• The source for a karpaf

The next Mishnah states, נותנין קרפף לעיר – we grant a karpaf, an open area that is 70 2/3 amos wide, to a city before measuring the techum, according to Rebbe Meir. The Chochomim say, לא אמרו קרפף אלא בין שתי עיירות – they did not say the rule of a karpaf except with regard to the separation between two cities. Which means that אם יש לזו שבעים אמה ושיריים ולזו שבעים אמה ושיריים - if this one has seventy amos and a fraction, and that one has seventy amos and a fraction, meaning the cities are separated by no more than 141 1/3 amos, עושה קרפף את שתיהן להיות אחד – the karpaf granted to each of them causes the two of them to become one.

The Gemara asks for the source for adding a karpaf, and Rava brings the passuk regarding Levitical cities, מקיר העיר וחוצה – from the wall of the city outward, which means that אמרה תורה תן חוצה ואחר כך מדוד – the Torah is stating that one needs to grant an outside area to the city, and only then measure the techum.

• Machlokes about the Chochomim’s opinion regarding a karpaf

There is a machlokes Amoraim regarding what the Chochomim hold regarding a karpaf.

- Rav Huna said, נותנין קרפף לזו וקרפף לזו – the Chochomim mean that we grant a karpaf to each city, meaning a distance of up to 141 1/3 amos may separate the two cities and they are still considered as one.

- Chiya bar Rav said, קרפף אחד לשתיהן – the Chochomim hold that there is one karpaf for both, meaning that there cannot be more than 70 2/3 amos between the two cities for them to be considered as one. The Gemara goes through a lengthy analysis of these two opinions.

• The case of three villages

It was stated in the Mishnah, וכן שלשה כפרים המשולשין – so too, regarding three villages grouped together, אם יש בין שנים חיצונים מאה וארבעים ואחת ושליש – if there are 141 1/3 amos between the two outer villages, עשה אמצעי את שלשתן להיות אחד – the middle village causes the three of them to become one.

The Gemara assumes that the three villages are in a row, which would mean that they all become one because of the middle village which unites them. Rashi explains that there is not more than 70 2/3 amos separating any two villages. This seems to be a תיובתא to Rav Huna.

The Gemara answers that Rav Huna interprets the Mishnah differently. The three villages are in a triangle, and the two villages that serve as the base of the triangle are separated by much more than 141 1/3 amos. If the middle village was inserted in between the two outer villages so that they would be a row, then there would be no more than 141 1/3 amos between any village, and the middle village causes them to be combined to one. From here we see that two villages can be combined as long as there is no more than 141 1/3 amos between them.

Siman – Pinocchio’s Nose. When news got out that the Pinocchio factory was commissioned to make an exceptionally long nose to measure the karpaf of a city, two cities called to make an order double the length, followed by three villages that lived in a triangle.