Working Out the Post Assignments Under Conflicting Rules
You are the relief sergeant for a six-hour court session. Four officers - Acosta, Bell, Crane, and Duval - must each be posted at exactly one of Posts 1, 2, 3, and 4, with one officer per post. The post orders and the day's special instructions impose these rules:
- Acosta may not be assigned to Post 1 or Post 4.
- Bell's post number must be exactly one higher than Crane's.
- Duval must be assigned to an odd-numbered post.
- Crane may not be assigned to Post 1.
The lieutenant adds one rule: when an officer relieves another mid-session, the relieving officer may not take a post whose number is adjacent to his or her own assigned post.
1. Determine the full assignment, showing how you eliminate the alternatives.
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Begin with rule 2: Bell is exactly one post above Crane, and rule 4 bars Crane from Post 1. That leaves two candidate pairs: Bell 3 with Crane 2, or Bell 4 with Crane 3.
- If Bell is 3 and Crane is 2, Posts 1 and 4 remain for Acosta and Duval. Rule 1 bars Acosta from both, so this branch is impossible.
- Therefore Bell is 4 and Crane is 3. Posts 1 and 2 remain. Rule 1 forces Acosta to Post 2, leaving Duval at Post 1, which satisfies rule 3.
Assignment: Post 1 Duval, Post 2 Acosta, Post 3 Crane, Post 4 Bell. The solution is forced and unique.
2. A colleague argues that rule 3 is unnecessary. Is the claim correct? Should the rule be dropped?
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The claim is technically correct. Rule 1 already eliminates the Bell 3 / Crane 2 branch, because that branch strands Acosta with only Posts 1 and 4 available. So rules 1, 2, and 4 alone place Duval at Post 1.
Rule 3 is therefore redundant - but it is consistent with the solution and it functions as a check. A scheduler who arrives at Duval on Post 2 has made an error somewhere, and rule 3 catches it immediately.
Recommendation: keep it. Redundancy in a post order costs nothing; an undetected assignment error on a courtroom post does not.
3. Mid-session, Duval must leave Post 1 for 90 minutes to escort a prisoner. Under the adjacency rule, which officers may relieve Post 1, and what practical problem does your answer create?
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Acosta holds Post 2, which is adjacent to Post 1, so Acosta is barred from relieving. Bell (Post 4) and Crane (Post 3) are both non-adjacent and therefore eligible.
Practical problem: relief is a move, not a copy. If Crane leaves Post 3 to cover Post 1, Post 3 sits uncovered for 90 minutes; the same is true of Post 4 if Bell goes. The correct answer is to send Bell or Crane only after the sergeant backfills the vacated post, or to request a fifth officer for the escort window. Filling one hole by opening another is not coverage.