How come 35 Taalas then?

Basically the 35-talas are an extension of the Sapta talas. The only element that changes is the Laghu. We already came across the fact that a laghu has five Jaatis (Chaturasra, Tisra, Misra, Khanda and Sankeerna). By incorporating that, we get a total of 35 varieties (7 Talas * 5 Jaatis). For instance, consider Dhruva tala with a Chaturasra laghu. A Chaturasra jaati dhruva tala would have a Chaturasra laghu followed by a dhrutam and two more Chaturasra laghus (It would be represented as I 4 0 I 4 I 4, the 4 near the laghu indicating a Chaturasra laghu). So we get an external count of 14 beats in all (4+2+4+4). Now the same Dhruva tala could have a Tisra laghu, in which case, we render a Tisra laghu instead of a Chaturasra laghu and thereby get a total external count of 11 beats (3+2+3+3) (This would be represented as I 3 0 I 3 I 3, the 3 representing the Tisra laghu). This is applied to all the other talas in a similar fashion. The important thing to be remembered is that it is always advisable to specify the Jaati (type) of the laghu to avoid confusion.