Scheme 1: From the first day, find out the eggs left over from grandma's house every day (left over from the previous day+a newly laid egg-two eaten eggs) in turn.

Day 1 day: 20+1-2 =19;

The next day:19+1-2 =18;

……;

Until the 20th day: 1+ 1-2=0.

So grandma's eggs can be eaten for 20 days in a row.

Scheme 2: Grandma eats two eggs every day, and the old hen lays one egg every day, so grandma only needs to take out one egg from 20 eggs every day, plus the eggs laid by the old hen, which is enough to eat. 20 eggs, one a day, can be eaten for 20 days. 2 1 day, the old hen lays only one egg, which is less than one day. So grandma's eggs can be eaten for 20 days in a row.