Checked into the Hilton Lima Miraflores today (fantastic hotel by the way) and checking out on November 3rd. Checking Into the Hilton Buenos Aires on November 3rd and out the 7th. Based on the FAQ informaion above it seems that my days at the Hilton Lima Miraflores from Nov 1 to 3 will count as first stay and that I should get double points for the stay in Buenos Aires. Hope it works this way as a significant number of points at stake.