Problem 5.7. After the World Hockey Championship, three journalists wrote an article about the German national team - each for their newspaper.

- The first wrote: “The German national team scored more than 10 but fewer than 17 goals throughout the championship.”
- The second: “The German national team scored more than 11 but fewer than 18 goals throughout the championship.”
- The third: “The German national team scored an odd number of goals throughout the championship.” In the end, it turned out that only two journalists were correct. How many goals could the German national team have scored in the championship? List all possible options.
Answer: $11,12,14,16$ or 17.

Solution. Let's consider all possible cases.

If no more than 10 goals were scored, then for an odd number of goals, one statement would be true, and for an even number, none would be true. This does not fit.

If 11 goals were scored, then exactly two statements are true. This fits.

If the number of goals scored is between 12 and 16, then for an odd number of goals, all three statements are true, and for an even number, two are true. Only even values fit: $12,14,16$.

If 17 goals were scored, then exactly two statements are true. This fits.

If 18 or more goals were scored, then for an odd number of goals, one statement would be true, and for an even number, none would be true. This does not fit.

Thus, five values fit: $11,12,14,16,17$.