ושרץ היאר צפרדעים ועלו ובאו בביתך ובחדר משכבך ועל מטתך ובבית עבדיך ובעמך ובתנוריך ובמשארותיך
The frogs will swarm the river, and will go up and come into your house, and your bedroom, on your bed, and into the house of your servants, and in your ovens, and in your bread
The second of the Ten Plagues was that of the swarm of frogs. More than just a noisy nuisance, they made life unbearable. They were literally everywhere, and in everything. An Egyptian couldn’t feel safe taking a bath, or going to bed, or putting on clothes, without bumping into dozens or hundreds of frogs. The Torah says that the frogs even became suicidal, jumping into the Egyptians’ ovens. Food that they were baking became contaminated by the corpses of the frogs. It’s no wonder that Pharaoh begged Moshe to stop the plague.
One of the most dramatic episodes in all of Tanach is that of Chananya, Mishael, and Azariah. The wicked Babylonian King Nebuchadnezzar ordered all the Jews to bow down to a statue he had made of himself. Anyone who failed to comply would be thrown into a fiery furnace. Chananya, Mishael, and Azariah were prominent Jewish members of Nebuchadnezzar’s court. All three of them publicly defied his orders, preferring to remain faithful to G-d instead of bowing down to this false idol. They accepted that this would be their demise, and were glad to fulfill the mitzvah of dying al Kiddush Hashem, sanctifying Hashem’s name. After calmly walking into the furnace, a miracle happened, and they remained unscathed. They emerged alive, having created an even bigger Kiddush Hashem.
The gemarra wonders where Chananya, Mishael, and Azariah got the idea to go into the fiery furnace, rather than just run away. It answers that they made a logical deduction known as a kal vachomer from the frogs in the second plague in Egypt. They deduced that if the frogs, who weren’t obligated in the mitzvah of Kiddush Hashem, chose to jump into the fiery furnaces of the Egyptians, us, who are obligated in the mitzvah of Kiddush Hashem, should throw ourselves into the fiery furnace.
One of the greatest authorities from the 18th century, known as the Sha’agas Aryeh, asked a question on this logical deduction. It has a very clear flaw. How can we say that the frogs weren’t commanded to go into the ovens, yet Chanania, Mishael, and Azariah were commanded in Kiddush Hashem? The Torah explicitly says that the frogs will go into the Egyptians’ ovens! We see that they were in fact commanded! Hashem altered their nature to go into the ovens, even though it was suicidal. This is the same as a command from Hashem. The logical deduction is therefore flawed.
Legend has it that the Vilna Gaon, when he was only seven years old, proposed an answer to this major problem. It’s true that the frogs were commanded to enter the ovens. However, that wasn’t their only command. The frogs were also commanded to enter the Egyptian’s bread, their beds, their bedrooms. Each and every frog could have told its comrade to enter the oven, while it will go to the other places. They could have avoided going into the ovens altogether. The fact that there were some who volunteered, is a lesson for us. If the frogs, who could have avoided giving up their lives for Hashem, chose not to, Chanania, Mishael, and Azariah, who were commanded in the mitzvah of Kiddush Hashem, surely should have given up their lives. According to this, the logical deduction is sound.
This explanation is similar to one provided by the Rambam to resolve a theological dilemma. Hashem decreed that Avraham’s descendants would be enslaved by a foreign nation. If this is something that was foretold and predetermined, how could the Egyptians be punished for it? He answers that no specific nation was forced to enslave the Jews. Every nation had the option to let someone else do the dirty work. Since the Egyptians volunteered, they were punished. This is similar to the frogs, although with the opposite effect. The Egyptians were punished for volunteering, since they could have avoided it. The frogs were viewed favorably for volunteering, since they could have avoided it. Good Shabbos
 Based on Peninim MiShulchan HaGra to Exodus 7:28, citing Parparos by Rav Asher Zelig Karman from Brooklyn (second ed., 5689), parshas Kedoshim, and Hadras Kodesh to Midrash Rus HeChadash 1:27
 Exodus loc. cit.
