[shaftway]

The algorithm for the checksum (the sixth digit) is subject to one of the most common human errors, swapping adjacent digits. The UPC checksum algorithm handles this without significantly more complexity. They have you multiply all of the numbers in odd positions by 3 and then add up all numbers. The last digit is chosen to make the sum a multiple of 10.

To use your example: 51076, you'd do `5*3 + 1 + 0*3 + 7 + 6*3 = 15 + 1 + 0 + 7 + 18 = 41`. The sixth digit would be 9 ((10 - (41 mod 10)) mod 10). If you were to transpose any two adjacent numbers the checksum would be off. 3 is chosen because it's the smallest number that is co-prime with 10.