When I see a good question I toss it at my son to keep his brain working. Last night I gave him the following problem (from Shu"T R' Akiva Eiger Mh"T 129): Tosfos (Chulin 11b) writes that if someone who is chayav sereifah gets mixed into a group of people who are all chayav sekilah we cannot give sekilah to everyone in the group based on the principle of rov. Rov can be used in capital cases to determine if someone is chayav (e.g. is the victim a treifah or not?), but it cannot be used to determine what form of death penalty to inflict.
The gemara (Sanhedrin 84b) questions how we know the pasuk "makeh Aviv v'Imo mos yumas" refers to hitting a parent -- perhaps the pasuk is referring to murder? The gemara answers that this cannot be. The penalty for violating this pasuk is death by chenek; the penalty for killing a non-parent is sayeif -- it makes no sense to say that killing a parent should be less severely punished than killing a non-parent. This logic assumes that sayeif is the more severe punishment. However, asks the gemara, how would one answer the question if one assumes (like other opinions do) that chenek is more severe?
R' Akiva Eiger objects to the whole question and argues that even if chenek is the more severe punishment, the pasuk still cannot be read as referring to the murder of a parent. Remember that the murderer is chayav at a minimum the punishment of sayeif. The theoretically more severe penalty of chenek would apply only if the victim were the murderer's father. How do we know who the murderer's father is? Paternity is determined based on the principle of rov be'ilos achar haba'al. In effect, therefore, the gemara's question amounts to using a rov to determine which form of death to deliver. Since rov cannot be used to determine what type of death penalty to deliver (as we learned from Tosfos), the whole question of the gemara does not seem to get off the ground.
R' Akiva Eiger gives four answers, at least two of which are "easy" ones (whenever I tell my son that it's an easy one, he objects to my estimation. To his credit, this time he answered the kashe almost immediately by quoting a Hafla'ah at the end of the first perek of Kesubos. He is getting better at this game : )