Question

Suppose we have a 52 card deck with the cards in order ace , 2, 3, . . . , queen, king top to bottom, for clubs, then diamonds, then hearts, then spades. A step consists to taking the top card and moving it to the bottom of the deck. We start with the ace of clubs as the top card. After two steps, the top card is the 3 of clubs. What is the top card after 735 steps?

Answer 1

Answer:8 of clubs

Step-by-step explanation:

Given card is drawn and place at the bottom of deck

We can solve this by considering that after 52 steps card will  be at their initial original positions.

Thus

735=52K+b

Where K is the no of times card regains their positions

and b is the nth step between 1 to 52

here For k=14

b=735-728=7

Thus 7 card will be moved up to 735 steps and 8 of clubs will be on top of deck.