I have mixed 13 decks of cards.

What is the minimum number of cards must be taken out from the above mixed cards to guarantee at least one 'four of a kind'.

13 x 3 + 1 = 40

Explanation:

The number of decks is irrelevant i.e any number of decks can be mixed and still the answer would be same.

Any card drawn will be a Ace,2,3,4,5,6,7,8,9,10,Jack,Queen or King, so there are 13 possibilities each time a card is drawn.

The fastest and luckiest way would need just 4 cards of the same kind.

The slowest way is our solution as it will guarantee a four of a kind.

i.e draw 3 of each kind =>39 cards will be fetched. now next card will guarantee 4 of a kind.