6.4 Scheduling Puzzles (Day-Month-Year combinations & Time Slots)

6.4 Scheduling Puzzles (Day-Month-Year combinations & Time Slots)

Scheduling puzzles are a regular fixture in SBI PO Preliminary and Main exams. These problems require arranging candidates, events, or transactions into a strict chronological matrix defined by days of the week, combinations of months and dates, birth years, or continuous time slots.

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1. Calendar Mechanics & Mathematical Grid Rules

Month Length Classification

To rapidly solve month-date scheduling puzzles, candidates must memorize calendar month lengths:

• 31-Day Months (7 Months): January, March, May, July, August, October, December.
• 30-Day Months (4 Months): April, June, September, November.
• 28/29-Day Month (1 Month): February.

Date-Month Grid Structure

A standard SBI PO template involves 2 specific dates (e.g., 12th and 25th) across 4 months (e.g., March, April, July, September), yielding $2 \times 4 = 8$ chronological slots.

Chronological Index | Month | Days in Month | Date | Candidate | Attribute
--------------------+-------+---------------+------+-----------+-----------
1                   | March | 31            | 12th |           | 
2                   | March | 31            | 25th |           | 
3                   | April | 30            | 12th |           | 
4                   | April | 30            | 25th |           | 

Chronological Offset Algebra

• "$N$ persons attend between Person $P$ and Person $Q$": $|\text{Slot}(P) - \text{Slot}(Q)| = N + 1$ Example: If 3 persons schedule between $P$ and $Q$, and $P$ is in Slot 1, $Q$ must be in Slot $1 + 3 + 1 = 5$.
• "$P$ attends two months before $Q$": Warning: "Two months before" refers to the calendar month gap, NOT necessarily two slot positions! If $Q$ attends in July, two months before $Q$ means May.

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2. Age Calculation & Birth Year Matrix Strategy

In year-based age puzzles, candidates are given birth years (e.g., 1986, 1992, 1997, 2002) and a fixed reference base year (e.g., 2026).

Workflow for Age Puzzles:

1. Calculate Base Ages Immediately: Compute age for every birth year right at the beginning before reading placement clues: $\text{Age} = \text{Base Year} - \text{Birth Year}$
2. Sort by Age / Birth Year: Keep ages sorted chronologically to evaluate statements like "$A$ is older than $B$".
3. Evaluate Numerical Age Constraints: Test age difference, age sum, or square/cube conditions against the pre-calculated age list.

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3. Fully Worked Step-by-Step Example: Date-Month Scheduling Puzzle

Problem Statement

Eight candidates—P, Q, R, S, T, U, V, and W—are scheduled to attend bank promotional interviews on either the 11th or the 22nd of four different months: March, April, July, and September in the same year. Each candidate specializes in a different domain: IT, HR, Marketing, Operations, Risk, Credit, Treasury, and Audit.

Clues:

1. $P$ attends the interview on an odd-numbered date in a month having 30 days.
2. Only three candidates attend between $P$ and the candidate specializing in Audit.
3. The candidate specializing in Risk attends immediately before the Audit specialist.
4. $T$ attends on the 22nd of a month having 31 days.
5. Two candidates attend between $T$ and $W$.
6. $W$ does not specialize in Audit.
7. $Q$ attends immediately after $U$, and neither of them attends in September.
8. The candidate specializing in IT attends on the 11th of July.
9. $R$ specializes in Credit and attends in the same month as $S$.
10. $V$ specializes in Operations. The Marketing specialist attends before the HR specialist.

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Step-by-Step Deduction & Case Resolution

Step 1: Initializing the Chronological Slot Table

Total slots = 8 (numbered 1 to 8 chronologically):

• Slot 1: March 11th (31 days)
• Slot 2: March 22nd (31 days)
• Slot 3: April 11th (30 days)
• Slot 4: April 22nd (30 days)
• Slot 5: July 11th (31 days)
• Slot 6: July 22nd (31 days)
• Slot 7: September 11th (30 days)
• Slot 8: September 22nd (30 days)

Step 2: Placing P, Audit, and Risk

• Clue 1: $P$ attends on an odd date (11th) in a month having 30 days.
  • Months with 30 days: April and September.
  • So $P$ is either at Slot 3 (April 11th) or Slot 7 (September 11th).

