Strange numbers

Some, but not all, of the first \(11\) positive integers is called strange. Here are some details:

  • If a number \(n\) is strange (\(1\leq n\leq 11\)), then \(12-n\) is also strange.

  • If a number is strange, then the positive divisors of the numbers are strange numbers.

  • At least one of the strange numbers is even.

  • If there are \(k\) number of strange numbers, then \(11-k\) is not a strange number.

  • Not all integers between \(1\) and \(11\) are strange.

What is the sum of the strange numbers?


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