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ZA-SAMO 1999 Problem 6

    You are at a point (a,b)(a,b) and you need to reach another point (c,d)(c,d) . Both points are below the line x=yx = y and have integer coordinates. You can move in steps of length 1, either upwards of to the right, but you may not move to a point on the line x=yx = y . How many different paths are there?

    Dataset text AI-MO AoPS. Quoted with source.

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