# Cause and Effect Mr.11 & divisibility!

Computer Science Level 5

We call a natural number $$n$$ as 'awesome' if at least one of the numbers formed by permutations of digits of $$n$$ is divisible by 11.

There are $$x$$ 'awesome' numbers and $$y$$ 'non-awesome' numbers less than 1001.

Find the ratio $$\dfrac{y}{x}$$ (as a decimal value).

Details and assumptions:

• All the numbers are represented in base 10.

• If a number already has zeroes, they can be brought to the start during permutations. e.g $$1102$$ can be permuted to $$0121$$

• You can't add zeroes at the start of the number like $$01201$$ being permuted to $$12100$$ is not allowed, because the original number is intended to be $$1201$$ and not $$01201$$.

• A number is 'non-awesome' if it is not awesome, i.e. none of its permutations is divisible by 11.

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