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Question Number 133419 by liberty last updated on 22/Feb/21

$$\mathrm{Prove}\mathrm{the}\mathrm{set}\{1,2,3,...,1989\}$$$$\mathrm{can}\mathrm{be}\mathrm{expressed}\mathrm{as}\mathrm{the}\mathrm{disjoint}$$$$\mathrm{union}\mathrm{of}{\mathrm{A}}_1,{\mathrm{A}}_2,...,{\mathrm{A}}_{117}\mathrm{such}\mathrm{that}$$$$\left(\mathrm{i}\right)\mathrm{each}{\mathrm{A}}_{\mathrm{i}}\mathrm{contains}\mathrm{the}\mathrm{same}\mathrm{number}\mathrm{of}\mathrm{elements},\mathrm{and}$$$$\left(\mathrm{ii}\right)\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{elements}\mathrm{of}\mathrm{each}{\mathrm{A}}_{\mathrm{i}}\mathrm{is}$$$$\mathrm{the}\mathrm{same}\mathrm{for}\mathrm{i}=1,2,3,...,\mathrm{m}$$

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