Responsa for Bava Batra 258:1

Q. A and B hired a tutor for their sons [for several terms] and paid him for one term in advance. Five weeks after the term began, A's son died. Since the tutor had to continue to teach B's son, he demanded that A pay him for the remaining term (or terms). A, however, claimed that when the tutor came to console him, after his son's death, he told him that he forwent the balance of his fee and that he would even repay him whatever he had received in excess of the fee for five weeks. A, therefore, demanded that amount from the tutor. At first the tutor admitted that he had forgone the balance of his fee, but claimed that his act was not valid since it was merely a verbal statement without a formal act of transference. Later, however, he completely denied ever having relinquished his claim.
A. If the tutor definitely admitted A's claim, and later retracted his admission, A is free from obligation to the tutor. However, he cannot collect anything he has already paid, since the tutor's promise of a refund was not accompanied by a formal act of transference. But, if the tutor's denial followed immediately upon his admission, or if the denial merely explained that the admission was really no admission, or if the admission was only implied but not definitely stated, A must pay the tutor his fee for the whole year. A, however, may bring another pupil to the teachr to be taught in place of his son.
SOURCES: Pr. 434–435. Cf. Agudah B. M. 118.

Q. In the presence of witnesses Leah asked A to betroth her. While she was in a yard not owned by her, A threw a ring into her lap for the purpose of betrothal. The witnesses, although they saw Leah shake her dresses in order to brush the ring away, did not see whether or not the ring actually fell into her lap. Does Leah need a divorce from A?
A. Had the witnesses seen the ring fall into Leah's lap, she would need a divorce in spite of her claim that she never intended to become A's wife and that she was joking when she asked him to betroth her. For we would, then, be concerned only with facts and not with her thoughts and unexpressed intentions. But, since the witnesses did not see the ring fall into Leah's lap, and the yard where the incident took place did not belong to Leah, she needs no divorce, for no betrothal took place. R. Meir adds: If my teachers agree with my decision, all will be well. But if they do not agree I shall subscribe to whatever they decide to do. However, I should prefer not to be strict in this matter and not to require Leah to obtain a divorce, lest A become rebellious and refuse to divorce her, and lest he travel to a distant land and thus render it impossible for the unfortunate woman ever to marry again.
This Responsum is addressed to: "My teacher Rabbi Haim and his court."
SOURCES: Pr. 993: Mord. Git. 451; ibid. Kid. 548: Tesh. Maim. to Nashim. 1.