A Walk in the Plane
Given a Cartesian coordinate system x-y in the plane. You need to get from the point (1,0) to the point (2006,2005), where in each step you are allowed to move one unit up (in the positive direction of y) or one unit to the right (in the positive direction of the x-axis).
a. In how many different paths can the task be performed?
b. In how many different paths can the task be performed if it is forbidden at any stage to pass through a point on the line x=y?
Difficulty level (1 very easy - 10 very hard): 7
Topics:
Combinatorics
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Combinatorial Geometry
Combinatorics
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Binomial Coefficients and Pascal's Triangle
Geometry
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Plane Geometry
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Plane Transformations
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Congruence Transformations (Isometries)
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Reflection
- Grossman Math Olympiad, 2006 Question 7
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