2. (7 points) From Monday to Wednesday, the gnome eats semolina porridge for breakfast, from Thursday to Saturday - rice porridge, and on Sunday he makes himself an omelet. On even-numbered days of the month, the gnome tells the truth, and on odd-numbered days - lies. On which of the first ten days of August 2016 could he have said: "Tomorrow I will be eating semolina porridge for breakfast"? Justify your answer.

| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 8 | 9 | 10 |  |  |  |  |
Answer. On Tuesday, August 2, on Wednesday, August 3, on Friday, August 5, on Monday, August 8

Solution. If today is Sunday, Monday, or Tuesday, then tomorrow the gnome eats porridge and the statement turns out to be true. This means that the gnome could have said the given statement only if such a day falls on an even number. There are two such days: Tuesday, August 2, and Monday, August 8. On the other days of the week (from Wednesday to Saturday), the statement becomes false, and the gnome could have said it only if the date was odd: on Wednesday, August 3, and on Friday, August 5.

A complete solution by enumeration is possible, where for each of the 10 days it is specified whether the gnome could have said the given statement on that day, and an explanation is provided for why he could or could not.

## Grading Criteria.

- $\quad$ A fully justified solution - 7 points.
- A generally correct solution, with main reasoning conducted, but one of the days is not specified in the answer - 4 points.
- A correct answer with incomplete reasoning - 2-3 points.
- Only the correct answer - 1 point.