Gemara

(R. Chiya bar Aba): I saw R. Yochanan bless after eating a salted (i.e. pickled) olive.

Question (R. Yirmeyah): Since the pit was removed, it is less than a k'Zayis!

Answer (R. Zeira): He ate a big olive. Without the pit, it was the volume of an average olive. This suffices for a Berachah Acharonah;

(Mishnah): Whenever Mishnayos refer to a k'Zayis, it is not a big or small olive, rather, an average olive, i.e. Aguri.

45b (Rav Dimi bar Yosef citing Rav): If three ate together and one went out to the market, we call to him, and (if he does not come) we make a Zimun Alav (in his absence).

(Abaye): This is only if he can hear the Zimun and answer.

(Mar Zutra): This applies only to a Zimun of three. One cannot be counted for a Zimun of 10 (to say "Baruch Elokeinu") unless he comes.

Objection (Rav Ashi): Just the contrary! Nine look like 10 (we are not concerned if one does not come), but two do not look like three!

The Halachah follows Mar Zutra.

47b (R. Yehoshua ben Levi): Even though we may not include a baby in a crib for a Zimun, he may be included for 10 (to mention Hash-m's name in the Zimun).

48a (Rav Yehudah brei d'Rav Shmuel bar Shilas): If nine people ate bread and one ate vegetables, they join (to make 10 to say Hash-m's name in the Zimun).

Questions (R. Zeira): If seven ate bread and three ate vegetables, do they join?

Answer (Rav Yehudah): They join.

R. Zeira: I need not ask whether or not four can join to six who ate bread.

R. Yirmeyah: It is good that you did not ask. Three join, because the majority ate bread. Surely, the same applies when four ate vegetables!

R. Zeira held that a noticeable majority is required.

Yanai ha'Melech and his queen ate bread. She called Shimon ben Shetach to bless for them. They gave him a cup.

Shimon ben Shetach: Should I bless "blessed is He from Whom Yanai and his friends ate"?!

He drank the cup. They gave him another cup, and he blessed (for everyone).

(R. Aba: This is Shimon ben Shetach's opinion (that Birkas ha'Mazon exempts wine. Chachamim argue with him);

(R. Chiya bar Aba citing R. Yochanan): One may not be Motzi others (in Birkas ha'Mazon) unless he ate a k'Zayis of grain.

(Rav Chana bar Yehudah): If one sat with people, even if he ate only vegetables dipped in brine or one fig, he joins;

(Rav Chana bar Yehudah): The Halachah is, if one ate a vegetable leaf or drank a cup of wine, he joins for a Zimun;

He may not be Motzi others unless he ate a k'Zayis of grain.

50a: Ravina and Rav Chama bar Buzi visited the Reish Galusa. Rav Chama was trying to get 100 people to bless together.

Ravina: This is unnecessary. Rava taught that the Halachah follows R. Akiva! (There is no difference between 10 and 100.)

Shabbos 81a (Beraisa - R. Yosi): On Shabbos, one may take into a Beis ha'Kisei three rocks. The sizes are that of an olive, a nut, and an egg.

Kerisus 13b (Mishnah): One can be liable four Chata'os and one Asham for one eating, e.g. if a Tamei person ate Chelev that was Nosar of Kodshim on Yom Kipur.

14a (Rav Ada bar Acha): The text says that one is liable five Chata'os (and an Asham), i.e. he is liable also for a k'Zayis of Pigul.

Question: If so, he can be liable a sixth Chatas, if he ate also a k'Zayis of blood!

Answer: The Tana teaches the Chiyuvim that can come for one swallowing. One cannot swallow more than two k'Zeisim at once.

Rishonim

Rif and Rosh (35b and 7:21): Rav Yehudah bar Shilas taught that if nine ate bread and one ate vegetables, they join. Even if he only (ate vegetables) dipped in brine or drank one cup with them, he joins. Even if seven ate bread and three ate vegetables, they join for "Nevarech lEilokeinu." If only six ate bread and four ate vegetables, they do not join, for we require a recognizable majority.

Rif: This is to join to make a Zimun with 10. To be Motzi others, he must eat a k'Zayis of grain. Rabanan say that this is to join to make a Zimun with 10. To join to a Zimun of three, he must eat a k'Zayis of grain.

Rambam (Hilchos Berachos 5:8): We are Mezamen only on one who ate a k'Zayis of bread or more. To join to three, each of them must eat a k'Zayis of bread, and then they are Mezamen.

Hagahos Maimoniyos (7): Tosfos, R. Yehudah and Avi ha'Ezri rule that even one who ate vegetables joins to make a Zimun with three. However, the Rif, Re'em and Sefer ha'Chachmah rule like the Rambam. This is the custom of my Rebbi (Tashbatz 307). However, in his Hilchos Berachos, he wrote that even drinking joins, like Tosfos. Perhaps he explained according to each, and did not rule like either opinion. He wrote that if two ate, it is a Mitzvah to pursue a Zimun. If a third comes, it is a Mitzvah to give to him to eat or drink, like it says in Berachos. Rav Chama was trying to get 100 people to bless together. Ravina said that it is unnecessary, for the Halachah follows R. Akiva. In any case, we learn that it is a Mitzvah to pursue 10. I found in my Rebbi's name that if he ate with someone else and a third came, he would not give to him to drink if he could not get him or someone else to eat a k'Zayis of bread, to avoid the argument. If the third person only drank, he relied on Tosfos to make a Zimun.

Beis Yosef (DH v'Chasav): This is proper.

