Workstation Allocation During a Core-Banking Migration
A branch has five probationary officers-Amit, Bela, Chirag, Divya and Esha-who must be assigned to five core-banking migration workstations numbered 1 to 5 in a single row for a three-hour cut-over window. No workstation may hold more than one officer. The branch head has fixed the following conditions: Amit cannot sit at workstation 1 or 5; Bela must sit immediately to the left of Chirag; Divya cannot sit next to Esha; Chirag cannot sit at workstation 5; and Esha must sit at an odd-numbered workstation. Separately, the migration batch converts each customer account prefix from decimal to binary and appends a check digit equal to the number of 1s in the binary form. A log entry for prefix 45 shows binary 101101 and check digit 4. The branch head wants to resolve the seating ambiguity by placing Divya at workstation 2. Before approving the roster, the operations manager asks three questions.
1. How many valid seating arrangements satisfy all five conditions? List them and show how you eliminated the invalid ones.
Read the worked answer
Let the positions be 1–5. The block B–C must occupy (1,2), (2,3) or (3,4), because C cannot be at 5.
Case B1 C2: remaining positions 3,4,5 for A, D, E. E must be odd, so E=3 or E=5.
- E=3: A and D occupy 4 and 5. A cannot be 5, so A=4, D=5. Valid: B C E A D.
- E=5: A and D occupy 3 and 4. D cannot be adjacent to E, so D cannot be 4; D=3, A=4. Valid: B C D A E.
Case B2 C3: remaining 1,4,5.
- E=1: A=4, D=5. Valid: E B C A D.
- E=5: A=4, D=1. Valid: D B C A E.
Case B3 C4: remaining 1,2,5.
- E=1: A=2, D=5. Valid: E A B C D.
- E=5: A=2, D=1. Valid: D A B C E.
The six valid arrangements are B C E A D; B C D A E; E B C A D; D B C A E; E A B C D; D A B C E. Branches were eliminated when D would sit next to E, or when A would be forced to an end seat.
2. Does placing Divya at workstation 2 produce a unique valid arrangement? What should the branch head do instead?
Read the worked answer
No. Check the six valid arrangements: Divya occupies positions 5, 3, 5, 1, 5 and 1 respectively. Divya is never at workstation 2, so adding that condition does not select one roster-it makes the roster unsatisfiable.
Reasoning independently: if D=2, then D is adjacent to positions 1 and 3. The B–C block must occupy (1,2), (2,3) or (3,4). The first two put B or C at 2, conflicting with D. The third leaves D=2 possible only if E is at 1 or 5 and A takes the other end; E=1 makes D adjacent to E, and E=5 forces A=1, which violates A's restriction. So no arrangement exists.
The branch head should not impose D=2. Use a documented tie-breaker compatible with the constraints-for example, keep A away from the ends and place D in a non-adjacent slot-or accept the six valid rosters and choose one on an operational criterion such as supervisor proximity.
3. Is the log entry for prefix 45 internally consistent? What does your answer imply about using the check digit as a validation control?
Read the worked answer
45 = 32 + 8 + 4 + 1, so 45 in binary is 101101. The string has four 1s (the 32, 8, 4 and 1 places), so a check digit equal to the number of 1s is 4. The log entry is internally consistent.
Implication: the rule is a weak validation control, not a robust error-detecting code. For a short prefix the count can take only a few values, and many different prefixes share the same count. A single-bit error changes the count and may be caught, but two compensating errors can cancel out. For a migration batch, the branch should use a proper checksum such as mod-97 or a CRC, and log the algorithm and version so that the validation can be audited.