Rob the Robber and the Staircase

Level pending

Rob the Robber has stolen into a house. He climbs 1/2 way up the stairs, but something upstairs stirs so he goes down 1/3 of the way. Then he climbs up 1/2 way again, and then somebody coughs so he goes down 1/3 of the way. Finally he climbs up 8 steps and makes it to the top! But then Bob the Police officer catches him. How many stairs are in the staircase?

If the staircase is 42 stairs and he climbs up 1/2 the way, he climbs up 21 steps. So if Rob starts at stair #2 and climbs up 1/2 the way he ends up at stair #23, not #21.

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