## Task 3 - 080523

Heinz asks Gerd: "How many years old are you?"

Gerd answers: "My sister is four times as old as my brother. I am more than twice, but less than four times as old as my sister. Together, the three of us are 17 years old."

Calculate how many years old Gerd is!

(All age statements should be in full years.)
Since Gerd is more than twice as old as his sister and his sister is four times as old as her brother, Gerd must be more than eight times as old as his brother.

If his brother were two or more years old, then Gerd would have to be more than 16 years old. This would contradict the statement that the sum of their ages is 17.

Therefore, the brother is 1 year old, the sister is thus 4 years old, and since $17 - 1 - 4 = 12$, Gerd must be 12 years old.

Since $4 \cdot 4 > 12$, the condition that Gerd is less than four times as old as his sister is also satisfied. The given solution thus meets all conditions and is the only possible one.