
Show that 058200488265 is a valid UPC Code number. Suppose you entered a "7" instead of the "6" when recording this UPC number. Explain why the UPC method will detect this error.

Do you think the UPC method will detect all such singledigit errors? Either give several examples of numbers with an error that will not be detected or explain why you think all such singledigit errors will be detected.

Suppose you used the weights {9,1,9,1,9,1, 9,1} instead of {3,1,3,1,3,1, 3, 1} in the UPC method; that is, replace multiples of 3 with multiples of 9 to define the "check digit." Do you think this method will detect singledigit errors? Either give several examples of numbers with an error that will not be detected or explain why you think all such singledigit errors will be detected.

Suppose you used the weights {2,1,2,1,2,1, 2, 1} instead of {3,1,3,1,3,1, 3, 1} in the UPC method. Do you think this method will detect singledigit errors? Either give several examples of numbers with an error that will not be detected or explain why you think all such singledigit errors will be detected.

In entering UPC code numbers, will the error of transposing 3 and 8 be detected? [i.e..….83… is recorded as ….38….] How about 3 and 7? Make a conjecture about the values of a and b for which the error of transposing ab and ba is detected by the UPC method. Explain your reasoning in making your conjecture.
UPC Investigation Continued