(Discrete Math) A routing transit number (RTN) is a bank code that appears in the bottom...

(Discrete Math) A routing transit number (RTN) is a bank code that appears in the bottom of checks. The most common form of an RTN has nine digits, where the last digit is a check digit. If d1d2 . . . d9 is a valid RTN, the congruence 3(d1 + d4 + d7) + 7(d2 + d5 + d8) + (d3 + d6 + d9) ≡ 0 (mod 10) must hold.

(a) Show that the check digit of the RTN can detect all single errors.

(b) Determine which transposition errors an RTN check digit can catch and which ones it cannot catch.

Expert Solution

(Discrete Math) A routing transit number (RTN) is a bank code that appears in the bottom of checks. The most common form of an RTN has nine digits, where the last digit is a check digit. If d1d2 . . . d9 is a valid RTN, the congruence 3(d1 + d4 + d7) + 7(d2 + d5 + d8) + (d3 + d6 + d9) ≡ 0 (mod 10) must hold. (a) Show that the check digit of the RTN can detect all single errors. (b) Determine which transposition errors an RTN check digit can catch and which ones it cannot catch.

Colby Messinger answered 1 year ago

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