If 2 people have a common great-grandfather, what is their relationship to each other?

Here are 5 generations, with the child below the parent, and with spouses and siblings omitted for clarity.

Generation 1: Andrew & Alice = siblings

Generation 2: Bruce & Bernard = 1st cousins

Generation 3: Charles & Carol = 2nd cousins

Generation 4: Daniel & Dorothy = 3rd cousins

Generation 5: Elizabeth & Edward = 4th cousins

You and the lady in question are "Charles & Carol" - 2nd cousins. User "Librayanna" is getting thumbs down because she is off by one degree.

Removed comes in when cousins are in different generations.

Carol and Bruce are first cousin once removed through Bernard.

Dorothy and Bruce are first cousin twice removed through Bernard and Carol.

There is a word, "thrice", but no one uses it these days.

You'd say Edward and Bruce are first cousins three times removed through Bernard, Carol and Dorothy.

You put "half in front of everything if Andrew & Alice were half-siblings.

There are two ways to remember degree.

1) Children of first cousins are second cousins, children of second cousins are third cousins, and so forth. By "children of" I mean Bruce marries Zelda and has children with her, while Bernard marries Alicia and has children with her; not that someone married his first, 2nd, 3rd or 4th cousin.

2) The greatness of the common grandparents is one less than the degree of cousins;

Common 1st GGP = 2nd cousins

Common 2nd GGP = 3rd cousins

and so on.

If they didn't share the same Great Grandmother why would be Half Second cousins.

People who share a great grandparent are second cousins

People who share a grandparent are first cousins

Removed means generation difference, so for example your parents first cousins are your first cousin once removed as you are one generation different and your grandparents cousins are one of your parents first cousin once remove and your first cousin twice removed as you are two generation difference

Usually strangers.

Children of siblings are first cousins to each other as they share grandparents.

Children of first cousins are second cousins to each other as they share the same great grandparents.

However you did not say you share the same great grandparents but only the great grandfather. If this is the case you are 1/2 second cousins to each other.

The removes come in when you are in a different generation coming down from a common ancestor. You are a first cousin once removed to your parents' first cousins as their grandparents are your great grandparents. You are also a first cousin once removed to your first cousins' children as your grandparents are their great grandparents. In both cases one generation different.

Here is a relationship chart

http://www.islandregister.com/cousin.html

The great grandfather is the common ancestor. The grandfathers are brothers. The fathers are first cousins. The people in question are second cousins. Their children will be third cousins. Their grandchildren will be fourth cousins.

When the first of these two people has a child, it will be the second person's second cousin once removed. When the child grows up and has the first person's grandchild, the grandchild will be the second person's second cousiin twice removed. The first, second, third, etc. cousins stay the same and each generation is one removed, either higher or lower.

Cousins. First, second, third, just depends on the connection. First cousins, have sisters or brothers as parents. First cousin's kids are second cousins to each other.

The once removed means that the child of a first cousin is a first cousin once removed. (The once removed refers to which generation they are in.)

In your example, third cousins.