To find out what stairs you can currently challenge someone in, first go to the Main Stairs Page, then click on "Show your stairs only" link. The ones in BOLD are ones you can make a challenge in. .
Vikings: Or that new people starting on a stair have no option other to battle those that are already inactive (waiting sometimes almost a month before climbing up and maybe playing a game for real).
Also, with all the inactive players pilling up in the first level, the staircase may grow articially longer than it should be...