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Last active March 1, 2022 09:02
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The Problem

In the set {1, 2, 3, 4, 5, 6, 7, 8, 9}, how many subsets have at least 5 consecutive elements

All subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9}

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{}
{1}
{2}
{3}
{4}
{5}
{6}
{7}
{8}
{9}
{1, 2}
{1, 3}
{1, 4}
{1, 5}
{1, 6}
{1, 7}
{8, 1}
{1, 9}
{2, 3}
{2, 4}
{2, 5}
{2, 6}
{2, 7}
{8, 2}
{9, 2}
{3, 4}
{3, 5}
{3, 6}
{3, 7}
{8, 3}
{9, 3}
{4, 5}
{4, 6}
{4, 7}
{8, 4}
{9, 4}
{5, 6}
{5, 7}
{8, 5}
{9, 5}
{6, 7}
{8, 6}
{9, 6}
{8, 7}
{9, 7}
{8, 9}
{1, 2, 3}
{1, 2, 4}
{1, 2, 5}
{1, 2, 6}
{1, 2, 7}
{8, 1, 2}
{1, 2, 9}
{1, 3, 4}
{1, 3, 5}
{1, 3, 6}
{1, 3, 7}
{8, 1, 3}
{1, 3, 9}
{1, 4, 5}
{1, 4, 6}
{1, 4, 7}
{8, 1, 4}
{1, 4, 9}
{1, 5, 6}
{1, 5, 7}
{8, 1, 5}
{1, 5, 9}
{1, 6, 7}
{8, 1, 6}
{1, 6, 9}
{8, 1, 7}
{1, 9, 7}
{8, 1, 9}
{2, 3, 4}
{2, 3, 5}
{2, 3, 6}
{2, 3, 7}
{8, 2, 3}
{9, 2, 3}
{2, 4, 5}
{2, 4, 6}
{2, 4, 7}
{8, 2, 4}
{9, 2, 4}
{2, 5, 6}
{2, 5, 7}
{8, 2, 5}
{9, 2, 5}
{2, 6, 7}
{8, 2, 6}
{9, 2, 6}
{8, 2, 7}
{9, 2, 7}
{8, 9, 2}
{3, 4, 5}
{3, 4, 6}
{3, 4, 7}
{8, 3, 4}
{9, 3, 4}
{3, 5, 6}
{3, 5, 7}
{8, 3, 5}
{9, 3, 5}
{3, 6, 7}
{8, 3, 6}
{9, 3, 6}
{8, 3, 7}
{9, 3, 7}
{8, 9, 3}
{4, 5, 6}
{4, 5, 7}
{8, 4, 5}
{9, 4, 5}
{4, 6, 7}
{8, 4, 6}
{9, 4, 6}
{8, 4, 7}
{9, 4, 7}
{8, 9, 4}
{5, 6, 7}
{8, 5, 6}
{9, 5, 6}
{8, 5, 7}
{9, 5, 7}
{8, 9, 5}
{8, 6, 7}
{9, 6, 7}
{8, 9, 6}
{8, 9, 7}
{1, 2, 3, 4}
{1, 2, 3, 5}
{1, 2, 3, 6}
{1, 2, 3, 7}
{8, 1, 2, 3}
{1, 2, 3, 9}
{1, 2, 4, 5}
{1, 2, 4, 6}
{1, 2, 4, 7}
{8, 1, 2, 4}
{1, 2, 4, 9}
{1, 2, 5, 6}
{1, 2, 5, 7}
{8, 1, 2, 5}
