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Puzzles

21 December

There are ten ways to make a list of four As and Bs that don't contain an even* number of consecutive As:
How many ways are there to make a list of eleven As and Bs that don't contain an even number of consecutive As?
* We don't count 0 consecutive As as being an even number of consecutive As.

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18 December

There are 5 different ways to make a set of numbers between 1 and 5 such that the smallest number in the set is equal to the number of numbers in the set. These 5 sets are: {1}, {2, 3}, {2, 4}, {2, 5} and {3, 4, 5}.
How many ways are there to make a set of numbers between 1 and 14 such that the smallest number in the set is equal to the number of numbers in the set?

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Tags: numbers, sets

14 December

There are five ways to make a list of four As and Bs that don't contain an odd number of consecutive As:
How many ways are there to make a list of eleven As and Bs that don't contain an odd number of consecutive As?

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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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