2. (M. Evdokimov) On the table, there are 23 boxes arranged in a row, one of which contains a prize. On each box, it is either written "There is no prize here" or "The prize is in the adjacent box." It is known that exactly one of these statements is true. What is written on the middle box?
Answer: "The prize is in the adjacent casket."

Solution: Note that on the casket adjacent to the one containing the prize, a true statement is always written. Since we have only one true statement, there is only one such "adjacent" casket. However, this means the prize must be in one of the outer caskets, and the true statement is written on the adjacent casket. Therefore, the casket in the center does not contain the prize and must have a false inscription. This means its inscription is: "The prize is in the adjacent casket."

## Criteria.

"+" - A correct and justified solution is provided;

"+." - A correct and justified solution is provided, but some non-essential details are omitted or not explained;

"土" - The work contains a justified statement about the impossibility of the prize being in the center and the correct answer is obtained, but a significant part of the solution is not explained or omitted, or the correct answer is obtained, but some non-essential cases are not considered/explained, and/or errors were made in the consideration of cases that did not affect the solution;

"干" - The work contains a justified statement about the impossibility of the prize being in the center, but the correct answer was not obtained, or the work contains an unjustified statement about the impossibility of the prize being in the center and the correct answer was obtained, or the correct answer was obtained, but at least one significant case was not considered/explained, and/or errors were made in the consideration of cases that affected the solution; 

"-. " - The work contains an unjustified statement about the impossibility of the prize being in the center and the correct answer was not obtained, or some significant cases were considered, but the correct answer was not obtained;

"-" - All other cases.