The CMC reception desk has a tray in which to stack letters as they arrive. Starting at 12:00, the following process repeats every five minutes:

- Step 1 - Three letters arrive at the reception desk and are stacked on top of the letters already in the stack. The first of the three is placed on the stack first, the second letter next, and the third letter on top.
- Step 2 - The top two letters in the stack are removed.

This process repeats until 36 letters have arrived (and the top two letters have been immediately removed). Once all 36 letters have arrived (and the top two letters have been immediately removed), no more letters arrive and the top two letters in the stack continue to be removed every five minutes until all 36 letters have been removed. At what time was the 13th letter to arrive removed?
(A) $1: 15$
(B) $1: 20$
(C) $1: 10$
(D) 1:05
(E) $1: 25$
The easiest way to keep track of the letters here is to make a table of what letters arrive at each time, what letters are removed, and what letters stay in the pile.

| Time | Letters  Arrived | Letters  Removed | Remaining Pile  (bottom to top) |
| ---: | :--- | :--- | :--- |
| $12: 00$ | $1,2,3$ | 3,2 | 1 |
| $12: 05$ | $4,5,6$ | 6,5 | 1,4 |
| $12: 10$ | $7,8,9$ | 9,8 | $1,4,7$ |
| $12: 15$ | $10,11,12$ | 12,11 | $1,4,7,10$ |
| $12: 20$ | $13,14,15$ | 15,14 | $1,4,7,10,13$ |
| $12: 25$ | $16,17,18$ | 18,17 | $1,4,7,10,13,16$ |
| $12: 30$ | $19,20,21$ | 21,20 | $1,4,7,10,13,16,19$ |
| $12: 35$ | $22,23,24$ | 24,23 | $1,4,7,10,13,16,19,22$ |
| $12: 40$ | $25,26,27$ | 27,26 | $1,4,7,10,13,16,19,22,25$ |
| $12: 45$ | $28,29,30$ | 30,29 | $1,4,7,10,13,16,19,22,25,28$ |
| $12: 50$ | $31,32,33$ | 33,32 | $1,4,7,10,13,16,19,22,25,28,31$ |
| $12: 55$ | $34,35,36$ | 36,35 | $1,4,7,10,13,16,19,22,25,28,31,34$ |
| $1: 00$ | None | 34,31 | $1,4,7,10,13,16,19,22,25,28$ |
| $1: 05$ | None | 28,25 | $1,4,7,10,13,16,19,22$ |
| $1: 10$ | None | 22,19 | $1,4,7,10,13,16$ |
| 1:15 | None | 16,13 | $1,4,7,10$ |

(At 12:55, all 36 letters have been delivered, so starting at 1:00 letters are only removed and no longer added.)

Letter \#13 is removed at 1:15.

ANSWER: (A)