Four JEs and Four Project Sites
A zonal engineer must post four junior engineers-Asha (A), Bhavan (B), Chetan (C) and Divya (D)-one each to four project sites numbered 1 to 4. Site 1 is the drainage site, Site 2 the water-treatment site, Site 3 the school-building site and Site 4 the flyover site. The posting must satisfy four conditions: (i) Divya must be at Site 3, because she holds the structural-design certification needed there; (ii) Asha must be at an even-numbered site; (iii) Bhavan must not be at Site 1; and (iv) Chetan's site must be exactly one number below Bhavan's site. The engineer also has a note from the previous rotation saying that Site 4 should go to the JE with the longest service, but that note is not a formal condition. Before signing the order, the engineer is told that Divya may have to move to Site 4 for a month. The engineer must decide whether the posting order can still satisfy the four conditions, and whether any condition is doing no work at all.
1. Find the only posting that satisfies conditions (i) to (iv). Show each deduction.
Read the worked answer
From (i), D = 3. From (ii), A is 2 or 4. Test A = 2: the remaining sites for B and C are 1 and 4. Condition (iv) requires C to be exactly one below B, so the possible pairs are (C1, B2) or (C3, B4). B2 is blocked by A and C3 is blocked by D, so A cannot be 2. Therefore A = 4. The remaining sites are 1 and 2. Condition (iii) rules out B = 1, so B = 2 and C = 1. Check (iv): C is at 1, exactly one below B at 2. Final order: A-4, B-2, C-1, D-3.
2. If Divya is moved to Site 4, can the four conditions still be satisfied? If not, identify one single condition that could be relaxed and give the resulting posting.
Read the worked answer
With D = 4, A must be even and cannot be 4, so A = 2. The remaining sites are 1 and 3. Condition (iii) forces B = 3 and C = 1. But C at 1 is two numbers below B at 3, so condition (iv), which requires exactly one number, fails. There is no valid posting. One workable relaxation is to change (iv) from "exactly one number below" to "below": then C = 1, B = 3, A = 2, D = 4 satisfies (i), (ii) and (iii). Alternatively, dropping (ii) allows A = 1, C = 2, B = 3, D = 4, which keeps the immediate-before relation. The engineer should state which operational requirement is truly negotiable before altering the order.
3. Is condition (iii), "Bhavan must not be at Site 1", redundant? Explain.
Read the worked answer
Yes, as long as condition (iv) stands. If C must be exactly one number below B, then B cannot be at Site 1 because there is no Site 0 for C. So (iii) adds nothing and the puzzle would still have the same unique solution without it. It becomes useful only if (iv) is relaxed or removed; in that situation B could otherwise occupy Site 1. This matters practically: a posting order that lists a redundant condition may create a false impression that an extra constraint has been checked, while the real constraint is the adjacency rule.