibition on placing incense on coals on Yom Tov, by placing incense on coals in a closed container before Yom Tov, and opening the container on Yom Tov, causing the aroma to spread through the house.
