The Shulhan Aruch (Orah Haim 199:10) rules that a minor who knows that Birkat Hamazon is being recited to Hashem may be counted as part of a Zimun. The Shulhan Aruch specifies that a minor may only be counted to complete a Zimun, that is, by being the third in a group of three or the tenth in a group of ten. On the other hand, the Rama (ibid.) writes that in Ashkenazic lands, the custom was to include only those thirteen years of age and above.
Practically speaking, the Rif and the Rambam say that a minor may be counted for Zimun as of the age six or seven. The Mishna Berura (O.H. 199:24) concurs as long as the minor is aware to Whom the blessing is being recited, and this is the opinion of all contemporary Sephardic Poskim.
In a situation in which people of Ashkenazic and Sephardic background are eating together, Rabbi Shlomo Zalman Auerbach (quoted in Vezot Haberacha, pg. 132) rules that the Ashkenazim may participate in a Zimun that includes a minor, so long as the one leading the Zimun is Sephardic.
Summary: A child as young as six years old may be the third or tenth member of a Zimun as long as he knows to Whom Birkat Hamazon is being recited.
Practically speaking, the Rif and the Rambam say that a minor may be counted for Zimun as of the age six or seven. The Mishna Berura (O.H. 199:24) concurs as long as the minor is aware to Whom the blessing is being recited, and this is the opinion of all contemporary Sephardic Poskim.
In a situation in which people of Ashkenazic and Sephardic background are eating together, Rabbi Shlomo Zalman Auerbach (quoted in Vezot Haberacha, pg. 132) rules that the Ashkenazim may participate in a Zimun that includes a minor, so long as the one leading the Zimun is Sephardic.
Summary: A child as young as six years old may be the third or tenth member of a Zimun as long as he knows to Whom Birkat Hamazon is being recited.