📅 Days Based Puzzles - Basic
Learn day-of-week puzzles - Mon to Sun arrangement, after/before terminology, gaps, time slots, and variable assignment
Days Based Puzzles - Basic
Days-based puzzles use the 7 days of the week as the base for arrangement. Persons are assigned to different days based on conditions about relative positions, gaps, and adjacency.
Understanding the Base: Days of the Week
The standard week runs from Monday to Sunday:
- 1 Day = 24 hours (one position in the arrangement)
- Odd days: Mon(1), Wed(3), Fri(5), Sun(7)
- Even days: Tue(2), Thu(4), Sat(6)
Note: Some questions start the week from Sunday or even Tuesday. Always read the question setup carefully.
Key Terminology
This is the most critical section. Misinterpreting a single phrase can lead to a completely wrong answer.
| Exam Phrase | Meaning | Example |
|---|---|---|
| "After one day" / "Next day" | The very next day | After Thursday = Friday |
| "Before one day" / "Previous day" | The day immediately before | Before Thursday = Wednesday |
| "One day gap" / "After two days" | Skip one day (2 positions apart) | Two days after Monday = Wednesday |
| "One day after Thursday" | The day right after Thursday | = Friday |
| "Any day after Thursday" | Any day from Fri to Sun | Could be Fri, Sat, or Sun |
| "On the day before" / "One day prior" | Previous day | Before Friday = Thursday |
| "Immediately followed by" | The very next day | A on Wed, immediately followed by B = B on Thu |
| "Immediately preceded by" | The day right before | A on Wed, immediately preceded by B = B on Tue |
| "Followed by" (without "immediately") | After, but not necessarily next day | A on Wed, followed by B = B is on Thu, Fri, Sat, or Sun |
| "Preceded by" (without "immediately") | Before, but not necessarily previous day | A on Wed, preceded by B = B is on Mon or Tue |
Gap Calculation for Days
Gap = |Day number of A - Day number of B| - 1
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Days Based Puzzles - Basic
Days-based puzzles use the 7 days of the week as the base for arrangement. Persons are assigned to different days based on conditions about relative positions, gaps, and adjacency.
Understanding the Base: Days of the Week
The standard week runs from Monday to Sunday:
- 1 Day = 24 hours (one position in the arrangement)
- Odd days: Mon(1), Wed(3), Fri(5), Sun(7)
- Even days: Tue(2), Thu(4), