This problem is from hard to solve brainteasers #8, pg "Up and down".
This morning I had to take the stairs because the elevator was out of service. I had already gone down seven steps when I saw my professor on the ground floor coming up. I continued descending at my usual pace, greeted my professor when we passed, and was surprised to see that when I still had four more steps to go, the professor had gone up the whole flight. I When I go down one step, he goes up.
How many steps does the staircase have?
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