Practice question · Multiple choice
The ISBN check digit is chosen so a weighted sum of the digits is divisible by 11. Why does that catch a transposed pair, which a simple sum would miss?
Hints
- Add 1+2 and 2+1. Now compute 1×1 + 2×2 against 1×2 + 2×1.
- Ask what information a plain sum throws away.
Show the answer
D. Because each position carries a different weight
Why
A plain sum is order-blind, so the commonest human error, swapping adjacent digits, sails through. Position-dependent weights make order part of the total, and the same idea runs bank account validation, barcodes and every error-detecting code in use.
Practise Modular Arithmetic
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More questions on Modular Arithmetic
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