Bekhorot 55A

מיתיבי: היה לו חמש בכפר חנניה וחמש בכפר עותני ⁠— אין מצטרפות עד שיהא לו אחת בציפורי. תיובתא דרב!

The Talmud raises an objection to the opinion of Rav from a baraita: If one had 5 sheep in the village of Ḥananya and 5 sheep in the village of Otnai, which is a distance of 32 mil from the village of Ḥananya, they do not combine, unless he also has one sheep between them, in Tzippori. This is apparently a conclusive refutation of the opinion of Rav that there must be at least 5 sheep in the middle.

תרגמה שמואל אליבא דרב: כגון שהיו תשע מכאן ותשע מכאן ואחת באמצע, דההיא חזיא להכא וחזיא להכא.

Shmuel interpreted the baraita in accordance with the opinion of Rav. The baraita does not mean he had 5 sheep on either side, but rather it is referring to a case where he had 9 sheep from here and 9 sheep from there and one in the middle. This case is different, as that one sheep in the middle is fit to combine with the animals here and is fit to combine with the animals there, to constitute a total of 10 animals on either side, to which the obligation applies.

אמר רב פפא: ולשמואל, אפילו רועה מצרפן, ואפילו כליו של רועה מצרפן.

Rav Pappa says: And according to the opinion of Shmuel that one animal in the middle is sufficient to combine the two groups on either side of it, even if the shepherd himself is in the middle without any sheep, he combines the two flocks on either side. And even if only the implements of the shepherd are in the middle, they combine the two flocks on either side into one flock. Since the shepherd must go there to collect his implements it is considered as though he is already there and therefore the two flocks are combined.