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EXAMPLE
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For n = 4 there are 6 sets (up to equivalence) that with their reflections and translations cover {1..4}:
{{1}, {2}, {3}, {4}};
{{1, 2}, {2, 3}, {3, 4}};
{{1, 3}, {2, 4}};
{{1, 2, 4}, {1, 3, 4}};
{{1, 2, 3}, {2, 3, 4}};
{{1, 2, 3, 4}}.
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For n = 5 there are 8 sets (up to equivalence) that with their reflections and translations cover {1..5}:
{{1}, {2}, {3}, {4}, {5}};
{{1, 2}, {2, 3}, {3, 4}, {4, 5}};
{{1, 3}, {2, 4}, {3, 5}};
{{1, 2, 4}, {1, 3, 4}, {2, 3, 5}, {2, 4, 5}};
{{1, 2, 3}, {2, 3, 4}, {3, 4, 5}};
{{1, 2, 3, 5}, {1, 3, 4, 5}};
{{1, 2, 3, 4}, {2, 3, 4, 5}};
{{1, 2, 3, 4, 5}}.
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