[Evnoir]

After you hear GO, take one of the strings and light it at both ends. Precisely after the first string completely burns, light the second string at one end only.
In the mean time, you can take the piece of cloth and write down with your pencil a sudoku puzzle you wanted to solve:

+-------+-------+-------+
| 8 7 9 | 4 3 1 | 6 5 2 |
| 6 2 3 | 5 9 7 | 1 4 8 |
| 1 5 4 | 2 6 8 | 7 9 3 |
+-------+-------+-------+
| 4 3 2 | 8 1 6 | 5 7 9 |
| 5 1 7 | 9 4 3 | 8 2 6 |
| 9 6 8 | 7 5 2 | 4 3 1 |
+-------+-------+-------+
| 7 9 6 | 3 8 4 | 2 1 5 |
| 3 4 1 | 6 2 5 | 9 8 7 |
| 2 8 5 | 1 7 9 | 3 6 4 |
+-------+-------+-------+

While you wait for the rest of the string to burn, you suddenly realize that the solution to igot's riddle was that

the poles are beside each other.

When the second string completely burns out, 45 minutes have elapsed and the door will be open.

Reincarnate's riddle is still boggling my mind.

@Zapmeister: I couldn't solve the puzzle and this post was just more for laughs than for solutions. When I solved for all the potential numbers, there was only one spot (6th row, 8th column) that had 2 possible numbers. All the rest were 3+ so I gave up lol