Eight classmates and I tried the procedure for 10 books each. My friends couldn’t find anything that the results had in common but I noticed that all my results were 3 digit numbers where if you add the hundreds digit and the units digit you get the tens digit e.g. 242. We checked my theory with my friends’ results and found that it mostly worked. However, a few times we saw the number 209, which didn’t fit with my theory. Also, one of my friends had a total of 77 which is not a three digit number, but would still fit the theory as you could consider the hundreds digit to be 0. We talked as a group and remembered something about a divisibility rule for 11 and when we checked we realised that all our numbers were divisible by 11. There were about 5 other answers which didn’t fit my theory, but when we checked these, the calculations had been done incorrectly!
We could then work out the missing digit from the ISBN code in the problem. We used trial and error to find the missing digit, 8. This made the total sum 264. It was the only possible solution.
We didn’t really know why ISBN numbers needed to be coded, but we thought maybe it was something to do with security, regulation and copywright issues?
We REALLY enjoyed working on this problem.