UPC Investigation Continued

  1. Show that 0-58200-48826-5 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.
  2. Do you think the UPC method will detect all such single-digit errors? Either give several examples of numbers with an error that will not be detected or explain why you think all such single-digit errors will be detected.
  3. 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 single-digit errors? Either give several examples of numbers with an error that will not be detected or explain why you think all such single-digit errors will be detected.
  4. 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 single-digit errors? Either give several examples of numbers with an error that will not be detected or explain why you think all such single-digit errors will be detected.
  5. 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