Scheduling Five Verification Teams in a Festival Week
Five verification teams must be sent out, one per working day from Monday to Friday, in the week before a festival bandobast. The teams are A (boundary and route check), B (CCTV and bank records), C (witness examination), D (medical report collection) and E (records verification at the RTA office). The sub-inspector's notebook records these fixed conditions: D must go on Wednesday because the doctor is available only that day; C must go the day immediately after A; B cannot go on Monday or Friday; E must go later in the week than A; and B's visit needs the bank manager, who sits only on Tuesday and Thursday. The notebook also carries a standing preference that the medical report team should go last, because it closes the evidence. A sixth team F (fingerprint expert) may be added in the same week, but the expert can come only on Wednesday.
1. Fix the one schedule that satisfies every condition, and prove that the alternative placement of team A fails.
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Fixed point: D = Wednesday.
C must be the day after A. From Monday–Friday with Wednesday taken by D, the only consecutive pairs available for A and C are (Monday, Tuesday) and (Thursday, Friday).
Test pair (Thursday, Friday): A = Thursday, C = Friday. B and E then take Monday and Tuesday. B cannot be Monday, so B = Tuesday and E = Monday. But the rule that E must come later than A is now broken (Monday is earlier than Thursday). This placement is rejected.
Test pair (Monday, Tuesday): A = Monday, C = Tuesday. B and E take Thursday and Friday. B cannot be Friday, so B = Thursday and E = Friday. Cross-checks: B on Thursday matches the bank manager's Thursday sitting; E is later than A; E is also last, satisfying the note's preference.
Final schedule:
| Day | Team |
|---|---|
| Monday | A |
| Tuesday | C |
| Wednesday | D |
| Thursday | B |
| Friday | E |
Note that the bank manager clue is satisfied but is not what makes the answer unique - the E-later-than-A rule does that.
2. The medical officer now says he can come only on Monday. Can the week be rebuilt? Set out the options and recommend one.
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Rebuild attempt with E = Monday Wednesday stays with D. A, C and B must occupy Tuesday, Thursday and Friday. The only consecutive pair left for A and C is (Thursday, Friday), so A = Thursday, C = Friday, and B = Tuesday - which the bank manager's Tuesday sitting permits.
Check the four rules
- D on Wednesday ✓
- C the day after A ✓
- B not Monday or Friday ✓
- E later than A ✗ (Monday is earlier than Thursday)
Conclusion: no arrangement satisfies all four conditions once E is forced to Monday. The conflict is not a puzzle trick; it is a genuine clash between an external availability (the medical officer) and an internal sequencing rule.
Options
- Treat the E-after-A rule as the notebook's preference rather than a rule, and run E = Monday, B = Tuesday, D = Wednesday, A = Thursday, C = Friday. The closing report then arrives first, so the inspector must re-diary the final review.
- Keep the rule and get a substitute medical officer, or move D out of the week.
Recommendation: option 1 with a written note that the medical report will be reviewed on Friday, because the doctor's availability is immovable while the sequencing rule is administrative. Silently breaking a rule without recording it is the wrong answer.
3. Can team F be absorbed on Wednesday with D shifted to Thursday? Show your reasoning.
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New fixed points: F = Wednesday, D = Thursday. Free days for A, B, C, E: Monday, Tuesday, Friday.
Consecutive pair for A and C must come from {Monday, Tuesday, Friday}. The only consecutive option is (Monday, Tuesday), so A = Monday and C = Tuesday.
What is left is Friday alone for two teams, B and E. One day cannot hold two teams under the stated condition of one team per day, and B cannot be placed on Friday in any case.
Answer: F cannot be absorbed under the present rules. The plan fails not because of the fingerprint expert but because moving D off Wednesday destroys the only working slot for the A–C pair. Remedies: declare Saturday a working day for B or E, or send B and E together on Friday only if their visits are in the same part of town and two officers can be spared from bandobast duty. The inspector should record the reason for the change, since the original schedule is now disturbed.