The Length of Memory
In the game of Memory,
there are many different cards, each having one matching card to make
its pair.
To start the game, all the cards are spread out face down.
On each turn, a player chooses a card and turns it over, then chooses a
second card and turns it over.
If the cards match, they are removed from the play area.
If the cards do not match, they are returned to their facedown positions.

Assuming you have perfect memory (you can remember where all previously
seen cards are), what is
the expected number of turns needed to clear the play area for N pairs?

How does this result change if two cards must first be selected,
then turned over simultaneously?

How does the first result change if there are mulitple identical pairs,
such as
in a standard deck of cards (any Queen could be paired with any other Queen)?
In all cases, assume you play to minimize the number of turns.
Source: Original.
Solution
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