{1, 2, 5, 9}
{1, 2, 6, 7}
{8, 1, 2, 6}
{1, 2, 6, 9}
{8, 1, 2, 7}
{1, 2, 9, 7}
{8, 1, 2, 9}
{1, 3, 4, 5}
{1, 3, 4, 6}
{1, 3, 4, 7}
{8, 1, 3, 4}
{1, 3, 4, 9}
{1, 3, 5, 6}
{1, 3, 5, 7}
{8, 1, 3, 5}
{1, 3, 5, 9}
{1, 3, 6, 7}
{8, 1, 3, 6}
{1, 3, 6, 9}
{8, 1, 3, 7}
{1, 3, 9, 7}
{8, 1, 3, 9}
{1, 4, 5, 6}
{1, 4, 5, 7}
{8, 1, 4, 5}
{1, 4, 5, 9}
{1, 4, 6, 7}
{8, 1, 4, 6}
{1, 4, 6, 9}
{8, 1, 4, 7}
{1, 4, 9, 7}
{8, 1, 4, 9}
{1, 5, 6, 7}
{8, 1, 5, 6}
{1, 5, 6, 9}
{8, 1, 5, 7}
{1, 5, 9, 7}
{8, 1, 5, 9}
{8, 1, 6, 7}
{1, 9, 6, 7}
{8, 1, 6, 9}
{8, 1, 9, 7}
{2, 3, 4, 5}
{2, 3, 4, 6}
{2, 3, 4, 7}
{8, 2, 3, 4}
{9, 2, 3, 4}
{2, 3, 5, 6}
{2, 3, 5, 7}
{8, 2, 3, 5}
{9, 2, 3, 5}
{2, 3, 6, 7}
{8, 2, 3, 6}
{9, 2, 3, 6}
{8, 2, 3, 7}
{9, 2, 3, 7}
{8, 9, 2, 3}
{2, 4, 5, 6}
{2, 4, 5, 7}
{8, 2, 4, 5}
{9, 2, 4, 5}
{2, 4, 6, 7}
{8, 2, 4, 6}
{9, 2, 4, 6}
{8, 2, 4, 7}
{9, 2, 4, 7}
{8, 9, 2, 4}
{2, 5, 6, 7}
{8, 2, 5, 6}
{9, 2, 5, 6}
{8, 2, 5, 7}
{9, 2, 5, 7}
{8, 9, 2, 5}
{8, 2, 6, 7}
{9, 2, 6, 7}
{8, 9, 2, 6}
{8, 9, 2, 7}
{3, 4, 5, 6}
{3, 4, 5, 7}
{8, 3, 4, 5}
{9, 3, 4, 5}
{3, 4, 6, 7}
{8, 3, 4, 6}
{9, 3, 4, 6}
{8, 3, 4, 7}
{9, 3, 4, 7}
{8, 9, 3, 4}
{3, 5, 6, 7}
{8, 3, 5, 6}
{9, 3, 5, 6}
{8, 3, 5, 7}
{9, 3, 5, 7}
{8, 9, 3, 5}
{8, 3, 6, 7}
{9, 3, 6, 7}
{8, 9, 3, 6}
{8, 9, 3, 7}
{4, 5, 6, 7}
{8, 4, 5, 6}
{9, 4, 5, 6}
{8, 4, 5, 7}
{9, 4, 5, 7}
{8, 9, 4, 5}
{8, 4, 6, 7}
{9, 4, 6, 7}
{8, 9, 4, 6}
{8, 9, 4, 7}
{8, 5, 6, 7}
{9, 5, 6, 7}
{8, 9, 5, 6}
{8, 9, 5, 7}
{8, 9, 6, 7}
{1, 2, 3, 4, 5}
{1, 2, 3, 4, 6}
{1, 2, 3, 4, 7}
{1, 2, 3, 4, 8}
{1, 2, 3, 4, 9}
{1, 2, 3, 5, 6}
{1, 2, 3, 5, 7}
{1, 2, 3, 5, 8}
{1, 2, 3, 5, 9}
{1, 2, 3, 6, 7}
{1, 2, 3, 6, 8}
{1, 2, 3, 6, 9}
{1, 2, 3, 7, 8}
{1, 2, 3, 7, 9}
