Each entry in the list below is a positive integer:

$$
a, 8, b, c, d, e, f, g, 2
$$

If the sum of any four consecutive terms in the list is 17 , what is the value of $c+f$ ?
Since the sum of any four consecutive terms is 17 , then $8+b+c+d=17$ or $b+c+d=9$.

Also, $b+c+d+e=17$ and so $9+e=17$ or $e=8$.

Similarly, $e+f+g+2=17$ and $d+e+f+g=17$ tell us that $d=2$.

But $c+d+e+f=17$ and $e=8$ and $d=2$, which gives $c+f=17-8-2=7$.

ANSWER: 7