Scheduling Puzzles

A scheduling puzzle asks you to assign a set of tasks, events, or people to a set of time slots (e.g., Monday–Friday, 9 am–1 pm). Each slot gets exactly one assignment. Clues give ordering constraints, gap constraints, or direct placements.

Draw a timeline table: time slots as columns, the thing being assigned as rows (or vice versa).

1. List all slots and all items to be placed — match counts confirm one-to-one assignment.
2. Place fixed clues first — "Math is on Monday" → fill Monday = Math immediately.
3. Apply ordering clues — "Science is before History" → note Science slot < History slot.
4. Apply gap clues — "English is two days after Math" → if Math = Mon, English = Wed.
5. Use elimination: once a slot is filled, no other item can go there.
6. Test remaining options — if two items can swap, look for a clue that breaks the tie.

Example 1: Five subjects (Maths, English, Science, Hindi, Art) scheduled Mon–Fri. Clues:

• Maths is on Wednesday.
• Science is the day before Maths.
• English is on Friday.
• Hindi is before Art.

Step 1: Maths = Wed. Science is day before → Science = Tue. English = Fri. Remaining: Hindi and Art for Mon and Thu. Hindi before Art → Hindi = Mon, Art = Thu. Schedule: Mon–Hindi, Tue–Science, Wed–Maths, Thu–Art, Fri–English.

Example 2: Four meetings (A, B, C, D) in four 1-hour slots (10 am, 11 am, 12 pm, 1 pm). Clues:

• D is not at 10 am.
• B is immediately after A.
• C is at 1 pm.

Step 1: C = 1 pm. B immediately after A → possible pairs: A=10,B=11 or A=11,B=12. D not at 10 am. If A=10, B=11, then D must be at 12 pm. Valid. Check: C=1 pm confirmed. If A=11, B=12, then D at 10 am — violates the clue. Invalid. Schedule: A–10 am, B–11 am, D–12 pm, C–1 pm.

• "Immediately before/after" vs "before/after" — "immediately" means adjacent slots with no gap; plain "before" allows any earlier slot.
• Ignoring impossible placements early — use negative clues to cross out cells from the start, not at the end.
• Forgetting that two items cannot share a slot — especially in longer puzzles, double-check uniqueness at every step.

1. Three events (X, Y, Z) in slots 1, 2, 3. Z is not in slot 1. Y is immediately before Z. What is the order?
2. Four tasks (P, Q, R, S) in slots Mon–Thu. P is on Mon. R is two days after P. Q is the day before R. Where is S?

(Answers: 1 → X=1, Y=2, Z=3; 2 → P=Mon, R=Wed, Q=Tue, S=Thu)