 Ibid 8:4. Although, almost irrationally, Pharaoh tells Moshe to wait until the next day to remove them (v. 6)
 Daniel Chapter 3
 Leviticus 22:32; Sefer HaMitzvos Aseh § 9
 Pesachim 53b; Shemos Rabbah 10:2; Midrash Tehillim 28:2; Zohar Chadash Rus § 78
 Tosafos ad. loc. s.v. מה ראו, quoting Rabbeinu Yitzchak. Rabbeinu Tam (ibid) gives a different explanation, in order to explain Rashi ad. loc., who says that they chose to die, even though a person doesn’t have to give up their life for mitzvah observance (וחי בהם ולא שימותו בהם, Leviticus 18:5 and Yoma 85b). Tosafos ask that this was a public display of religious oppression, to which everyone agrees creates an obligation to give up one’s life rather than transgress (Sanhedrin 74a) (I would have asked that everyone agrees idol worship is one of the exceptions to וחי בהם, and that one always has to give up their life rather than worship idols. In fact, Tosafos HaRosh, Tosafos Rid and the Ran ad. loc. ask from this. Maharsha ad. loc. points out that perhaps this gemarra could hold like Rabbi Yishmael, who holds that idol worship is not an exception to וחי בהם. Therefore, Tosafos chose to ask from the fact that it was in public, which is unanimous). Rabbeinu Tam therefore answers that the statue of Nebuchadnezzar wasn’t a real idol, just a symbol of honor. Therefore, they weren’t really obligated to give up their life, and that is why the gemarra asked where it is that they got this idea. Rabbeinu Tam brings support for this from Daniel 3:12, and also says this idea in Kesubos 33b and Megillah 12a (to answer different questions on this episode). The Maharsha, to answer Tosafos’ question, suggests that there weren’t ten Jews present when this episode took place. According to him, again, there would be no formal obligation in Kiddush Hashem
 The Maharsha loc. cit. points out a different problem: inasmuch as the frogs were exempt from the mitzvah of Kiddush Hashem, they were also exempt from the mitzvah of preserving one’s life (וחי בהם). Not only were Chananya, Mishael, and Azariah commanded in the mitzvah of Kiddush Hashem, but they were also commanded in the mitzvah of וחי בהם. He concludes that this is no problem, as we see many times that a kal vachomer has a flaw and is accepted nonetheless. This would address the Sha’agas Aryeh’s question as well
 I saw one contemporary sefer question the veracity of this story, as they didn’t see any room for a question. They claim that we see no such command. The Torah is just telling us what will happen with a lot of frogs. However, this claim doesn’t hold much ground. It’s against the nature of the frogs to go into the ovens, so it must have been Hashem “commanding” them. We see similarly with Hashem in Jonah 2:11, where Hashem “commanded” the fish to spit out Jonah, against its very nature. Furthermore, Midrash Tanchuma Va’eira § 14 says כל כך למה? לעשות רצון בוראם
 The Maharil Diskin ad. loc. brings the same question in the name of the Sha’agas Aryeh, but says that he himself answered his question
 The story ends with the Sha’gas Aryeh kissing the Vilna Gaon on the forehead for his brilliant answer. See ibid, who asks his own question on this resolution to the Sha’agas Aryeh’s’ question
 Mishneh Torah Hilchos Teshuvah 6:5; Cf. Hasagos HaRa’avad ad. loc. and Ramban to Genesis 15:13
 Genesis loc. cit.
 I thought of this similarity, and subsequently found that in the Additions and Corrections section of the Maharil Diskin Shemos § 27, they bring this comparison from the Machane Yehudah, a student of the Maharil Diskin. He also notes that the Maharil Diskin’s above-mentioned question is similar to that of the Ra’avad’s on the Rambam