What is the Talmudic source for the idea that any halachic question has numerous answers?

Question

I remember hearing a story about a rav who was going for smicha and was challenged first to explain 100 reasons for why a chicken was kosher and then afterwards challenged to provide 100 reasons why it wasn't kosher. Anyone know the source?

Answer 1

The Talmud states (Sanhedrin 17a) that one can only be appointed to the Sanhedrin if he can prove that a sheretz is pure (despite the fact that a sheretz is impure):

אמר רב יהודה אמר רב אין מושיבין בסנהדרין אלא מי שיודע לטהר את השרץ מה"ת

Rab Judah said in Rab's name: None is to be given a seat on the Sanhedrin unless he is able to prove the cleanness of a reptile from Biblical texts.

(Soncino translation)

This is apparently a way to test someone's intellectual abilities; if one cannot come up with such a proof he is unworthy of sitting on the Sanhedrin. It is certainly possible that someone giving semicha would set a similar requirement.

The Talmud elsewhere (Eruvin 13b) mentions individuals who provided numerous reasons for something to be pure or impure:

א"ר אבהו א"ר יוחנן תלמיד היה לו לר"מ וסומכוס שמו שהיה אומר על כל דבר ודבר של טומאה ארבעים ושמונה טעמי טומאה ועל כל דבר ודבר של טהרה ארבעים ושמונה טעמי טהרה תנא תלמיד ותיק היה ביבנה שהיה מטהר את השרץ במאה וחמשים טעמים

R. Abbahu stated in the name of R. Johanan: R. Meir had a disciple of the name of Symmachus who, for every rule concerning ritual uncleanness, supplied forty-eight reasons in support of its uncleanness, and for every rule concerning ritual cleanness, forty-eight reasons in support of its cleanness. One taught: There was an assiduous student at Jamnia who by a hundred and fifty reasons proved that a [dead] creeping thing was clean.

(Soncino translation)

Earlier in the same discussion the Talmud states that R. Meir himself would convincingly argue both sides of the argument:

א"ר אחא בר חנינא גלוי וידוע לפני מי שאמר והיה העולם שאין בדורו של רבי מאיר כמותו ומפני מה לא קבעו הלכה כמותו שלא יכלו חביריו לעמוד על סוף דעתו שהוא אומר על טמא טהור ומראה לו פנים על טהור טמא ומראה לו פנים תנא

R. Aha b. Hanina said: It is revealed and known before Him Who spoke and the world came into existence, that in the generation of R. Meir there was none equal to him; then why was not the halachah fixed in agreement with his views? Because his colleagues could not fathom the depths of his mind, for he would declare the ritually unclean to be clean and supply plausible proof, and the ritually clean to be unclean and also supply plausible proof.

(Soncino translation)

R. Yom Tov Asevili in his commentary to another statement on the same page cites the French rabbis as follows:

ותירצו כי כשעלה משה למרום לקבל תורה הראו לו על כל דבר ודבר מ"ט פנים לאיסור ומ"ט פנים להיתר ושאל להקב"ה על זה ואמר שיהא זה מסור לחכמי ישראל שבכל דור ודור ויהיה הכרעה כמותם

And they answer that when Moses went on high to receive the Torah they showed him on every issue 49 ways to forbid and 49 ways to permit, and he asked God about this and He said that this is given over to the Sages of Israel in each generation and the decision follows them.