61. Suppose that a company uses a check-digit scheme similar to the UPC scheme, except that instead of using the UPC weights 3, 1, 3, 1, …, it uses , 1, , 1, …. If two of the ID numbers used by the company are 73215674 and 73215661, determine .
61.
Because both numbers are valid, the difference of the weighted sums is divisible by 10. That is, is divisible by 10. The difference simplifies to . So, .