Day / Month Scheduling
Overview
Day/Month Scheduling is a core puzzle type in SBI Clerk Prelims where you assign a set of persons (typically 5–7) to specific days of the week or months of the year based on given conditions. These puzzles test your ability to process multiple constraints simultaneously and arrive at a unique arrangement.
The difficulty is moderate—conditions are usually direct without heavy negation or layered variables.
Success requires a systematic approach: create a clean grid, process definite clues first, and use elimination for remaining slots. Speed comes from recognizing clue patterns and avoiding re-reading conditions multiple times.
Key Concepts
- Fixed-slot assignment: Each person occupies exactly one day/month, and each day/month has exactly one person (unless stated otherwise).
- Definite vs. conditional clues: Definite clues give exact positions ("P works on Monday"). Conditional clues give relative positions ("Q works immediately after R").
- Gap-based clues: "Two persons work between A and B" means there are exactly two slots separating them, not two persons on either side.
- Boundary constraints: Days like Monday/Sunday or months like January/December have only one neighbor—use this to eliminate impossible positions.
- Negative clues: "X does not work on Wednesday" eliminates one option. Process these after placing definite information.
- Ordinal nature: Days follow Monday→Sunday sequence; months follow January→December. "Before" means earlier in this sequence, "after" means later.
- Either-or scenarios: When clues create two possible cases, work both in parallel until one contradicts a condition.
Formulas / Key Facts
- 7 days of week (in order): Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday
- 12 months (in order): January, February, March, April, May, June, July, August, September, October, November, December
- "Immediately before/after": Adjacent slots with no gap
- "n persons between A and B": Total gap = n slots; A and B are (n+1) positions apart
- "A works before B": A's position number < B's position number (not necessarily adjacent)
- If 6 persons for 7 days: One day remains empty—identify which day has no assignment
- Processing order: Definite clues → Gap-based clues → Negative clues → Either-or cases
Worked Examples
Example 1: Basic Day Scheduling
Problem: Six persons P, Q, R, S, T, and U work on six different days from Monday to Saturday.
- R works on Wednesday.
- T works immediately after R.
- Two persons work between P and Q, with P working before Q.
- S works on Monday.
- U does not work on Friday.
Which day does U work on?
Solution:
Step 1: Place definite clues
- R → Wednesday
- S → Monday
Step 2: Process "immediately after" clue
- T works immediately after R (Wednesday), so T → Thursday
Step 3: Process gap-based clue
- Two persons between P and Q, P before Q
- Remaining days: Tuesday, Friday, Saturday
- Available slots for P and Q with 2-person gap:
- P on Tuesday → Q needs position (Tuesday + 3) = Friday ✓
- So P → Tuesday, Q → Friday
Step 4: Remaining person and day
- U is left, Saturday is left
- U → Saturday
Step 5: Verify negative clue
- U does not work on Friday ✓ (U works on Saturday)
Answer: U works on Saturday
Example 2: Month Scheduling with Cases
Problem: Five persons A, B, C, D, and E have birthdays in five different months—March, May, July, September, and November.
- Three persons have birthdays between A and D.
- B's birthday is immediately before C's birthday.
- E's birthday is in May.
In which month is D's birthday?
Solution:
Step 1: List months in order: March, May, July, September, November (positions 1–5)
Step 2: Place definite clue
- E → May (position 2)
Step 3: Process gap-based clue
- Three persons between A and D
- With 5 positions, only possibility: positions 1 and 5
- Case 1: A in March, D in November
- Case 2: D in March, A in November
Step 4: Process "immediately before" clue
- B immediately before C (consecutive months)
- Remaining persons: B, C (remaining months: March, July, September, November minus A/D positions)
Case 1 (A-March, D-November):
- Remaining months for B, C: July, September
- B before C: B → July, C → September ✓
Case 2 (D-March, A-November):
- Remaining months for B, C: July, September
- B before C: B → July, C → September ✓
Both cases satisfy all conditions! But wait—check if question asks for D specifically:
- Case 1: D → November
- Case 2: D → March
If additional clue needed: Without more information, both are valid. In actual exams, there will be a deciding clue. If question states "D's birthday is after A's birthday," then Case 1 applies, and D's birthday is in November.
Common Mistakes
- Confusing "between" count: "Two persons between A and B" means 2 slots in the gap, so A and B are 3 positions apart. Students often count A or B in the "between" count → Always count only the gap slots.
- Ignoring boundary limits: Placing someone "two positions before Monday" is impossible. Students forget edge constraints → Always check if calculated positions exist.
- Misreading "before/after": "A works before B" doesn't mean immediately before. Students assume adjacency → Read whether "immediately" is mentioned.
- Not tracking empty slots: In 6-person/7-day problems, one day is empty. Students forget this and force all days to be filled → Note the mismatch at the start.
- Abandoning valid cases too early: When two cases emerge, students sometimes pick one randomly → Work both cases until a clue eliminates one.
Quick Reference
- Draw a grid first: Days/Months as columns, write person names below as you solve.
- Process order: Definite → Relative → Negative clues.
- "n persons between" = gap of n slots = (n+1) positions apart.
- Boundary days (Mon/Sun) and months (Jan/Dec) have only one neighbor.
- When stuck, list remaining persons and slots—sometimes only one combination works.
- Double-check by verifying all original conditions against your final arrangement.