How many people must eat to make a Zimun of ten with Elokeinu?
In order to be obligated/allowed to make a Zimun of ten people with the saying of Elokeinu, one needs to have at least seven people who have eaten [a Kezayis of] bread, and another three people who have eaten a Kezayis of vegetables [or any other food] or have drank a Revius of a liquid, including even water. However, if only six people have eaten [a Kezayis of] bread, another four people who did not eat bread cannot join for the making of a Zimun with Elokeinu even if they ate a Kezayis or Revius of other foods and drinks.
 Admur 197/2; Michaber 197/2; Brachos 48; Tur 197; Levush 197; Bach 197; Chayeh Adam 48/13; Derech Hachaim 5; Kitzur SHU”A 45/14; Beis Menucha 197/2; Chesed Lealafim 197/9; Ben Ish Chaiy Korach 5; Kaf Hachaim 197/17; Ketzos Hashulchan 45/3
Other opinions: Some Poskim rule four people who ate a Kezayis of foods other than bread can join six people who ate bread for the saying of Elokeinu. [Iggur in name of Or Zarua, brought in Beis Yosef 197; Erech Hashulchan 197/1 in name of Razah; Yerushalmi; Bereishis Raba 91; See Kaf Hachaim 197/17]
 The reason: The reason three non-bread eaters can only join seven bread eaters is because seven is a recognizable majority [Rov Hanikur] which has eaten bread. However, six is not a recognizable majority, and hence is not valid to have another four people join. [Admur ibid; Michaber ibid; Brachos ibid]
If one of the four ate Mezonos? It is questionable whether according to the Tur who rules that Meznos is valid like bread for a third person to join a Zimun of two bread eaters, whether a Mezonos eater is considered like a bread eater in this regard as well, and hence if six ate bread and four ate Mezonos, or even one ate Meznons and three ate or drank other foods and liquids, then they join for Elokeinu. Practically this matter requires further analysis. [Ketzos Hashulchan 45 footnote 9]