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For n \equiv 0, 1, 2(mod 9)$n \equiv 0, 1, 2 \pmod 9$, write {1,...,3n}$\{\,1,\dots,3n\,\}$ as the disjoint union of arithmetic progressions A1, A2,...,An$A_1, A_2,\dots,A_n$ of length 3, where Ai$A_i$ has step i$i$.
For n \equiv 0, 1, 2(mod 9), write {1,...,3n} as the disjoint union of arithmetic progressions A1, A2,...,An of length 3, where Ai has step i.
For $n \equiv 0, 1, 2 \pmod 9$, write $\{\,1,\dots,3n\,\}$ as the disjoint union of arithmetic progressions $A_1, A_2,\dots,A_n$ of length 3, where $A_i$ has step $i$.
