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Puzzles

11 December

There are 6 sets of integers between 1 and 5 (inclusive) that contain an odd number of numbers whose median value is 3:
How many sets of integers between 1 and 11 (inclusive) are there that contain an odd number of numbers whose median value is 5?

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Tags: sets, medians

7 December

There are 8 sets (including the empty set) that contain numbers from 1 to 4 that don't include any consecutive integers:
\(\{\}\), \(\{1\}\), \(\{2\}\), \(\{3\}\), \(\{4\}\), \(\{1,3\}\), \(\{1,4\}\), \(\{2, 4\}\)
How many sets (including the empty set) are there that contain numbers from 1 to 14 that don't include any consecutive integers?

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Tags: number, sets

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