The prisoners that will be able to escape at the end of the rounds will be the numbers:

1 , 4 , 9 , 16 , 25 , 36, 49, 64, 81, 100

That is, the difference between each number of prisoner who will be able to escape increments in every odd:

1 - 4 -> 3
4 - 9 -> 5
9 - 16 -> 7
16 -25 -> 9
25 - 36 -> 11
36 - 49 -> 13
49 - 64 -> 15
64 - 81 -> 17
81 - 100 -> 19

etc...

That would be: 10 prisoners...

Javier Novoa C.
jstitch @ gmail . com