Consider a string of n positions, i.e. a discrete string of length n. Units of length k are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring units have length less than k. When centered and scaled by n−1/2 the resulting numbers of spacings of length 1, 2,…, k−1 have simultaneously a limiting normal distribution as n→∞. This is proved by the classical method of moments.