ISBN Investigation

  1. Find the check digit D for the ISBN number 0-394-84494-D.
  2. The incorrect ISBN number 0-669-03925-4 is the result of transposing two adjacent digits not involving the first or last digit. Find the correct ISBN number. Explain your reasoning.
  3. Suppose, instead, that the check digit a10 is chosen so that the sum a1 + 2a2 + ... + 10a10 is evenly divisible by 11. How does the "check digit" determined using this calculation compare to the one found using the given method? Explain your answer.
  4. Explain why the ISBN method detects all single-digit errors.
  5. Does it also detect all transposition of adjacent-digit errors? Explain your reasoning in each case.

ISBN Investigation