Problem:
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
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 , 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.
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