Question 80
Lorenza is on a track in the shape of a regular polygon with 2007 sides, whose vertices are numbered from 1 to 2007 counterclockwise. Lorenza, starting from vertex 6, each time jumps over 4 vertices and lands on the fifth one ahead (for example, from 20 she jumps to 25), but she jumps back 2 vertices when she lands on a vertex labelled by a power of 2 (for example, after a possible jump from 27 to 32, she must jump back to 30). After how many jumps will Lorenza have passed vertex 1 for the first time?