The game "Spot It!" consists of a deck of cards.
In the original version of the game, every card has 8 symbols on it. If you pick any two cards, exactly one symbol will be the same on the cards.
In the kids version of the game, every card has 6 symbols instead, but you still have exactly one match of symbols if you pick any two cards.
You may also assume that the deck contains the same number of every symbol (that is, no symbol is more common than another).
Suppose you want to create a more complex version of the game, where you have N symbols on each card and every two cards share exactly M symbols.
a) Is this possible?
In a deck with N symbols on each card, and each pair of cards share M symbols:
b) How many cards will there be at most?
c) How many symbols will there be in total?
(See also https://brilliant.org/discussions/thread/spot-it-problem-version-1/)
Note: The combination of symbols matching two cards should, if possible, be different for every two cards. (Thanks for Utkarsh Dwivedi for the question leading to this clarification.)