The Gemara in Masechet Berachot (48) addresses the case of nine people who ate a meal with bread, and a tenth, who ate with them, ate only vegetables, without bread. In such a case, the Gemara writes, the group of ten may conduct a Zimun with "Elokenu," meaning, with the full text of "Nebarech L’Elokenu She’achalnu Mi’shelo." Since nine out of the ten ate bread, they may recite the special Zimun for a Minyan, even though the tenth ate food other than bread. This Halacha is codified by the Shulhan Aruch (Orah Haim 196:3), who adds that in such a case, the tenth person must recite a Beracha Aharona; he cannot fulfill his obligation of Beracha Aharona by listening to the recitation of Birkat Ha’mazon.
Tosefot (commentaries by Medieval French and German scholars) comment that according to some authorities, this Halacha does not apply in a case of two people who ate bread and a third ate other food. In such a situation, the third person, who did not eat bread, cannot combine with the other two to allow reciting a Zimun. Even though a tenth person who ate food other than bread suffices to allow a group to recite "L’Elokenu," a third person who did not eat bread does not allow the group to recite a Zimun. This is the view of several other authorities, as well, including Rav Hai Gaon (10th century, Babylonia), the Rambam (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204) in Hilchot Berachot (5:8), the Rashba (Rabbi Shelomo Ben Aderet of Barcelona, Spain, 1235-1310) and the Ra’a (Rabbi Aharon Halevi, Spain, 1235-1303). According to this view, if two people ate bread together with a third person who ate or drank something other than bread, they do not recite a Zimun before Birkat Ha’mazon.
The Talmud Yerushalmi, however, states otherwise, and rules that in the case of three people, too, they may recite a Zimun even if one of the three ate or drank something other than bread. Several Rishonim (Medieval scholars) follow this ruling of the Yerushalmi.
The Shulhan Aruch (Orah Haim 196:3; listen to audio recording for precise citation) cites three opinions on this issue. He first cites the aforementioned view of Tosefot, the Rambam and others that three men cannot conduct a Zimun unless all three ate bread. The second view he cites maintains that they may make a Zimun even if one of the three did not eat bread, but ate "Mezonot" food. The Shulhan Aruch then cites the ruling of the Yerushalmi, that even if the third person ate a Ke’zayit of vegetables or a Rebi’it of wine, the three men may make a Zimun.
As for the final Halacha, the Shulhan Aruch writes that people who eat together should avoid this situation given the different opinions that exist. Meaning, if two people eat bread together, and they are joined by a third person, that third person should either eat bread, so they can recite a Zimun according to all views, or not eat or drink anything, so that they do not require a Zimun according to all views. Rabbi Moshe Halevi (Israel, 1961-2001), in his work Birkat Hashem (vol. 3, p. 468; listen to audio recording for precise citation), rules that the three may recite a Zimun even if the third eats only "Mezonot" food.
The Shulhan Aruch adds that if the third person nevertheless eats other foods, such as vegetables, or only drinks, they may recite a Zimun. Although they should preferably avoid this situation, as discussed, if the third eats foods other than bread they recite a Zimun, in accordance with the view of the Yerushalmi.
As mentioned, this discussion refers only to the situation of one of three people who eats foods other than bread. When ten people eat together and one of the nine ate or drank something other than bread, they may recite a Zimun with "L’Elokenu."
Summary: If nine people ate bread, and there was a tenth person with them who ate a Ke’zayit of another food, they may recite a Zimun with "L’Elokenu." If three people eat together, and one of the three does not want to eat bread, they should see to it that he either eats bread or a "Mezonot" food, or does not eat or drink anything, to avoid the question of whether a Zimun would be recited. If he did eat or drink something other than bread, then they recite a Zimun.
