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Brain Teaser
How many Steps? 

The lift was out of order. I had gone down 6 steps of the last flght of stairs when I saw another resident just starting up the staircase. We greeted each other as we passed and I continued descending without change in pace. I had noticed that for every step I took he was taking two. Consquently when he had reached the top I still had four steps to go.
How many steps were there in the staircase?

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