Scheduling Six Demarcation Hearings
Six farmers - A, B, C, D, E and F - must be heard on a single day in six fixed slots numbered 1 to 6 at the tehsil office. The clerk has recorded the following conditions from the parties' written requests: D must be heard immediately before B. F is available only in the last slot. A must be heard before C. E has been fixed in slot 3 because he is arriving by the morning bus and leaving immediately after. No two farmers can share a slot, and the peon has already written the final order on the notice board in chalk. A dispute has arisen because one party claims the order cannot be fixed at all, and a second claims that 'A immediately before C' was an instruction from the tehsildar. Your job is to establish what the six conditions actually force, what they merely permit, and what additional restriction would settle the day's order beyond argument.
1. Determine every schedule consistent with the six conditions, and state how many there are.
Read the worked answer
Step 1 - fix the certainties. F is in slot 6. E is in slot 3. Remaining slots for A, B, C, D: 1, 2, 4, 5.
Step 2 - place the pair D-B. D must be immediately before B, so the pair occupies two consecutive slots. In the remaining slots {1, 2, 4, 5} the only consecutive pairs are (1, 2) and (4, 5).
Case 1: D-B in slots 1-2. Then A and C take 4 and 5, and A must be before C, so A=4, C=5. Order: D, B, E, A, C, F.
Case 2: D-B in slots 4-5. Then A and C take 1 and 2 with A before C, so A=1, C=2. Order: A, C, E, D, B, F.
Answer: exactly two schedules are possible. The party who says no order can be fixed is wrong, and the peon who chalked one order on the board has published one of two possibilities without saying so. Both satisfy every written condition, so neither can be challenged on those grounds alone.
2. One party claims that 'A is heard immediately before C' was the tehsildar's instruction. Test this claim. Then state which of these must be true: (i) B is in slot 2; (ii) A is before E; (iii) A is immediately before C.
Read the worked answer
Testing the claim. The given conditions are: D immediately before B; F in slot 6; A before C; E in slot 3. 'A immediately before C' is nowhere stated. It is derived: because E occupies slot 3, the D-B pair must fall either wholly before or wholly after it, and the two slots left to A and C are therefore always consecutive. So the claim about the tehsildar's instruction misdescribes a consequence of the conditions as an order. That matters - a derived fact can change if a condition changes; an instruction cannot.
Checking each option against both schedules (D,B,E,A,C,F and A,C,E,D,B,F):
- (i) B in slot 2 - true in the first, false in the second. Not forced.
- (ii) A before E - A is in slot 4 in the first schedule and slot 1 in the second; E is in slot 3. So in the first, A comes after E. Not forced.
- (iii) A immediately before C - true in both (4-5 and 1-2). Forced.
Answer: only (iii) must be true. Note the trap: (ii) looks safe because A 'feels early', but the first schedule breaks it.
3. Which single additional restriction makes the day's order unique, and why does it work? Give the resulting order.
Read the worked answer
The restriction: D cannot be heard in slot 1 (for example, because D's counsel is arriving from another tehsil and cannot reach before the second slot).
Why it works: the only two candidate schedules differ precisely in where the D-B pair sits - slots 1-2 in the first, slots 4-5 in the second. Barring D from slot 1 eliminates the D-B pair at 1-2 completely, leaving only one arrangement. A restriction that touches a feature on which the two candidates differ is decisive; a restriction that both candidates already satisfy would change nothing.
Resulting order: slot 1 A, slot 2 C, slot 3 E, slot 4 D, slot 5 B, slot 6 F.
Check against every condition: D immediately before B (4, 5) ✓; F last ✓; A before C (1, 2) ✓; E in slot 3 ✓; one farmer per slot ✓.
Practical point for the notice board: also record why D is barred from slot 1, with the date of the request. An order that is unique but unexplained invites the same dispute again; an order that cites the reason forecloses it.