The Mishnah (3:3) records a debate regarding how one separates challah from tameh dough on the yom tov of Pesach. Recall that if one produces a significant amount of dough (5/4 of a kav) they are required to separate a portion of the dough and give it to a kohen. The portion is referred to as challah and is treated like terumah. Consequently, if the challah is tameh then a kohen is not allowed to eat it and the challah must be burnt.
On a regular Yom Tov, if one separated tameh challah then they must wait until after Yom Tov to burn the challah. The Tosfot Yom Tov explains that this is because the Torah prohibits one from burning kodshim that have become pasul on Yom Tov. He cites the Tosfot who explains that burning tameh terumah on Yom Tov was rabbinically prohibited in case one confuses the case with kodshim and end up burning pasul kodshim on Yom Tov.
On Pesach however we have a further issue. One cannot leave that challah till after Yom Tov since it will become chametz and one is prohibited from having chametz in their possession. Furthermore, one cannot bake the challah on Yom Tov because since it is tameh and may not be consumed, baking it, shelo letzorech (for no use), is prohibited. Consequently, the Mishnah records a debate regarding how this situation is resolved.
R’ Eliezer maintains that one should bake all the dough, and only separate challah from the already baked rolls. Delaying the separation means that all the dough can be baked since (ho’il) each role is potentially consumable. Only after they are baked is one roll selected as challah. R’ Yehuda ben Beteira disagrees. He maintains that a small amount of dough must be separated but then placed in cold water to prevent it from becoming chametz. He argues that one cannot bake all the dough since some of the dough must be challah then some of the baking is shelo letzorech.
Finally R’ Yossi maintains that one can separate some dough as challah and he is not bothered if it becomes chametz. Since the prohibition of having chametz is only regarding chametz in your possession, once the challah is designated, it no longer belongs to him and the prohibition would not be violated.
The Bartenura explains that R’ Eliezer disagrees with this solution because since (ho’il) one has the capacity to do she’elat chacham and undo the designation, it is still considered his property and the prohibition would be violated if the challah became chametz.
The Tosfot Yom Tov cites Rashi’s question. R’ Eliezer maintains the logic of ho’il. This prevents him from using the solution of R’ Yossi as we just explained, and enables him to bake the entire batch of dough together as explained above. Rashi asks that since the logic of ho’il makes the separated dough considered as if it is his, then it follows that R’ Eliezer should allow separating the challah from dough and then baking the entire amount along with the challah. The Tosfot answer that one cannot rely on the ho’il if there is another solution available. Since one can separate the challah after the dough has been baked without relying on the ho’il this is the preferred solution.
The Tosfot follows with a further question. If one cannot use the ho’il if another solution is available, and since R’ Eliezer relies on ho’il to bake the entire batch of dough, he should instead use R’ Yehuda’s solution of separating some dough and placing it in cold water since it does not rely on a ho’il. The Ri answers that R’ Eliezer was concerned that R’ Yehuda’s technique would not be executed adequately and the separated dough become chametz.
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