Interesting combinatorics question As a child I had a deck of cards which consisted of maybe 50 cards. On each card there were 6 objects. Players had to pick 2 cards from the deck, and the player who first spotted the difference between the 2 cards won.  The interesting thing was, that for evry 2 cards it was true that they only differed in 1 object. 
Can someone explain how to construct such cards?

One trivial way to construct such cards is to use a total of $55$ objects.  Let's label the objects $A,B,C,D,E,1,2,\ldots,50$.  Each card shows a set $\{A,B,C,D,E,k\}$ with $1\le k\le 50$.  But this is almost certainly not what the OP wants!
