A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all

A farmer is taking her eggs to the market in a cart, but she hits a
pothole, which knocks over all the containers of eggs. Though she is
unhurt, every egg is broken. So she goes to her insurance agent, who
asks her how many eggs she had. She says she doesn't know, but she
remembers somethings from various ways she tried packing the eggs.

When she put the eggs in groups of two, three, four, five, and six
there was one egg left over, but when she put them in groups of seven
they ended up in complete groups with no eggs left over.

What can the farmer figure from this information about the number of
eggs she had? Is there more than one answer?


We need a number (n) that leaves a remainder of 1 when divided by 2, 3, 4, 5, 6 but no remainder when divided by 7.
217 + 84 = 301.
Other solutions are multiples of 3 x 4 x 5 x 7, but we want the lowest one here.