Five Sessions, Four Rules: Testing a Claim That the Timetable Is Fixed
The student council is scheduling five sessions, one per day from Monday to Friday: Python (P), Quiz (Q), Robotics (R), Turbo (T) and Sports (S). The rules are:
- Robotics is on Wednesday.
- Turbo is on the day immediately before Sports.
- Python is before Turbo.
- Quiz is not on Friday.
A candidate's answer sheet states: 'Sports must be Thursday, because Turbo needs a day after it and Friday is too late for a session that has to be followed by another. Python is fixed on Monday by rule 3, so the only free day is Tuesday.'
The marker must decide whether any part of that answer is sound, whether the puzzle has a unique solution as printed, and whether one additional rule - not contradicting rules 1–4 - could make the timetable unique. No session may be added or dropped.
1. Work out every schedule that satisfies rules 1–4. Show how the impossible cases are eliminated.
Read the worked answer
Robotics occupies Wednesday. Turbo and Sports form an adjacent pair (T immediately before S), and neither can use Wednesday.
Possible positions for the pair (T, S):
- T = Monday, S = Tuesday: rule 3 needs Python before Turbo, and there is no day before Monday. Eliminated.
- T = Tuesday, S = Wednesday: Wednesday is Robotics. Eliminated.
- T = Wednesday: Wednesday is Robotics. Eliminated.
- T = Thursday, S = Friday: allowed. Remaining days are Monday and Tuesday for Python and Quiz. Rule 3 (Python before Turbo) is satisfied on either day, and rule 4 (Quiz not Friday) is satisfied because Friday is Sports.
- T = Friday: there is no day after Friday for Sports. Eliminated.
So the framework is forced: Python and Quiz in some order on Monday and Tuesday, Robotics on Wednesday, Turbo on Thursday, Sports on Friday.
Two schedules survive:
- Monday Python, Tuesday Quiz, Wednesday Robotics, Thursday Turbo, Friday Sports.
- Monday Quiz, Tuesday Python, Wednesday Robotics, Thursday Turbo, Friday Sports.
The solution is not unique; only the Wednesday–Friday block is determined.
2. Critique the candidate's answer line by line. Which specific error produced the conclusion that Sports is on Thursday?
Read the worked answer
Claim 1: 'Turbo needs a day after it and Friday is too late' - false. Rule 2 says only that Sports is the day after Turbo. Nothing in the rules requires a session after Sports. So Turbo may sit on Thursday with Sports on Friday; Friday is not 'too late', it is exactly where Sports must be. The candidate has silently imported a rule that does not exist, which is the classic over-reading error in ordering puzzles.
Claim 2: 'Sports must be Thursday' - false. Sports is Friday, forced by the elimination: Turbo cannot be Monday (nothing before it for Python), cannot be Tuesday or Wednesday (Wednesday is Robotics), and cannot be Friday (no following day).
Claim 3: 'Python is fixed on Monday by rule 3' - false. Rule 3 only says Python precedes Turbo (Thursday), so Python can be Monday or Tuesday. The candidate confused 'before' with 'immediately before' and then treated the weaker rule as if it pinned a single day.
Method error. The candidate reasoned forward from a misread rule instead of testing each possible position of the Turbo–Sports pair. Two errors compound: an invented constraint (something must follow Sports) and a strengthened constraint (Python immediately before rather than merely before). Only one of the two surviving schedules is compatible with the candidate's answer, so it would score as an unjustified guess even though Thursday for Turbo happens to be correct.
3. Propose one additional rule that would make the schedule unique, and verify that it does not contradict rules 1–4 or merely restate them.
Read the worked answer
Proposed rule: Python is immediately before Robotics.
Verification. Robotics is Wednesday, so Python would have to be Tuesday. In both surviving schedules Tuesday is available (the two schedules differ only in the Monday–Tuesday order), and Python on Tuesday still satisfies rule 3 because Tuesday precedes Thursday. Quiz then takes Monday, which satisfies rule 4.
The forced schedule becomes: Monday Quiz, Tuesday Python, Wednesday Robotics, Thursday Turbo, Friday Sports - one solution, no contradictions.
Why it is not a restatement. Rules 1–4 permit Python on Monday or Tuesday; the new rule cuts exactly one of those two cases. It is independent of rule 3, which only requires 'before'.
Other acceptable answers, for comparison. 'Quiz is on Monday' also works, because it forces Python to Tuesday. 'Quiz is not on Monday' works for the same reason. What would not work: 'Python is before Robotics' - true in both surviving schedules, so it eliminates nothing; or 'Turbo is on Thursday' - it restates the conclusion already derived from rules 1–3, so the puzzle stays ambiguous but is now easier to guess. A good extra rule must separate the two survivors, not describe the block they share.