Stam mishna against R' Yehuda (Pesachim 13a)
The gemara asks how Rav Nachman could pasked like Rav Yehuda that you can't eat chametz at four hours on Erev Pesach and you can't get hanaah (benefit) at 5 hours against R' Meir when we have a stam mishna on daf 21a that supports R' Meir. The mishna there says that "As long as you can eat you can give to eat." This seems to support R' Meir that the isur of hanaah and the isur of achila both come at the same time - at 5 hours. The gemara answers that (summary courtesy of Kollel Iyun Hadaf), "[We prove on Daf 21A that] that Mishnah is not Stam, because it says '[as long as it is] permitted [to eat', as opposed to 'as long as one may eat'], i.e. some people are permitted at the same time that others are forbidden - it is like R. Gamliel, who permits [Kohanim to eat] Terumah and forbids [Yisraelim, who eat only] Chulin in the fifth hour."
Tosafos asks what I think is the obvious question: That means that this stam mishna is like R' Gamliel and definitely not like R' Yehuda. So the gemara's initial question still remains: How could R' Nachman pasken like R' Yehuda? Tosafos gives a forced answer which really doesn't solve anything (see the Maharsha). The Ran and Pnei Yehoshua also offer suggestions. The Tzlach though has an answer that I enjoyed so I'll post it here.
The Tzlach says that the gemara there is really saying that from the fact that it says "mutar" in the mishna it proves that we're talking about two different types of people or two different types of things. Once we say that then the mishna can be like R' Yehuda also. Even though we don't see clearly from our gemara that R' Yehuda makes any distinction between different people or different types of chametz we can logically deduce that he does. Why does he say that you get an extra hour for hanaah than you get for eating? It must, says the Tzlach, because eating is an isur kares whereas hanaah is only a lav. Therefore, all things for which there is no kares the prohibition only begins at 5 hours. For example chametz nukshe (inedible chametz). I just googled chametz nukshe and it looks like we actually pasken that way that you can eat it until the end of the fifth hour. So then the mishna on 21a works out according to R' Yehuda: "As long as you can eat chametz nukshe then you can feed all chametz to the animals." Now we no longer have a stam mishna against R' Yehuda.