The gibson family have bought tickets to the christmas market. there are 4 mothers, 2 grand-mothers and 4 daughters. what is the minimum number of tickets they need?

The minimum number of tickets that could admit all of them is six (6).

This thing is impossible to explain in words, so I shall attempt it with a diagram:

Here are the six ladies:

       ( A )      ( B )
          |           |
          |           |
       ( C )      ( D )
          |           |
          |           |
       ( E )       ( F )  

--  'E'  and  'F'  are the daughters of  'C'  and  'D' .

--  'C'  and  'D'  are the daughters of  'A'  and  'B' .

So look what we have now:

--  'A'  and  'B'  are the mothers of  'C'  and  'D' .
     There's 2 of the mothers.

--  'C'  and  'D'  are the mothers of  'E'  and  'F' .
     There's the OTHER 2 mothers. 
 
--  'A'  and  'B'  are the grandmothers of  'E'  and  'F' .
    There's the 2 grandmothers.

--  'E'  and  'F'  are the daughters of  'C'  and  'D' .
     There's 2 of the daughters.

--  'C'  and  'D'  are the daughters of  'A'  and  'B' .
     There's the OTHER 2 daughters.

You want to know what ? !
The group is even bigger than THAT.
There are also 2 GRAND-daughters in the family ...  'E'  and  'F' .

So now you have a list of 12 people ! ... 4 mothers, 2 grandmothers,
4 daughters, and 2 grand-daughters ... and they all get in to the
Christmas Market with only six tickets.    Legally !

Such a deal !

Don't forget :  Christmas this year is also the first day of Chanukah !
                     All for the same price !