Today's daf is sponsored by Rochel Cheifetz in loving memory of her aunt, Rose Rubelow, Rachel bat haRav Moshe v'Tzipora Mashbaum whose yartzeit was 26 Adar. 

When the law is to split an item, the meaning is to split the market value. There are three attempts to prove this from our Mishna or tannatic sources. The first two are rejected but the last is accepted. Rami bar Hama teaches that one can derive from our Mishna that one who finds an item on the street and picks it up on behalf of another, is effective. Rava disagrees and only permits it in a case where the one who lifted it acquired part of it for him/herself and therefore can acquire the rest for someone else. But if one acquired it exclusively for someone else, it would not be effective. Rava proves this by comparing a case of one who stole on behalf of another and one who stole on behalf of oneself and another (partners). Rava teaches a halakha based on this principle but the Gemara modifies it as it is incomprehensible as transmitted. From which line in the Mishna did Rami bar Hama derive his opinion? The Gemara suggests five possibilities - all are rejected except the last one. Shmuel is quoted as having said about riding on an animal and leading it - one is an act of acquiring and the other is not. Which one is it? Rav Yehuda infers from a Mishna that riding is not an act of acquiring as holding the reigns will only work in a sale where one is passing to the other, but holding the reigns on an ownerless animal is not a valid act of acquiring. How does this all fit with our Mishna where it is clear that riding on the animal enables one to acquire a lost animal? To answer this, they explain the Mishna in a case where the one riding was also leading the animal with his/her feet. If so, why does the Mishna mention leading in two different ways?