Rosh (ibid.): Even if seven ate bread and three ate vegetables, they join. The same applies if two ate grain and one ate vegetables, but not vice-versa. The Yerushalmi says that if two ate bread and one ate vegetables, they join. The Rif says that to join to a Zimun of three, one must eat a k'Zayis of grain. What is his source? On 45b, we say that the Halachah follows Mar Zutra, who is more stringent about joining to 10 than about joining to three. With difficulty, we can say that there we require reclining together. The Shechinah dwells only when they recline together. Regarding three, which is a small amount, all must eat (grain, so this is more stringent than 10). However, the Sugya connotes that one must eat ate a k'Zayis of grain only to be Motzi others, like R. Chiya bar Aba taught.

Rosh: If one drank or ate vegetables, he cannot be Motzi others. We require something on which one says Birkas ha'Mazon. Perhaps me'Ein Shalosh suffices, for the Gemara said 'ate a k'Zayis of grain.' It did not say 'k'Zayis of bread.' Since there is eating, and there is a Berachah mid'Oraisa, this is fine.

Ma'adanei Yom Tov (1:50): The Rosh holds that Birkas me'Ein Shalosh is mid'Oraisa.

Poskim

Shulchan Aruch (OC 197:3): One who ate any food may join to make a Zimun with 10.

Mishnah Berurah (17): There is a Chiyuv Zimun even without him. He is needed only to mention Hash-m's name.

Shulchan Aruch (ibid.): One may join to make a Zimun with three only if he ate a k'Zayis of bread.

Beis Yosef (DH v'Chasav): The Kol Bo (25:22b) says that perhaps a k'Zayis of porridge or others cooked foods (with grain) is considered like a k'Zayis of grain. However, the Rambam requires that each ate a k'Zayis of bread.

Beis Yosef (DH v'Chasav ha'Roke'ach): The Roke'ach says that Shabbos 81a connotes that a k'Zayis is less than a nut. However, it seems that we require a big olive, like it says in Shabbos. Also Kerisus 14a connotes like this.

Eliyahu Rabah (184:8): The Gemara says that an average olive suffices! Perhaps he means that we require the volume of a big olive without its pit.

Magen Avraham (486): A k'Zayis is half a large dates. This is less than k'Beitzah. However, Kerisus 14a connotes that one can swallow only two k'Zeisim at once. We know that one can swallow a k'Beitzah at once! We must say that the Gemara means that one cannot swallow three k'Zeisim at once (but one can swallow more than two k'Zeisim at once).

Kaf ha'Chayim (19): There is a Safek whether or not one blesses Al Netilas Yadayim for less than k'Beitzah of bread, so he should avoid the Safek and eat k'Beitzah.

Shulchan Aruch (ibid.): Some say that a k'Zayis of grain helps, even if it was not bread.

Beis Yosef (DH Kasav ha'Rif): The Rosh and R. Yonah (DH Afilu) disagree with the Rif. However, the Rashba (DH ul'Inyan) says 'the Yerushalmi is like the Rif. It says that one must eat a k'Zayis of grain in order to be Mezamen. A Beraisa says that vegetables suffice. We establish it to be like R. Shimon ben Gamliel, but the Halachah does not follow him, for Rabanan disagree. However, Tosfos says that he joins even to a Zimun of three.' In Tosfos, the Ri rules like R. Shimon ben Gamliel, but the Sar mi'Kutzi disagrees, for he is an individual. Also, if so R. Yochanan contradicts himself, for in the Bavli he requires eating a k'Zayis of grain in order to be Motzi others. This implies that he joins even if he only drank, like the case of R. Shimon ben Shetach.

Note: We do not learn from the fact that he joined the king and queen for a Zimun, for women do not join. There was at least one other man there. Perhaps there were at least to others! ('Yanai and his friends' connotes like this.) Rather, since he could be Motzi, all the more so he joins. However, R. Shimon ben Shetach holds that Birkas ha'Mazon exempts wine. How can we learn that one who drank (something that Birkas ha'Mazon does not exempt) joins?

Beis Yosef (ibid.): In the Yerushalmi, R. Yochanan requires a k'Zayis for a Zimun, i.e. even to join. Rather, we must say that in the Bavli, R. Yochanan holds that even drinking helps for joining to 10, and in the Yerushalmi he requires a k'Zayis in order to joins to a Zimun with three. Also Semag says that the Yerushalmi supports the Rif. Semak says that the custom is that he joins. The Rambam holds like the Rif. The Rashba and Yerushalmi support them, so we follow them.

Shulchan Aruch (ibid.): Some say that vegetables or any food helps.

Gra (DH Aval): This opinion holds that it is harder to join to 10 than to three. Also, 'in order to be Motzi the Rabim' connotes that grain is needed only to be Motzi (but not to join). The first opinion holds that it is harder to join to 10 only regarding reclining. R. Yehoshua ben Levi holds that a baby joins to make a Zimun with 10, but not to a Zimun with three. R. Yochanan holds that in every case, he does not join (unless he ate grain).

Shulchan Aruch (ibid.): Therefore, if two ate and a third comes, if they can get him to eat a k'Zayis of bread, this is best. If he does not want, they should not give to him to drink, or any other food. If they gave to him to drink or another food, they make a Zimun with him, even though he does not want to eat bread.

Magen Avraham (9): Keneses ha'Gedolah said that his Rebbeyim would give to him to drink if he did not want to eat, and he would join. This is the custom nowadays.

Kaf ha'Chayim (21): Also others say so. However, Chikrei Lev says that one should not be lenient l'Chatchilah against the Ge'onim and most Poskim. The Chida says that if the third eats a k'Zayis of Pas ha'Ba b'Kisnin (cake), all agree that they make a Zimun.

Mishnah Berurah (21): The Mechaber decides between the opinions and says that one should strive to get him to eat bread to avoid the argument. B'Di'eved, one must be concerned for the latter opinion and make a Zimun.

Kaf ha'Chayim (22): Regarding a liquid, he must drink a Revi'is. It need not be wine.