A: There are 7 boxes arranged in a row and numbered 1 through 7 . You have a stack of 2015 cards, which you place one by one in the boxes. The first card is placed in box \#1, the second in box \#2, and so forth up to the seventh card which is placed in box \#7. You then start working back in the other direction, placing the eighth card in box \#6, the ninth in box \#5, up to the thirteenth card being placed in box \#1. The fourteenth card is then placed in box \#2, and this continues until every card is distributed. What box will the last card be placed in?
Solution: The answer is box \#3. Card \#1 is placed into box \#1, and this gets visited again by card \#13. Hence, box \#1 is visited every 12 times. Since $2004=167 \cdot 12$, we see that card \#2005 will be placed into box \#1. Now, counting "by hand," we see that card \#2015 will go into box \#3.