Fixing a Five-Witness Examination Schedule Under a Court Deadline
Five witnesses to a chain-snatching near Baramunda bus stand, Bhubaneswar, must be examined on five consecutive working days, Monday to Friday, one per day. The investigating officer's note records: (i) T is to be examined on Friday; (ii) Q must be examined on the day immediately after R; (iii) P must be examined before R, but not on the day immediately before R; (iv) S must be examined before Q. The IO falls ill on Monday morning and the sub-inspector must fix the schedule before the court's 11 a.m. deadline. The court clerk points out that the witnesses are daily-wage workers who lose about ₹450 each per visit, so a wrong schedule means a fresh summons, a lost day's wage and a possible hostile-witness plea. While re-reading the note, the SI sees that the IO's diary carries a query mark against the words “not on the day immediately before”.
1. Determine the only examination order that satisfies all four conditions. Show the deduction step by step rather than testing orders at random.
Read the worked answer
Anchor the fixed point. T is on Friday, so positions 1–4 are open for Q, R, P and S.
Use the block. Condition (ii) makes RQ an unbreakable two-day block. It can sit at (1,2), (2,3) or (3,4) - not at (4,5), because Friday is T.
- Block at (1,2): R is on Monday. Condition (iii) needs P before R, and there is no day before Monday. Rejected.
- Block at (2,3): R is Tuesday. P must be before Tuesday, so P is Monday - but Monday is immediately before Tuesday, which condition (iii) forbids. Rejected.
- Block at (3,4): R is Wednesday, Q Thursday. P must be before Wednesday and not on Tuesday, so P is Monday. The only remaining slot, Tuesday, goes to S.
Check the leftover condition: S (Tuesday) is before Q (Thursday). Satisfied.
Answer: P, S, R, Q, T.
The useful habit here is to place the block and the fixed day first, then let the negative condition (“not immediately before”) eliminate branches. Random trial wastes the deadline you are working against.
2. If the queried phrase cannot be relied on, what orders remain possible, and what single additional fact would settle the schedule?
Read the worked answer
Dropping only the words “not on the day immediately before”, conditions (i), (ii) and (iv) still stand.
- Block at (1,2): R is Monday, so P cannot be before R. Rejected.
- Block at (2,3): R Tuesday, Q Wednesday, P Monday, S Thursday. But S is then after Q, breaking (iv). Rejected.
- Block at (3,4): R Wednesday, Q Thursday. P may be Monday with S Tuesday, or P may be Tuesday with S Monday. Both keep S before Q. Two survivors: P, S, R, Q, T and S, P, R, Q, T.
So the doubt costs exactly one degree of freedom: whether P or S is examined first.
The single fact needed: whether S was examined before P, or P before S. Any independent record settles it - the IO's case diary entry, the witnesses' own statements about who saw the incident first, or the order in which their statements under Section 180 BNSS were recorded.
Practical point: the two candidates for Monday differ only in P versus S, so the SI can call both for Monday with staggered times instead of risking a wasted summons and ₹450 of a daily-wage earner's money.
3. T's examination is adjourned to the following week. Over Monday to Thursday only, does the rest of the schedule still hold?
Read the worked answer
Re-run the same method with four slots, Monday to Thursday.
The RQ block can sit at (1,2), (2,3) or (3,4).
- (1,2): R Monday, nothing before R for P. Rejected.
- (2,3): R Tuesday, P must be Monday - immediately before R, forbidden. Rejected.
- (3,4): R Wednesday, Q Thursday. P is Monday and S is Tuesday. P on Tuesday instead would put him immediately before R, so that branch fails.
Result: P, S, R, Q - the same relative order as before, simply compressed into four days.
Consequence for the office: no fresh summons is needed for P, S, R or Q; only T's date changes. The SI can tell the four witnesses at once, in writing, that their days are unchanged, which protects their wages and their willingness to appear.
The general lesson: removing the fixed element and re-deriving is safer than assuming the old order survives. Here it happened to survive - but only because the block and the negative condition, not T, were doing the real work.