1. When strangers eat at the same table, one may eat milk while the other eats meat.
2. One is not allowed to sleep in the same bed as his wife who is a Nidah, even when they are both wearing clothes.
3. A Torah scholar suffered an early death because he transgressed this sin (#2).
4. Beis Shamai established 18 decrees in one day in the attic of Chananyah ben Chizkiyah.
5. Chananyah ben Chizkiyah defended the book of Yechezkel.
A BIT MORE
1. This is because there is no reason to suspect that one will take from the other's food, since they are not familiar with each other.
2. This is derived from the prohibition against sleeping in the same bed with another person's wife, even when they are both wearing clothes.
3. The wife of a Torah scholar who died young could not understand why Hashem took her husband away. Eliyahu ha'Navi questioned her and discovered that they used to sleep in the same bed when she was a Nidah. Eliyahu ha'Navi said that this was his sin for which he was punished.
4. Although Beis Hillel was usually the majority and the law usually followed Beis Hillel, on this day Beis Shamai was the majority (how this happened is explained by the Gemara later) and thus the law followed Beis Shamai in these matters.
5. The Sages questioned the apparent contradictions in the book of Yechezkel. Chananyah ben Chizkiyah successfully explained that there are in fact no contradictions.