IMO 1979 LL USS70

There are 1979 equilateral triangles: T1, T2, . . . , T1979. A side of

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IMO 1979 LL USS70

Origin: USS

Problem

There are 1979 equilateral triangles: T1, T2, . . . , T1979. A side of triangle Tk is equal to 1/k, k = 1, 2, . . . , 1979. At what values of a number a can one place all these triangles into the equilateral triangle with side length a so that they don’t intersect (points of contact are allowed)?