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How many numbers can you get by multiplying two or more distinct members of the set {1, 2, 3, 4, 5, 11, 12, 13, 14, 15} together?

 Oct 12, 2022
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2^10 ==1024 subsets (numbers)

 

∅ | {1} | {2} | {3} | {4} | {5} | {11} | {12} | {13} | {14} | {15} | {1, 2} | {1, 3} | {1, 4} | {1, 5} | {1, 11} | {1, 12} | {1, 13} | {1, 14} | {1, 15} | {2, 3} | {2, 4} | {2, 5} | {2, 11} | {2, 12} | {2, 13} | {2, 14} | {2, 15} | {3, 4} | {3, 5} | {3, 11} | {3, 12} | {3, 13} | {3, 14} | {3, 15} | {4, 5} | {4, 11} | {4, 12} | {4, 13} | {4, 14} | {4, 15} | {5, 11} | {5, 12} | {5, 13} | {5, 14} | {5, 15} | {11, 12} | {11, 13} | {11, 14} | {11, 15} | {12, 13} | {12, 14} | {12, 15} | {13, 14} | {13, 15} | {14, 15} | {1, 2, 3} | {1, 2, 4} | {1, 2, 5} | {1, 2, 11} | {1, 2, 12} | {1, 2, 13} | {1, 2, 14} | {1, 2, 15} | {1, 3, 4} | {1, 3, 5} | {1, 3, 11} | {1, 3, 12} | {1, 3, 13} | {1, 3, 14} | {1, 3, 15} | {1, 4, 5} | {1, 4, 11} | {1, 4, 12} | {1, 4, 13} | {1, 4, 14} | {1, 4, 15} | {1, 5, 11} | {1, 5, 12} | {1, 5, 13} | ... (total: 1024)

 

1024 - 1 empty subset - 10 single-digit subsets ==1013  subsets, or different products.

 Oct 12, 2022

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