Find the least common multiple of 2, 3, 4, 5 and 6, 60 first. Take one for every two, three for every time, four for every time, five for every time, and one for every six. So suppose there are 60k+ 1 eggs in this basket (k is an integer), take seven eggs at a time and just eat them up.

Let k=5+7(n- 1)=7n-2.

60k+ 1 = 420n- 120+ 1 = 420n- 1 19

When n = 1.23, the number of eggs is, 30 1, 72 1,141,... 420 n-1.

(Note that every two answers differ by the least common multiple of 2, 3, 4, 5, 6, 7, 420)