When three people ate bread together, they recite the introductory "Zimun" before Birkat Ha’mazon, whereby the leader announces, "Hab Lan Ve’nibrich Le’malka Ila’a Kadisha," inviting the other to bless G-d. He later announces, "Nebarech She’achalnu Mi’shelo" ("Let us bless to the One from whose [food] we ate"), and the others respond, "Baruch She’achalnu Mi’shelo U’b’tubo Hayinu" ("Blessed is the One from whose [food] we ate, and through whose goodness we live").
If a person is present at the time a Zimun is being recited, and he had not eaten anything, then he cannot respond, "Baruch She’achalnu Mi’shelo…" Since he did not eat, it would be dishonest to say "Achalnu" – "we ate." And so a person in such a case responds to a Zimun by reciting a different text: "Baruch U’meborach Shemo Tamid Le’olam Va’ed." The acrostic of these words is "Boshet Lo" ("Bet," "Vav," "Shin," "Tav," "Lamed," "Vav"), which can be used a mnemonic to help remember this response. If a person who had not eaten is present when ten people recite a Zimun together, such that the divine Name "Elokenu" is added, he responds, "Baruch Elokenu U’meborach Shemo Tamid Le’olam Va’ed."
This applies only if the individual did not eat or drink anything. If he ate or drank anything, then even if he drank only water, he answers to the Zimun with the standard response of "Baruch She’achalnu Mi’shelo…" This is the ruling of Hacham Ovadia Yosef, who distinguishes between this case and a case where two people ate bread and a third person only drank water, or water-based beverages such as tea, coffee, seltzer or soda. If the third person only drank these beverages, then he cannot be counted towards a Zimun, and so if only two people ate bread and a third only drank one of these beverages, a Zimun is not recited. A Zimun requires, at very least, two people who ate bread and a third who either ate a Ke’zayit of food (preferably bread, but if not, then "Mezonot" food, and if not, then other food), or drank a significant beverage, such as natural fruit juice (not from concentrate) or wine. If the third did not eat, and drank only water or a water-based drink, he cannot be counted and thus a Zimun is not made. However, if there are three people who ate and form a Zimun, and a fourth person is present, then as long as he ate or drank something, even water, he can recite "Baruch She’achalnu Mi’shelo…" along with the others.
Summary: If a group of three or more people is reciting a Zimun before Birkat Ha’mazon, and there is somebody present who did not eat or drink anything, he answers to the Zimun, but with a different text: "Baruch U’meborach Shemo Tamid Le’olam Va’ed." If he ate or drank anything, even just water, then he answers with the standard response of "Baruch She’achalnu Mi’shelo U’b’tubo Hayinu."
