אורח חיים קצ״זOrach Chayim 197

Se’if 1א׳

שְׁנַיִם שֶׁאָכְלוּ כְּאֶחָד וְגָמְרוּ, וּבָא שְׁלִישִׁי, כָּל הֵיכָא דְּאִי מַיְתֵי לְהוּ מִדִּי מָצוּ לְמֵיכַל מִנֵּיהּ, מִצְטָרֵף בַּהֲדַיְיהוּ; וְחַיָּבִים לִתֵּן לוֹ לֶאֱכֹל כְּדֵי שֶׁיִּצְטָרֵף עִמָּהֶם וְהוּא שֶׁבָּא עַד שֶׁלֹּא אָמְרוּ: הַב לָן וְנִבְרִיךְ, אֲבָל אִם אָמְרוּ: הַב לָן וְנִבְרִיךְ וְאַחַר כָּךְ בָּא הַשְּׁלִישִׁי, אֵינוֹ מִצְטָרֵף עִמָּהֶם. הַגָּה: וּנְטִילַת מַיִם אַחֲרוֹנִים כְּהַב לָן וְנִבְרִיךְ דָּמֵי (מָרְדְּכַי פֶּרֶק ג' שֶׁאָכְלוּ) וְעַיֵּן לְעֵיל סי' קע"ט.

Two who ate together and finished, and a third came: wherever, if something were brought to them, they would still be able to eat of it, he joins with them; and they are obligated to give him to eat so that he may join with them. And that is when he came before they said "Give us, and let us bless"; but if they said "Give us, and let us bless" and afterwards the third came, he does not join with them. Hagah [Rema]: And the washing of the last waters is like "Give us, and let us bless" (Mordechai, chapter "Three who ate"); and see above, siman 179.

Se’if 2ב׳

תִּשְׁעָה שֶׁאָכְלוּ דָּגָן וְאֶחָד אָכַל כַּזַּיִת יָרָק, מִצְטָרְפִין לְהַזְכִּיר שֵׁם וַאֲפִלּוּ לֹא טִבֵּל עִמָּהֶם אֶלָּא בְּצִיר אוֹ לֹא שָׁתָה עִמָּהֶם אֶלָּא כּוֹס אֶחָד שֶׁיֵּשׁ בּוֹ רְבִיעִית מִכָּל מַשְׁקֶה חוּץ מִן הַמַּיִם, מִצְטָרֵף עִמָּהֶם; וְהוּא שֶׁיִּהְיֶה הַמְבָרֵךְ אֶחָד מֵאוֹכְלֵי הַפַּת; וַאֲפִלּוּ שִׁבְעָה אָכְלוּ דָּגָן וְשְׁלֹשָׁה יָרָק, מִצְטָרְפִין; אֲבָל שִׁשָּׁה, לֹא, דְּרֻבָּא דְּמִנְכַּר בָּעֵינָן.

Nine who ate grain and one who ate an olive's bulk of vegetable join together to mention the Name. And even if he dipped with them only in brine, or drank with them only one cup that holds a reviit (a quarter of a log) of any drink except water, he joins with them — provided that the one who blesses is one of those who ate bread. And even if seven ate grain and three vegetable, they join together; but six, no, for we require a majority which is evident.

Se’if 3ג׳

הַמִּצְטָרֵף צָרִיךְ לְבָרֵךְ בְּרָכָה אַחֲרוֹנָה עַל מַה שֶּׁאָכַל וְאֵינוֹ נִפְטָר בְּבִרְכַּת הַמָּזוֹן שֶׁל אֵלּוּ; בַּמֶּה דְּבָרִים אֲמוּרִים דְּסָגֵי בְּכָל מַאֲכָל, לְהִצְטָרֵף לַעֲשָׂרָה; אֲבָל לִשְׁלֹשָׁה, אֵינוֹ מִצְטָרֵף עַד שֶׁיֹּאכַל כַּזַּיִת. וְיֵשׁ אוֹמְרִים דִּבְכַזַּיִת דָּגָן מְהָנֵי אֲפִלּוּ אֵינוֹ פַּת; וְיֵשׁ אוֹמְרִים דִּבְיָרָק וּבְכָל מַאֲכָל, מְהָנֵי; הִלְכָּךְ שְׁנַיִם שֶׁאָכְלוּ וּבָא שְׁלִישִׁי, אִם יְכוֹלִים לְהַזְקִיקוֹ שֶׁיֹּאכַל כַּזַּיִת פַּת, מוּטָב; וְאִם אֵינוֹ רוֹצֶה, לֹא יִתְּנוּ לוֹ לִשְׁתּוֹת וְלֹא מַאֲכָל אַחֵר; וְאִם אֵרַע שֶׁנָּתְנוּ לוֹ לִשְׁתּוֹת אוֹ מַאֲכָל אַחֵר, יְזַמְּנוּ עִמּוֹ אַף עַל פִּי שֶׁאֵינוֹ רוֹצֶה לֶאֱכֹל פַּת.

The one who joins must recite the final blessing over what he ate, and he is not exempted by the Grace after Meals of these others. In what case are these things said — that any food suffices? For joining to make ten; but for three, he does not join until he eats an olive's bulk. And there are those who say that with an olive's bulk of grain it is effective even if it is not bread; and there are those who say that with vegetable and with any food it is effective. Therefore two who ate and a third came: if they can press him to eat an olive's bulk of bread, well and good; and if he does not want to, they should not give him to drink nor any other food; and if it happened that they gave him to drink or other food, they should form the zimmun with him even though he does not want to eat bread.