### Instruction: Emily ordered her playing cards by suit in the order $$A,2,3,4,5,6,7,8,9,10,J,Q,K,A,2,3,\cdots.$$What is the $42$nd card?### Response: I want to find the 42nd card in this sequence, which is repeating the same pattern of 13 cards for each suit.
So I can divide 42 by 13 to see how many times the pattern repeats before the 42nd card.
42 divided by 13 is 3 with a remainder of 3.
That means the 42nd card is the third card after the third repetition of the pattern.
The third card in the pattern is 3, so I just need to figure out what suit it is.
Since the pattern starts with Aces, the suits are in alphabetical order: Clubs, Diamonds, Hearts, Spades.
The first repetition of the pattern is Clubs, the second is Diamonds, and the third is Hearts.
So the 42nd card is a 3 of Hearts.