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1979 equilateral triangles

Source: ILL 1979 - Problem 70.

June 5, 2011
geometry unsolvedgeometry

Problem Statement

There are 19791979 equilateral triangles: T1,T2,...,T1979T_1,T_2, . . . ,T_{1979}. A side of triangle TkT_k is equal to 1k\frac{1}{k}, k=1,2,...,1979k = 1,2, . . . ,1979. At what values of a number aa can one place all these triangles into the equilateral triangle with side length aa so that they don’t intersect (points of contact are allowed)?
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