1. Captain Jack Sparrow found a cave with a pirate treasure. In it, there are 6 chests, and the treasure is only in one of them, while the other chests are home to venomous snakes, ready to attack anyone who disturbs their peace.

On the first chest, it says “The treasure is in the third chest.”

On the second, “The treasure is in me or in the first chest.”

On the third, “There is no treasure in me.”

On the fourth, “The treasure lies in a chest with an odd number.”

On the fifth, “There is no treasure in the second and sixth chests.”

On the sixth, “There is no treasure in the fourth chest.”

Help Jack find the treasure, knowing that exactly half of the inscriptions are true. In your answer, indicate the number of the chest with the treasure.

ANSWER: 2.
Solution: Let's create a $6 \times 6$ table. In the і-th row and ј-th column, we will place a cross if the і-th statement is true when the treasure is in the ј-th chest:

|  | 1 | 2 | 3 | 4 | 5 | 6 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 1 |  |  | X |  |  |  |
| 2 | X | X |  |  |  |  |
| 3 | X | X |  | X | X | X |
| 4 | X |  | X |  | X |  |
| 5 | X |  | X | X | X |  |
| 6 | X | X | X |  | X | X |

According to the problem, the column that fits is the one with exactly 3 crosses - i.e., the second.