6. (6 points) Letters $a, b, c, d, e, f, g$ each represent one of the numbers from 1 to 7. If $a+b+c=c+d+e=c+f+g$, then the number of possible values for $c$ is $\qquad$.


【Solution】Solution: $a+b+c=c+d+e=c+f+g$, which means $a+b=d+e=f+g$, there can only be 3 cases:
(1) $1+7=2+6=3+5$, in this case $c=4$;
(2) $2+7=3+6=4+5$, in this case $c=1$;
(3) $1+6=2+5=3+4$, in this case $c=7$;

Therefore, the possible values of $c$ are $1, 4, 7$, a total of 3.