Answer#1: (Note: Tosfos is bothered by the law that we do not redeem prisoners for more than their value. How was Rebbi Yehoshua ben Chananya allowed to bypass that law?) When there is a danger to the prisoner's life, we allow the redemption of the prisoner to be even more than their true value. This is as stated earlier (47a) regarding someone who sells himself and his children to Nochrim, and certainly applies here that his life is in danger.

Answer#2: Alternatively, it could be this was permitted here because he was tremendously smart.

Explanation: Their argument is also on the case of the woman (55b, 58b), as is apparent from the Gemara later (58b).

Implied Question: The Gemara says in Kesuvos (95a) that if he wrote a sale document (for one of his fields) for the first person and she did not sign it, and he then wrote a sale document (for a different field) for the second person and she did sign it, she has lost her Kesuvah. This implies that when there is only one buyer she can say that she merely agreed to make her husband happy (even if she wrote a document). (Note: Our Gemara states that if she wrote a document it would be a valid sale, and she could not claim that she merely agreed in order to make her husband happy.)

Answer#1: The case there is when she signed on the sale document written by her husband. Here the case is where she wrote the document herself.

Answer#2: Additionally, the case where she signed there is where she agreed to the sale by her husband or decided to forgo his obligation to her. However, here when she wrote this document, she wrote that she is selling the field.

Answer#3: Rebbi Eliezer mi'Shanza's understands that Rav and Shmuel are arguing here regarding whether or not the omission of Acharyus in a document is considered a scribe's mistake. Shmuel holds as he explicitly states in Bava Metzia (14a) that it is not a mistake in sale documents, while Rav holds it is a mistake, and in a general document it is as if Achrayus is written as a condition.

Accordingly, the Gemara in Kesuvos (ibid.) could be talking about a case where she explicitly stated that she is not taking any Achrayus (unlike our case where this is an argument between Rav and Shmuel).

Opinion#1: Rashi explains that even according to the opinion in Bava Basra that we do not make claims (for a buyer or inheritor), here he would agree that we do.

Implied Question: We do not find any argument on this topic in Bava Basra. (Note: Why does Rashi say that even etc.?)

Opinion#2: Rather, we say in Bava Basra (23a) that we find a Beraisa that states that we make a claim for an inheritor, and another Beraisa stating that we make a claim for a buyer. When our Gemara says, "In a case like this we make a claim" it means that even in a case like this we would make a claim.

One might think that the owner is right, and he did not protest the ownership earlier due to his fear of the Sikrikun (Nochrim who stole his land and sold it to the first buyer).

Implied Question: The Gemara in Bava Basra (54b) states regarding a place called Dura Dira'usa that the fields of a valley there were originally owned by people who hid themselves. The king had said that whoever is willing to pay a tax on the land can use it. This caused the original owners to lose any rights (even Halachic rights) to the land. (Note: Why does our Gemara treat the people who ran away as if they are the rightful owners?)

Answer: The Gemara there is discussing people who ran away because they did not want to pay the tax. However, in our Gemara the people went away for other reasons, and did not run away from (i.e. because of) paying for the land. It therefore is understandable that whoever paid for the years they were away had the right to use the land (as this is the typical agreement in this situation, see Rashi DH "mi'Bnei Baga"). However, when the owners come back, the rights to the land revert to the original owners.

Explanation: He wasn't going to write a document saying that he could seize money from the other landowners in the valley, as why should they pay what the person who worked the land already paid? Rather, it refers to the original owners (who ran away, see Maharsha).

Explanation#1: A quarter of the money means one quarter of the amount that he paid for the land. The quarter of land or money that he is giving him is actually one fifth of the land, as is explained that the Nochri will sell the land for twenty percent less (than its true value).

Question: This is difficult. What is the question from the braisa that states, "either one quarter of the land or one quarter of the money?" According to Shmuel who says that one quarter of the land is one third of the money, as the Nochri gives a twenty-five percent discount, we can explain the opposite! This would mean that when the Beraisa says he should be given one quarter of the land either in actual land or in money, it would mean one third of the money (exactly as stated by Shmuel)!

Explanation#2: There are Sefarim that have the text in Rav and in the Beraisa that this refers to one quarter of the land which is one quarter of the money.

This is also the text of Rabeinu Chananel. He explains that one quarter of the land that he gave money for refers to a fifth. He gave money for four fifths of the land, because the Nochri sold it to him for twenty percent less than what it is worth.