Because the second day of Yom Tov was kept due to doubt as to which day was in fact Yom Tov, the rabbis permit one, under certain circumstances, to take advantage of the doubt. Thus, though eiruvei techumim for Shabbat can only extend the techum Shabbat to a total of 4,000 amot in one direction, on Yom Tov (but not on Rosh Hashanah) one may extend the techum Shabbat to 4,000 amot in two directions in the following manner. One places one eruv before the first day Yom Tov, thereby extending one’s techum on the first day of Yom Tov to 4,000 amot in one chosen direction. The following day one places a second eruv before the second-day Yom Tov, extending one’s techum Shabbat on the second day of Yom Tov to four thousand amot in the opposite direction.
Similarly, though an egg laid on a Shabbat preceding a Yom Tov may not be eaten on the next day of Yom Tov because food cannot be prepared on Shabbat for Yom Tov, an egg laid on the first day of Yom Tov may be eaten on the second. This is because one of the two days is not truly Yom Tov. Accordingly, the following logic may be applied: If the first day is truly Yom Tov, then the second day is a weekday and Yom Tov restrictions are inapplicable. If the second day is truly Yom Tov, then the first day was a weekday and one may, of course, prepare food on a weekday to eat on Yom Tov.