['This mishna sets out the essential halakhot pertaining to the invitation to recite Grace after Meals after a joint meal [zimmun]: Three people who ate as one are required to form a zimmun and recite Grace after Meals. If, among the diners, one ate doubtfully tithed produce [demai], and first tithe from which its teruma was already taken, or second tithe, and consecrated food that were redeemed and therefore permitted to be eaten; and even the waiter who served the meal to the diners and who ate at least an olive-bulk from the meal, and the Samaritan [Kuti] who ate with two others at a meal; each of these people is included among the three to obligate those with whom they ate in a zimmun. However, one who ate untithed produce [tevel], and first tithe from which its teruma was not separated, and second tithe, and consecrated food that were not redeemed, and the waiter who did not eat an olive-bulk, and the gentile who ate with two Jews, none of these people is included among the three to obligate those with whom they ate in a zimmun. ', 'Women, slaves, and minors do not obligate those with whom they ate in a zimmun. How much must one eat to obligate those with whom he ate in a zimmun? An olive-bulk of food suffices to obligate those with whom they ate in a zimmun. Rabbi Yehuda says: An egg-bulk is the minimum measure to obligate those with whom they ate in a zimmun.', 'The mishna delineates distinctions in the halakhot of the zimmun blessing, based on the number of people present. How does one recite the zimmun? In a group of three people, the one reciting the zimmun says: Let us bless the One from Whose food we have eaten. In a group of three people and him, the one reciting the zimmun says: Bless the One from Whose food we have eaten, as even without him there are enough people to recite the zimmun. With the increase in the number of participants, the blessing is more complex. In a group of ten people, the one reciting the zimmun says: Let us bless our God. In a group of ten people and him, the one reciting the zimmun says: Bless our God. This formula is recited both in a group of ten and in a group of one hundred thousand. In a group of one hundred people, the one reciting the zimmun says: Let us bless the Lord our God. In a group of one hundred people and him, the one reciting the zimmun says: Bless the Lord our God. In a group of one thousand people, the one reciting the zimmun says: Let us bless the Lord our God, the God of Israel. In a group of one thousand people and him, he says: Bless the Lord our God, the God of Israel. In a group of ten thousand people, the one reciting the zimmun says: Let us bless the Lord our God, the God of Israel, the God of Hosts, Who sits upon the cherubs, for the food that we have eaten. In a group of ten thousand people and him, the one reciting the zimmun says: Bless the Lord our God, the God of Israel, the God of Hosts, Who sits upon the cherubs, for the food that we have eaten. The principle is that just as he recites the blessing, so too those present recite in response: Blessed be the Lord our God, the God of Israel, the God of Hosts, Who sits upon the cherubs, for the food that we have eaten. On a similar note, Rabbi Yosei HaGelili says: According to the size of the crowd, they recite the blessing, as it is stated: “Bless you God in full assemblies, even the Lord, you who are from the fountain of Israel” (Psalms 68:27). Rabbi Akiva said that there are no distinctions based on the size of the crowd: What do we find in the synagogue? Both when there are many and when there are few, as long as there is a quorum of ten, the prayer leader says: Bless [barekhu] the Lord. Rabbi Yishmael said that in the synagogue, one recites: Bless the Lord the blessed One. ', 'Three people who ate as one are not permitted to divide and recite Grace after Meals individually; rather, they recite the zimmun together. And the same is true of four who ate together, and the same is true of five. However, a group of six, up to but not including ten people who ate as one, may divide into two groups, each reciting its own zimmun. And a group of ten may not divide into two groups until there are twenty people present. The general principle is that a group may not divide unless the smaller groups will be able to recite the same zimmun formula that the whole group would have recited.', 'The mishna states a halakha with regard to two groups joining together: Two groups that were eating in one house, when some members of each group can see each other, they may combine to form a zimmun. And if not, these recite a zimmun for themselves and those recite a zimmun for themselves. The mishna also speaks of the blessing over wine: One does not recite a blessing over wine until he adds water to it, that is the statement of Rabbi Eliezer. Undiluted wine is too strong to drink and a blessing is inappropriate. And the Rabbis say: Since it is possible to drink undiluted wine, one recites a blessing over it.']