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Source. Question 1.6 and the beginning of Section 3, printed pp. 1740--1741, physical PDF pp. 2--3.

Statement

Harrington asks (p. 1740): "Given an odd integer $n \geq 3$, does there exist a covering system that uses $n$ as a modulus at most twice, such that all other moduli are odd, distinct, and greater than 1?"

Case established in the source

Section 3 constructs such a covering for $n=3$. It uses the modulus $3$ exactly twice; all other moduli are distinct odd integers at least $5$. The paper states that the answer for $n\geq5$ remains open (p. 1740).

Proof pointer. The explicit nested congruence construction occupies printed pp. 1741--1743. Its full coverage and distinctness checks were not reconstructed or independently verified here.

Bears on. This is a repeated-modulus relaxation of Problem 7. The $n=3$ construction is not an odd covering with all moduli distinct.