IR-MO 2003 Problem 13

here is the most difficult and the most beautiful problem occurs in 21th iranian (2003) olympiad assume that P is n-gon ,lying on the plane ,we name its edge 1,2,..,n. if S=s1,s2,s3,.... be a finite or infinite sequence such that for each i, si is in {1,2,...,n}, we move P on the plane according to the S in this form: at first we reflect P through the s1 ( s1 means the edge which iys number is s1)then through s2 and so on like the figure below. a)show that there exist the infinite sequence S sucth that if we move P according to S we cover all the plane b)prove that the sequence in a) isn't periodic. c)assume that P is regular pentagon ,which the radius of its circumcircle is 1,and D is circle ,with radius 1.00001 ,arbitrarily in the plane .does exist a sequence S such that we move P according to S then P reside in D completely?