Pesachim 64B

שחל להיות בשבת, מניח ידו על כתף חבירו, ויד חבירו על כתיפו, ותולה ומפשיט. קרעו, והוציא את אימוריו. נתנו במגיס, והקטירן על גבי המזבח.

occurred on Shabbat, when moving the rods is prohibited (Rambam), he would rest his hand on another’s shoulder and the other’s hand on his own shoulder and suspend the offering and flay it. He would tear open the flesh of the offering and remove its sacrificial parts, i.e., the fats and other parts offered on the altar. He would place the sacrificial parts in a large basin [mageis] and burn them on the altar.

יצתה כת הראשונה וישבה לה בהר הבית. שניה בחיל, והשלישית במקומה עומדת. חשיכה ⁠— יצאו וצלו את פסחיהן.

If this took place on Shabbat, when carrying is prohibited, the first group would exit and remain on the Temple Mount; the second group would remain within the rampart, which was an area outside the women’s courtyard; and the third group would stand in its place in the Temple. They would wait there until nightfall, and as soon as it became dark, they would all go out and roast their Paschal lambs, everyone in his own place.

גמ׳ אמר רבי יצחק: אין הפסח נשחט אלא בשלש כתות של שלשים שלשים בני אדם. מאי טעמא? ״קהל״ ו״עדה״ ו״ישראל״. מספקא לן אי בבת אחת אי בזה אחר זה,

Talmud: R' Yitzḥak said: The Paschal lamb is slaughtered only in 3 groups of at least 30 people each. What is the reason for this rule? The verse says: Assembly, congregation, and Israel, and each of these terms refers to a group of no fewer than 10 people. We are uncertain as to whether this means that we need 3 groups of 10 people at the same time or one after another.

הלכך בעינן שלש כתות של שלשים שלשים בני אדם. דאי בבת אחת ⁠— הא איכא, ואי בזה אחר זה ⁠— הא איכא, הלכך בחמשין נמי סגיא, דעיילי תלתין ועבדי, עיילי עשרה ונפקי עשרה, עיילי עשרה ונפקי עשרה.

Therefore, in order to satisfy both possible interpretations, we require 3 groups of 30 people each. As, if you say we need all 30 at the same time, we have that, and if we need them one after another, we have that as well. Therefore, in pressing circumstances when there are not enough people present, even 50 people suffice. How so? 30 enter and perform the necessary rite, 10 others enter and 10 of the original group leave so that those present are considered a new group, and then 10 others enter and 10 more leave so that those present now comprise a third group. In this way the Paschal lamb is slaughtered in 3 groups of 30 people each, although the total number of people involved is only 50.