SAS programming "golf": Find the fake books

[RichardAD]

v = substr('1234567890X',11-mod(vsum,11)) =: substr(isbn,10,1) ;

has a bug. The 0X is transposed. It should be

v = substr('123456789X0',11-mod(vsum,11)) =: substr(isbn,10,1) ;

Based on the other solutions withs+r*i[r]there seems to be a mathematical tautology.

The righthand side being the algorithm steps stated initially.

[FreelanceReinh]

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@RichardAD wrote:

Based on the other solutions withs+r*i[r]there seems to be a mathematical tautology.

The righthand side being the algorithm steps stated initially.

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Unless you actually mean (11 − (S...)) mod 11 on the right-hand side, it should rather be (11 − (S...) mod 11) mod 11, where the outer (...) mod 11 corresponds to the last bullet point in Chris' description of the algorithm. For example, if all d_i are zero, the left-hand side is zero and so must be the right-hand side. The validity of the equation can be proved easily by applying the calculation rules of what mathematicians call the quotient ring Z₁₁=Z/11Z.

[ChrisHemedinger]

The response here have been of very high quality. Proc Studley thanks you all for your service!