{1, 2, 3, 8, 9}
{1, 2, 4, 5, 6}
{1, 2, 4, 5, 7}
{1, 2, 4, 5, 8}
{1, 2, 4, 5, 9}
{1, 2, 4, 6, 7}
{1, 2, 4, 6, 8}
{1, 2, 4, 6, 9}
{1, 2, 4, 7, 8}
{1, 2, 4, 7, 9}
{1, 2, 4, 8, 9}
{1, 2, 5, 6, 7}
{1, 2, 5, 6, 8}
{1, 2, 5, 6, 9}
{1, 2, 5, 7, 8}
{1, 2, 5, 7, 9}
{1, 2, 5, 8, 9}
{1, 2, 6, 7, 8}
{1, 2, 6, 7, 9}
{1, 2, 6, 8, 9}
{1, 2, 7, 8, 9}
{1, 3, 4, 5, 6}
{1, 3, 4, 5, 7}
{1, 3, 4, 5, 8}
{1, 3, 4, 5, 9}
{1, 3, 4, 6, 7}
{1, 3, 4, 6, 8}
{1, 3, 4, 6, 9}
{1, 3, 4, 7, 8}
{1, 3, 4, 7, 9}
{1, 3, 4, 8, 9}
{1, 3, 5, 6, 7}
{1, 3, 5, 6, 8}
{1, 3, 5, 6, 9}
{1, 3, 5, 7, 8}
{1, 3, 5, 7, 9}
{1, 3, 5, 8, 9}
{1, 3, 6, 7, 8}
{1, 3, 6, 7, 9}
{1, 3, 6, 8, 9}
{1, 3, 7, 8, 9}
{1, 4, 5, 6, 7}
{1, 4, 5, 6, 8}
{1, 4, 5, 6, 9}
{1, 4, 5, 7, 8}
{1, 4, 5, 7, 9}
{1, 4, 5, 8, 9}
{1, 4, 6, 7, 8}
{1, 4, 6, 7, 9}
{1, 4, 6, 8, 9}
{1, 4, 7, 8, 9}
{1, 5, 6, 7, 8}
{1, 5, 6, 7, 9}
{1, 5, 6, 8, 9}
{1, 5, 7, 8, 9}
{1, 6, 7, 8, 9}
{2, 3, 4, 5, 6}
{2, 3, 4, 5, 7}
{2, 3, 4, 5, 8}
{2, 3, 4, 5, 9}
{2, 3, 4, 6, 7}
{2, 3, 4, 6, 8}
{2, 3, 4, 6, 9}
{2, 3, 4, 7, 8}
{2, 3, 4, 7, 9}
{2, 3, 4, 8, 9}
{2, 3, 5, 6, 7}
{2, 3, 5, 6, 8}
{2, 3, 5, 6, 9}
{2, 3, 5, 7, 8}
{2, 3, 5, 7, 9}
{2, 3, 5, 8, 9}
{2, 3, 6, 7, 8}
{2, 3, 6, 7, 9}
{2, 3, 6, 8, 9}
{2, 3, 7, 8, 9}
{2, 4, 5, 6, 7}
{2, 4, 5, 6, 8}
{2, 4, 5, 6, 9}
{2, 4, 5, 7, 8}
{2, 4, 5, 7, 9}
{2, 4, 5, 8, 9}
{2, 4, 6, 7, 8}
{2, 4, 6, 7, 9}
{2, 4, 6, 8, 9}
{2, 4, 7, 8, 9}
{2, 5, 6, 7, 8}
{2, 5, 6, 7, 9}
{2, 5, 6, 8, 9}
{2, 5, 7, 8, 9}
{2, 6, 7, 8, 9}
{3, 4, 5, 6, 7}
{3, 4, 5, 6, 8}
{3, 4, 5, 6, 9}
{3, 4, 5, 7, 8}
{3, 4, 5, 7, 9}
{3, 4, 5, 8, 9}
{3, 4, 6, 7, 8}
{3, 4, 6, 7, 9}
{3, 4, 6, 8, 9}
{3, 4, 7, 8, 9}
{3, 5, 6, 7, 8}
{3, 5, 6, 7, 9}
{3, 5, 6, 8, 9}
{3, 5, 7, 8, 9}
