QUESTION: The Gemara discusses what one must do when he is unsure whether his Korban Pesach was offered. Five people offered their Korbanos, and then they discovered that one of the Korbanos was Pasul, but they do not know which one. The Gemara says that each person is exempt from bringing a second Korban Pesach on Pesach Sheni, because there is no way that he can bring another Korban Pesach out of doubt. He cannot offer an animal on condition that, if he is exempt, it is a Korban Shelamim, because the Korban may be eaten only for one day (in case it indeed is a Korban Pesach), for one may not limit the amount of time that a Korban may be eaten (the time limit of a Pesach is shorter than the limit of a Shelamim).

The Gemara asks that there is another recourse to bring a Korban Pesach out of doubt. Each person should bring a Mosar Pesach and stipulate that "if I am obligated to bring a Korban Pesach, then this animal is a Pesach, and if I am not obligated to bring a Korban Pesach, then this animal is a Mosar Pesach." A Mosar Pesach is a Korban Shelamim that is eaten for one day and one night. By offering an animal conditionally as a Mosar Pesach, each person avoids the problem of decreasing the amount of time in which a Korban may be eaten.

Why does the Gemara assume that such a condition will help? It is true that the Mosar Pesach is eaten for one day and one night, but the Korban Pesach -- according to Rebbi Elazar ben Azaryah -- is eaten only until Chatzos (midnight), and not for the full night! TOSFOS (Zevachim 57b, Megilah 21a) rules like Rebbi Elazar ben Azaryah. Consequently, if the Korban becomes a Korban Pesach, one is decreasing the amount of time in which the Korban may be eaten. The Gemara should answer that the option of bringing a Mosar Pesach is not viable, because the Beraisa follows the view of Rebbi Elazar ben Azaryah, and thus one still decreases the amount of time to eat the Korban. The Mosar Pesach is eaten for a day and a night (because it is compared to a Korban Todah, Zevachim 36a), while the Pesach itself is eaten only until midnight. (YESHU'OS YAKOV, OC 477:1)

(a) The YESHU'OS YAKOV answers that this Gemara supports the opinion of the RAMBAM, who rules like Rebbi Akiva, that the Korban Pesach may be eaten all night and not just until Chatzos.

(b) The OR SAME'ACH (Hilchos Chametz u'Matzah 6:1) writes that even according to Rebbi Elazar ben Azaryah, one may eat the Korban Pesach after Chatzos. However, when one eats it after Chatzos he does not fulfill the Mitzvah of eating the Korban Pesach; he is merely considered to be eating Kodshim Kalim. Therefore, when one treats a Mosar Pesach like a Korban Pesach, he does not decrease the amount of time in which it may be eaten. (The Or Same'ach, however, questions his approach from the Gemara in Pesachim (71a, 120b), which clearly implies that the meat of the Korban Pesach becomes Pasul at Chatzos. He gives a forced answer to this question.)

(c) The TORAS KOHANIM (Dibura d'Nedavah, Perek 18:4) states that the Mosar Pesach is eaten during the day and night "k'Techilas Hekdesho" -- because it was originally sanctified for that purpose. This implies that the Mosar Pesach is eaten for a day and a night not merely because of a Gezeiras ha'Kasuv, but because of a logical reason. A Mosar Pesach is a Korban that was originally designated as a Korban Pesach but was not offered (its owner offered another animal as his Korban Pesach), and thus it is offered as a Korban Shelamim instead. Since it was originally sanctified as a Korban Pesach, it may be eaten for the amount of time that a Korban Pesach may be eaten. According to Rebbi Elazar ben Azaryah, who maintains that the Korban Pesach is sanctified to be eaten only until Chatzos, the Mosar Pesach, too, may be eaten only until Chatzos. When the Gemara in Zevachim (36a) compares the Mosar Pesach to a Korban Todah, it is teaching only that the Mosar Pesach is not eaten for two days. (M. KORNFELD)

QUESTION: Rav Huna brei d'Rav Yehoshua left the meal he was sharing with Rav Papa when he saw that Rav Papa ate four times more than he did, and he went to join Ravina. When he saw that Ravina consumed eight times more than he did, he declared, "Give me one hundred Rav Papas instead of one Ravina!"

What was the point of Rav Huna's exaggeration? If he meant simply that he loses less when he eats with Rav Papa, why did he say that he prefers to eat with "one hundred" people like Rav Papa? On the contrary, he obviously will lose more if he eats with 100 "Rav Papas." A person loses much less when he shares a meal with someone who eats eight times more than he, than when he shares a meal with a hundred people who each eat four times more.

ANSWER: Rav Huna did not mean that there would be more food left over for him to eat if he eats with one hundred people like Rav Papa than if he eats with one Ravina. Rather, he meant that economically, it is more cost-effective to eat with one hundred people like Rav Papa than with one Ravina.

The key to understanding Rav Huna's declaration is the following point: the greater number of people with whom one shares a partnership, the less one pays relative to the total value of the food.

When one makes a partnership with one other person, they together pay for 5 portions, and thus each one is entitled to 2 1/2 portions. However, when one partner eats 4 times more food than the other partner, he ends up eating 4 portions, while the other partner is left with only 1 portion. He receives 1 1/2 portions less than what he was entitled to receive. In other words, he loses 60% of what he should have received.

If he makes a partnership with two people who both eat four times as much as he eats, they buy 9 portions together and each person pays for 3 portions, but the two larger eaters each receive 4 portions and the smaller eater receives 1. He loses 2 out of the 3 to which he was entitled, or 67%. The more "eaters" who join his partnership, the more he loses.

However, even if he joins with 100 people who each eat four times more than he eats ("100 Rav Papas"), he still does not lose as large of a percentage as he would lose if he would eat with a single Ravina. With many Rav Papas, his loss will never be more than 75% of the amount to which he is entitled, because if he were to eat four times more than he is eating now he would be eating as much as each Rav Papa. However, with one Ravina, out of the 9 portions available, he receives only 1 instead of the 4 1/2 for which he paid. He loses 3 1/2 portions out of 4 1/2, or 77%. Therefore, Rav Huna rightly complained that he would be better off with 100 Rav Papas than with one Ravina. (MIRKEVES HA'MISHNEH, in his "Bereichos b'Cheshbon," a collection of mathematical insights into the Gemara)