# Putnam 1985, A1

Discrete Mathematics Level 4

Determine, with proof, the number of ordered triples $$(A_{1}, A_{2}, A_{3})$$ of sets which have the property that

(i) $$A_{1} ∪ A_{2} ∪ A_{3} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$, and
(ii) $$A_{1} ∩ A_{2} ∩ A_{3} = ∅$$,

where $$∅$$ denotes the empty set.

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