Check digits and error detection

The first nine digits of an ISBN-10 are $9\text{-}97150\text{-}213$. What is the check digit? (If it is X, answer $10$.)

Exactly one of these is a valid ISBN-13. Which one?

Find the check digit $d_{13}$ of the ISBN-13 that begins $978\text{-}9966\text{-}25\text{-}118$.

What parity bit should be added to the message $1101011$ so that the total number of 1s is even? (Answer $0$ or $1$.)

Which swap of two neighbouring digits can go undetected in an ISBN-13?

In the proof that ISBN-10 catches every swap of neighbours, $x$ is in position $k$ and $y$ in position $k + 1$. By how much does the swap change the check sum?

One digit of a valid ISBN-10 is smudged: $3\text{-}16\text{-}14\,?\,410\text{-}X$. The smudged digit is in position $6$. Find it. (Hint: you will need a partner modulo $11$.)

A received ISBN-10 fails the check. Which statement is true?

In Lean, a code number is a list of digits and pre ++ x :: post is the list pre, then the digit x, then the list post. Which statement says that ISBN-10 detects every single-digit error?

Write luhn_valid(number), where number is a string of digits, returning True if it passes the Luhn test: from the right, keep the 1st, 3rd, 5th, … digits as they are; double the 2nd, 4th, … digits, subtracting $9$ when the double is more than $9$; the total must be a multiple of $10$. Then check the blind spot: 1099 and 1909 differ by a $09 \leftrightarrow 90$ swap.