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The spectrum of superstrings on AdS₃ × S³ × ₄ with pure NS-NS flux is analysed for the background where the radius of the AdS space takes the minimal value (k = 1). Both for ₄ = S³ × S¹ and ₄ = ⁴ we show that there is a special set of physical states, coming from the bottom of the spectrally flowed continuous representations, which agree in precise detail with the single particle spectrum of a free symmetric product orbifold. For the case of AdS₃ × S³ × ⁴ this relies on making sense of the world-sheet theory at k = 1, for which we make a concrete proposal. We also comment on the implications of this striking result.