If the numbers are a < b < c < d < e < f < g and e + f + g < 51
then
e < 16 (because e is greater or equal to 16, f is greater or equal to 17, g is greater or equal to 18 imply e + f + g is greater or equal to 51).
So
e is less than or equal to 15
d is less than or equal to 14
c is less than or equal to 13
b is less than or equal to 12
a is less than or equal to 11,
and 101 = 11 + 12 + 13 + 14 + 51 > a + b + c = d + (e+f+g)=101 is a contradiction.