Misspellings may be due to either typing errors ( e . g . the transposition error " teh " for " the " ), or lack of knowledge of the correct spelling.
12.
These could include a transposition error, a punch card ballot that is deliberately marked with a second vote to make it invalid, and a purposeful decision not to recount a set of ballots.
13.
This would catch any single-digit error, as such an error would always change the sum, but does not catch any transposition errors ( switching two digits ) as re-ordering does not change the sum.
14.
However, amateur musicians are much more likely to make note mistakes, transposition errors or play with incorrect intonation or rhythms; the conductor must point these issues out to the performers and give them advice on how to correct them.
15.
More complicated algorithms include the Luhn algorithm ( 1954 ), which captures 98 % of single digit transposition errors ( it does not detect 90 ?! 09 ) and the still more sophisticated Verhoeff algorithm ( 1969 ), which catches all single digit substitution and transposition errors, and many ( but not all ) more complex errors.
16.
More complicated algorithms include the Luhn algorithm ( 1954 ), which captures 98 % of single digit transposition errors ( it does not detect 90 ?! 09 ) and the still more sophisticated Verhoeff algorithm ( 1969 ), which catches all single digit substitution and transposition errors, and many ( but not all ) more complex errors.
17.
This system thus detects all single digit substitution and transposition errors ( including jump transpositions ), but at the cost of the check digit possibly being 10, represented by " X " . ( An alternative is simply to avoid using the serial numbers which result in an " X " check digit . ) instead uses the GS1 algorithm used in EAN numbers.
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