Collector's Five-Day Hearing Schedule
The District Collector of Kottayam has to hear five section heads - Anitha, Bineesh, Chandran, Deepthi and Elias - on five working days, Monday to Friday, one per day. The collector's office follows these fixed conditions. Chandran must be heard exactly two days after Anitha. Bineesh must be heard on the day immediately before Elias. Deepthi cannot be heard on Monday or on Friday. Elias cannot be heard on Tuesday. Anitha must be heard before Deepthi. The collector's assistant has prepared a draft schedule but the collector wants the arrangement checked before the notice is issued. A sixth officer, Fatima, may be added on Saturday if the office remains open, but the collector prefers to finish within the five days. The assistant also reports that Deepthi will be on leave on Wednesday, so her meeting cannot be held that day either.
1. Work out the only possible Monday-to-Friday schedule. Show how the Bineesh-Elias pair and the Anitha-Chandran pair interact.
Read the worked answer
Let the days be 1 = Monday to 5 = Friday. Chandran = Anitha + 2, so the Anitha-Chandran pair can be (Mon, Wed), (Tue, Thu) or (Wed, Fri). Bineesh is immediately before Elias, so the B-E pair can be (Mon, Tue), (Tue, Wed), (Wed, Thu) or (Thu, Fri).
Elias cannot be Tuesday, so (Mon, Tue) is out. Deepthi cannot be Monday, Wednesday or Friday.
Test B-E = (Tue, Wed): Anitha and Chandran must then occupy two of Mon, Thu, Fri, which cannot be two days apart. Reject.
Test B-E = (Wed, Thu): remaining days are Mon, Tue, Fri; again no Anitha-Chandran pair two days apart. Reject.
Test B-E = (Thu, Fri): remaining days are Mon, Tue, Wed. Anitha = Monday and Chandran = Wednesday works, leaving Deepthi = Tuesday, which is allowed.
Schedule: Monday Anitha, Tuesday Deepthi, Wednesday Chandran, Thursday Bineesh, Friday Elias.
2. Elias is transferred and cannot attend on Friday. Can the office still satisfy all five conditions within Monday-to-Friday? Explain.
Read the worked answer
No. Bineesh must be immediately before Elias, so Elias cannot be Monday. He is also barred from Tuesday. The possible Elias days are therefore Wednesday, Thursday or Friday.
If Elias is Wednesday, Bineesh is Tuesday. Anitha and Chandran must then fit into Monday, Thursday and Friday two days apart, which is impossible.
If Elias is Thursday, Bineesh is Wednesday. The remaining days are Monday, Tuesday and Friday; Anitha-Chandran cannot be placed two days apart there either.
Only Elias on Friday leaves Thursday for Bineesh and Monday-Wednesday for Anitha-Chandran-Deepthi. So removing Friday for Elias makes the five-day schedule impossible without relaxing at least one condition.
3. The Collector fixes Chandran on Wednesday. What schedule follows, and is it unique?
Read the worked answer
Chandran on Wednesday forces Anitha on Monday, because Chandran must be exactly two days after Anitha.
The remaining days are Tuesday, Thursday and Friday for Bineesh, Deepthi and Elias. Bineesh must be immediately before Elias. If Bineesh were Tuesday and Elias Thursday, Deepthi would be left with Friday, which is barred. Therefore Bineesh must be Thursday and Elias Friday, leaving Deepthi on Tuesday.
Schedule: Monday Anitha, Tuesday Deepthi, Wednesday Chandran, Thursday Bineesh, Friday Elias. It is unique: every alternative placement either breaks the two-day Anitha-Chandran gap or puts Deepthi on a barred day.