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Number of paths

Source: Greek MO 2012 - P4

May 12, 2013
geometrytrapezoidcombinatorics proposedcombinatorics

Problem Statement

The following isosceles trapezoid consists of equal equilateral triangles with side length 11. The side A1EA_1E has length 33 while the larger base A1AnA_1A_n has length n−1n-1. Starting from the point A1A_1 we move along the segments which are oriented to the right and up(obliquely right or left). Calculate (in terms of nn or not) the number of all possible paths we can follow, in order to arrive at points B,Γ,Δ,EB,\Gamma,\Delta, E, if nn is an integer greater than 33.
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