Five Highway Pickets: Verifying a Deployment Chart
A stretch of national highway in a battalion's area of responsibility has five pickets, CP1 to CP5, numbered in order from north to south. Five head constables - Ajay, Birendra, Chetan, Dinesh and Eshwar - must be posted, one to each picket, for the coming flood-relief window. The deployment cell works under four standing instructions: Chetan's picket must lie south of Birendra's but north of Dinesh's; Eshwar must not be posted at a picket adjacent to Dinesh's; Ajay must hold a terminal picket, that is CP1 or CP5; and Birendra cannot be at CP1, which is reserved for the head constable who operates the boat radio. A junior clerk's draft chart places Ajay at CP1, Birendra at CP2, Chetan at CP3, Dinesh at CP4 and Eshwar at CP5. The adjutant must check the chart before it goes to the Commandant, and also needs a fallback in case Birendra, whose transfer is under discussion, has to be accommodated at CP1 on special sanction.
1. Test the draft chart against the four standing instructions and determine the correct deployment.
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Testing the draft: it places Eshwar at CP5 and Dinesh at CP4, which are adjacent - a direct breach of the second instruction. The chart is therefore invalid even before other conditions are examined.
Working out the correct order. Number the pickets 1 to 5 from north to south. The first instruction fixes the relative order Birendra < Chetan < Dinesh, with Birendra ≠ 1.
Possible placements of that triple (excluding any starting at CP1) are: (2,3,4), (2,3,5), (2,4,5), (3,4,5).
- (2,3,4): free pickets 1 and 5 for Ajay and Eshwar. Ajay must be terminal. If Eshwar takes CP5 he is adjacent to Dinesh at CP4, so Eshwar must take CP1 and Ajay CP5. Works.
- (2,3,5): free pickets 1 and 4. Ajay must be terminal and CP5 is taken, so Ajay is at CP1 and Eshwar at CP4 - adjacent to Dinesh at CP5. Fails.
- (2,4,5): free pickets 1 and 3. Ajay must be terminal, so Ajay at CP1 and Eshwar at CP3 - adjacent to Dinesh at CP4. Fails.
- (3,4,5): free pickets 1 and 2. Ajay at CP1, Eshwar at CP2 - adjacent to Dinesh at CP3. Fails.
Correct deployment: CP1 Eshwar, CP2 Birendra, CP3 Chetan, CP4 Dinesh, CP5 Ajay. The solution is unique, so the chart must be redrawn, not merely corrected at one picket.
2. If Birendra must be posted at CP1 under special sanction, what follows? State the resulting order and what the Commandant is in effect approving.
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Under the standing instructions no such deployment exists, because the fourth instruction exists precisely to keep Birendra off CP1 - the boat-radio post. The first question to answer is therefore not 'where does everyone go' but 'what is being waived'.
If the CP1 restriction is waived, re-run the enumeration with Birendra fixed at CP1. Chetan must be south of Birendra and north of Dinesh, so Chetan and Dinesh occupy two of CP2 to CP5 in that order. Testing the triples:
- Birendra, Chetan, Dinesh at (1,2,3): remaining pickets 4 and 5 for Ajay and Eshwar. Ajay must be terminal, so Ajay at CP5 and Eshwar at CP4 - adjacent to Dinesh at CP3. Fails.
- (1,2,4): remaining 3 and 5; Ajay must be at CP5, Eshwar at CP3 - adjacent to Dinesh at CP4. Fails.
- (1,3,4): remaining 2 and 5; Ajay at CP5, Eshwar at CP2 - not adjacent to Dinesh at CP4. Works.
- (1,3,5) and (1,4,5): Ajay cannot reach a terminal picket, since CP1 and CP5 are both occupied. Fail.
Resulting order: CP1 Birendra, CP2 Eshwar, CP3 Chetan, CP4 Dinesh, CP5 Ajay.
What is being approved: the waiver shifts Birendra to the radio post and simultaneously moves the trained operator Eshwar off a terminal picket to CP2, and Ajay from CP1 to CP5. The Commandant is therefore not just waiving a posting rule; he is accepting that the boat-radio picket will be held by someone not cleared for it, or that Birendra must be radio-qualified before the deployment takes effect. That dependency should be recorded on the file before the order issues.