A team of several workers can complete a task in 7 full days. The same team, without two people, can complete the same task in several full days, and the same team, without six people, can also complete the same task in several full days. How many workers are in the team? (The productivity of the workers is the same.)

#
Let there be $n$ workers in the team. The daily productivity of one worker is called the norm.

Over 7 days, the reduced teams will fall short by 14 and 42 norms, respectively. This means that $n-2$ is a divisor of 14, and $n-6$ is a divisor of 42. Since $n>6$, then $n-2=7$ or 14, that is, $n=9$ or 15. Since 42 is divisible by $9-6=3$, but not by $15-6=9$, then $n=9$.

## Otvet

9 workers.