{3, 6, 7, 8, 9}
{4, 5, 6, 7, 8}
{4, 5, 6, 7, 9}
{4, 5, 6, 8, 9}
{4, 5, 7, 8, 9}
{4, 6, 7, 8, 9}
{5, 6, 7, 8, 9}
{1, 2, 3, 4, 5, 6}
{1, 2, 3, 4, 5, 7}
{1, 2, 3, 4, 5, 8}
{1, 2, 3, 4, 5, 9}
{1, 2, 3, 4, 6, 7}
{1, 2, 3, 4, 6, 8}
{1, 2, 3, 4, 6, 9}
{1, 2, 3, 4, 7, 8}
{1, 2, 3, 4, 7, 9}
{1, 2, 3, 4, 8, 9}
{1, 2, 3, 5, 6, 7}
{1, 2, 3, 5, 6, 8}
{1, 2, 3, 5, 6, 9}
{1, 2, 3, 5, 7, 8}
{1, 2, 3, 5, 7, 9}
{1, 2, 3, 5, 8, 9}
{1, 2, 3, 6, 7, 8}
{1, 2, 3, 6, 7, 9}
{1, 2, 3, 6, 8, 9}
{1, 2, 3, 7, 8, 9}
{1, 2, 4, 5, 6, 7}
{1, 2, 4, 5, 6, 8}
{1, 2, 4, 5, 6, 9}
{1, 2, 4, 5, 7, 8}
{1, 2, 4, 5, 7, 9}
{1, 2, 4, 5, 8, 9}
{1, 2, 4, 6, 7, 8}
{1, 2, 4, 6, 7, 9}
{1, 2, 4, 6, 8, 9}
{1, 2, 4, 7, 8, 9}
{1, 2, 5, 6, 7, 8}
{1, 2, 5, 6, 7, 9}
{1, 2, 5, 6, 8, 9}
{1, 2, 5, 7, 8, 9}
{1, 2, 6, 7, 8, 9}
{1, 3, 4, 5, 6, 7}
{1, 3, 4, 5, 6, 8}
{1, 3, 4, 5, 6, 9}
{1, 3, 4, 5, 7, 8}
{1, 3, 4, 5, 7, 9}
{1, 3, 4, 5, 8, 9}
{1, 3, 4, 6, 7, 8}
{1, 3, 4, 6, 7, 9}
{1, 3, 4, 6, 8, 9}
{1, 3, 4, 7, 8, 9}
{1, 3, 5, 6, 7, 8}
{1, 3, 5, 6, 7, 9}
{1, 3, 5, 6, 8, 9}
{1, 3, 5, 7, 8, 9}
{1, 3, 6, 7, 8, 9}
{1, 4, 5, 6, 7, 8}
{1, 4, 5, 6, 7, 9}
{1, 4, 5, 6, 8, 9}
{1, 4, 5, 7, 8, 9}
{1, 4, 6, 7, 8, 9}
{1, 5, 6, 7, 8, 9}
{2, 3, 4, 5, 6, 7}
{2, 3, 4, 5, 6, 8}
{2, 3, 4, 5, 6, 9}
{2, 3, 4, 5, 7, 8}
{2, 3, 4, 5, 7, 9}
{2, 3, 4, 5, 8, 9}
{2, 3, 4, 6, 7, 8}
{2, 3, 4, 6, 7, 9}
{2, 3, 4, 6, 8, 9}
{2, 3, 4, 7, 8, 9}
{2, 3, 5, 6, 7, 8}
{2, 3, 5, 6, 7, 9}
{2, 3, 5, 6, 8, 9}
{2, 3, 5, 7, 8, 9}
{2, 3, 6, 7, 8, 9}
{2, 4, 5, 6, 7, 8}
{2, 4, 5, 6, 7, 9}
{2, 4, 5, 6, 8, 9}
{2, 4, 5, 7, 8, 9}
{2, 4, 6, 7, 8, 9}
{2, 5, 6, 7, 8, 9}
{3, 4, 5, 6, 7, 8}
{3, 4, 5, 6, 7, 9}
{3, 4, 5, 6, 8, 9}
{3, 4, 5, 7, 8, 9}
{3, 4, 6, 7, 8, 9}
