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Regarding the rules as to how to put up a mezuzah here are the terms used by the poskim:
- Chelkat Yakov 161 - derech biyatcha, rov tashmish, door, rov kenisot. His reasoning is that the idea of rov kenisot is not found in the gemara, rishonim, or earlier poskim. The gemara when it says we follow the ragil it means only to determine if a doorway is obligated in mezuzah or not but not to determine the direction. The idea of rov tashmish helps determine which way is an entry.
- Rav Schachter - derech biyatcha, rov tashmish, rov kenisot, door. His reasoning is that rov tashmish helps clarify which way is an entry and rov kenisot does that also but it isn't as clear of a determining factor as rov tashmish since where a person spends more time determines the direction of entry and if that's not clear look at the way when majority of the time he actually walks.
- Igrot Moshe 4:43:4 - derech biyatcha, rov kenisot, rov tashmish, door. Teshuva Mahava 1:61, Minchat Yitzchak 1:89, Aruch Hashulchan 289:8, Chovat Hadar 8:1:4. Rov kenisot is the explanation of the gemara's idea of ragil and an explanation of the deoritta halacha of derech biyatcha. We follow that before we follow the doorway since the doorway was only used in the gemara when we're in doubt. The idea of rov tashmish is only an indication of what was the rov kenisot.
- Daat Kedoshim 289:11 - derech biyatcha, door, rov tashmish, rov kenisot. Since door is in the gemara we follow that before we look at any other factor. The other factors are just tie breakers and it is based on logic. It is logical that rov tashmish is more significant than rov kenisot.
Here is one piece of the argument of how to order these rules.
- The gemara Menachot 33a speaks about a house with two rooms one next to another one for the wife to do her work and one for the man to run his business and invite guests. The gemara says that the direction of the mezuzah is determined if a door is put up and see which way it opens. This is cited in Shulchan Aruch YD 289:3.
- Why didn't the gemara use the rule of usage? The Chelkat Yakov YD 161 writes that the rule of following whichever room is used more doesn't apply since the man and woman each use the room the whole day. Therefore, a door is necessary to establish the direction of the mezuzah.
- Why didn't the gemara use the rule of majority of walking? The Chelkat Yakov points out that even though many more times people will walk from the man's door into the woman's room rather than vice versa considering that the man is using his side for guests that doesn't establish which direction is an entrance. Rav Moshe YD 1:176, however, argues that the reason that the gemara needed the door to determine the direction is because the majority of her walking in one direction offsets the way that other walk. However, if everyone would use a doorway as an entrance a majority of the time then the mezuzah would be established in that direction. This dispute impacts whether the rule of majority of walking precedes the rule of doorway; according to Chelkat Yakov it doesn't, while according to Rav Moshe it does.