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It is very generous of you to want to help others avoid the problem you had, but please do not add editions with incorrect data to the GR database.

Ah, it sounds like it's good that I asked first. Is it possible make the bad ISBN's come up in a search in any other way?
I'm working on cataloging my book collection and I just found that one of my books has a bad bar code printed on the back cover. It has the correct ISBN-10 listed above it, but the ISBN-13 listed under the code has an invalid check digit, and when I scan the bar code using my cell phone camera, I get a still different number. I'd like to find a way for the GR database can reflect this, so that others who scan the book's bar code will be able to find the right book entry instead of finding nothing like I did.
Here are the details:
The book is How to Solve It: Modern Heuristics by Michalewicz and Fogel.
The correct ISBN-10 is 3-540-22494-7. This is printed above the bar code and listed on the book's copyright page.
The incorrect ISBN-13 printed below the bar code is 978-3-540-22494-6. The correct one should have a 5 as the check digit instead of a 6.
When I scan the bar code, I get the last part of the bogus ISBN-13, but with a different prefix: 977-3-540-22494-6. The check digit of 6 is correct for the EAN-13 format of this code, but the 977 prefix is not appropriate for a book (it's the prefix for an ISSN for a periodical).
So here's what I'm thinking of doing. I can add new editions of the book for each of the bad ISBNs (9783540224946 and 97753540224946). I'd put librarian notes on them explaining the situation and pointing out what the correct ISBN of the book is. This will allow other users who scan the bar code or type in the ISBN-13 to find the right thing when they search.
Is this the best solution, or even an appropriate solution at all? Do I need to create two new editions for the two different ISBNs, or is it possible to do just one? Any other suggestions?