{3, 5, 6, 7, 8, 9}
{4, 5, 6, 7, 8, 9}
{1, 2, 3, 4, 5, 6, 7}
{1, 2, 3, 4, 5, 6, 8}
{1, 2, 3, 4, 5, 6, 9}
{1, 2, 3, 4, 5, 7, 8}
{1, 2, 3, 4, 5, 7, 9}
{1, 2, 3, 4, 5, 8, 9}
{1, 2, 3, 4, 6, 7, 8}
{1, 2, 3, 4, 6, 7, 9}
{1, 2, 3, 4, 6, 8, 9}
{1, 2, 3, 4, 7, 8, 9}
{1, 2, 3, 5, 6, 7, 8}
{1, 2, 3, 5, 6, 7, 9}
{1, 2, 3, 5, 6, 8, 9}
{1, 2, 3, 5, 7, 8, 9}
{1, 2, 3, 6, 7, 8, 9}
{1, 2, 4, 5, 6, 7, 8}
{1, 2, 4, 5, 6, 7, 9}
{1, 2, 4, 5, 6, 8, 9}
{1, 2, 4, 5, 7, 8, 9}
{1, 2, 4, 6, 7, 8, 9}
{1, 2, 5, 6, 7, 8, 9}
{1, 3, 4, 5, 6, 7, 8}
{1, 3, 4, 5, 6, 7, 9}
{1, 3, 4, 5, 6, 8, 9}
{1, 3, 4, 5, 7, 8, 9}
{1, 3, 4, 6, 7, 8, 9}
{1, 3, 5, 6, 7, 8, 9}
{1, 4, 5, 6, 7, 8, 9}
{2, 3, 4, 5, 6, 7, 8}
{2, 3, 4, 5, 6, 7, 9}
{2, 3, 4, 5, 6, 8, 9}
{2, 3, 4, 5, 7, 8, 9}
{2, 3, 4, 6, 7, 8, 9}
{2, 3, 5, 6, 7, 8, 9}
{2, 4, 5, 6, 7, 8, 9}
{3, 4, 5, 6, 7, 8, 9}
{1, 2, 3, 4, 5, 6, 7, 8}
{1, 2, 3, 4, 5, 6, 7, 9}
{1, 2, 3, 4, 5, 6, 8, 9}
{1, 2, 3, 4, 5, 7, 8, 9}
{1, 2, 3, 4, 6, 7, 8, 9}
{1, 2, 3, 5, 6, 7, 8, 9}
{1, 2, 4, 5, 6, 7, 8, 9}
{1, 3, 4, 5, 6, 7, 8, 9}
{2, 3, 4, 5, 6, 7, 8, 9}
{1, 2, 3, 4, 5, 6, 7, 8, 9}

All subsets with at least five consecutive elements

Click here to open or close
{1, 2, 3, 4, 5}
{2, 3, 4, 5, 6}
{3, 4, 5, 6, 7}
{4, 5, 6, 7, 8}
{5, 6, 7, 8, 9}
{1, 2, 3, 4, 5, 6}
{2, 3, 4, 5, 6, 7}
{3, 4, 5, 6, 7, 8}
{4, 5, 6, 7, 8, 9}
{1, 2, 3, 4, 5, 6, 7}
{2, 3, 4, 5, 6, 7, 8}
{3, 4, 5, 6, 7, 8, 9}
{1, 2, 3, 4, 5, 6, 7, 8}
{2, 3, 4, 5, 6, 7, 8, 9}
{1, 2, 3, 4, 5, 6, 7, 8, 9}

All subsets with only five consecutive elements

Click here to open or close
{1, 2, 3, 4, 5}
{2, 3, 4, 5, 6}
{3, 4, 5, 6, 7}
{4, 5, 6, 7, 8}
{5, 6, 7, 8, 9}
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