# 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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