Question: Why does Rav Shlomo Zalman Auerbach say that we do say Tachanun on the 13th of Sivan even if living outside of Israel even according to the opinion that one does not say Tachanun for six days after Shavuos which was the make up time of when they would bring their Yom Tov offering in the beis hamikdash since not everyone could do it on Shavuos itself?
A. The Mishna Berura (131:7:36) writes that there are places who have the custom to not say Tachanun all six days after Shavuos since they used to make up the sacrifices of the holiday during those days.
B. Rav Shlomo Zalman Auerbach holds the count of those days does not start after the second day of Shavuos outside of Israel, rather after the first day which is the sixth of Sivan so there would be no Tachanun until the 12th and they would start back saying it on the 13th.
Answer: The sacrifices were only brought in the Beis Hamikdash in Israel which only keeps one day so that is why we don’t start counting from the day after Shavuos ends outside of Israel. (See Dirshu note 14 in Mishna Berura 494:3:8).