Branching Case A ($P$ at Slot 3 - April 11th):

• 3 candidates attend between $P$ (Slot 3) and Audit $\implies$ Audit is at Slot $3 + 4 = 7$ (September 11th).
• Clue 3: Risk attends immediately before Audit $\implies$ Risk is at Slot 6 (July 22nd).

Branching Case B ($P$ at Slot 7 - September 11th):

• 3 candidates between $P$ (Slot 7) and Audit $\implies$ Audit is at Slot $7 - 4 = 3$ (April 11th).
• Risk immediately before Audit $\implies$ Risk is at Slot 2 (March 22nd).

Step 3: Testing T, W, U, and Q in Case A

Let's analyze Case A:

• Slot 1: March 11th

• Slot 2: March 22nd

• Slot 3: April 11th ($P$)

• Slot 4: April 22nd

• Slot 5: July 11th (IT - Clue 8)

• Slot 6: July 22nd (Risk)

• Slot 7: September 11th (Audit)

• Slot 8: September 22nd

• Clue 4: $T$ attends on 22nd of a 31-day month $\implies T$ is at March 22nd (Slot 2) or July 22nd (Slot 6).

  • Slot 6 is Risk. If $T$ is at Slot 2 (March 22nd), 2 candidates between $T$ (Slot 2) and $W \implies W$ is at Slot 5 (July 11th).
  • But Clue 8 says July 11th is IT. So $W$ specializes in IT.

• Clue 7: $Q$ attends immediately after $U$, and neither attends in September.

  • Available consecutive slots not in September: Slot 1 & 2 (Slot 2 is $T$) or Slot 3 & 4 (Slot 3 is $P$).
  • Thus $U$ is at Slot 3? No, $P$ is at Slot 3. So $U$ is at Slot 1 (March 11th) and $Q$ is at Slot 2 (March 22nd) $\implies T$ must be at Slot 6 (July 22nd - Risk)!

Re-evaluating $T$ at Slot 6 (July 22nd):

• Two candidates between $T$ (Slot 6) and $W \implies W$ is at Slot 3 (April 11th)? But Slot 3 is $P$. Or $W$ is at Slot $6 + 3 = 9$ (out of bounds). Contradiction!

Testing Case B ($P$ at Slot 7 - September 11th)

• Slot 3 is Audit (April 11th). Slot 2 is Risk (March 22nd). Slot 5 is IT (July 11th).
• $T$ on 22nd of 31-day month $\implies T$ at Slot 2 (March 22nd - Risk).
• Two candidates between $T$ (Slot 2) and $W \implies W$ is at Slot 5 (July 11th - IT).
• $U$ and $Q$ consecutive, not in September $\implies U$ at Slot 3 (April 11th - Audit) and $Q$ at Slot 4 (April 22nd). (Note: $W$ is not Audit, $W$ is IT at Slot 5, satisfying Clue 6!).
• $R$ (Credit) and $S$ in same month $\implies$ September has Slot 7 ($P$) and Slot 8. So $R$ and $S$ occupy Slot 7 and Slot 8 or March.
• Placing $V$ (Operations) at Slot 1 (March 11th), $R$ (Credit) at Slot 7, $S$ at Slot 8 (Treasury).
• Marketing before HR $\implies$ Marketing at Slot 4 (April 22nd), HR at Slot 6 (July 22nd).

Final Chronological Schedule Table

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4. Exam Strategies & High-Yield Avoidance Traps

1. Confusing 'Slots Between' with 'Months Between': "Two slots between $A$ and $B$" means $|Pos(A) - Pos(B)| = 3$. "Two months between $A$ and $B$" means looking at month names (e.g., March to June).
2. Ignoring Month Day Counts: Always write down '30' or '31' next to each month name in your scratch pad grid before reading clues.
3. Age Calculation Base Errors: Always calculate ages by subtracting birth year from base year before evaluating prime, square, or sum conditions.