Question 555561
Let the number of words typed by the girl on the right be {{{a[1]}}}.
The girl to her left typed {{{a[2]=2a[1]}}} words.
The next girl typed {{{a[3]=2a[2]}}} words, and so on.
The number of words typed by each girl, from right to left, forms a geometric sequence with common ratio 2.
The sum of the words typed by n girls is
{{{S[n]=a[1](2^n-1)/(2-1)=a[1](2^n-1)}}}
Since both factors must be integer,
{{{635=5*127}}}, and
5+1=6 is not a power of 2,
it must be {{{a[1]=5}}} and
{{{2^n-1=127}}}
So {{{2^n=127+1=128=2^7}}} and n=7.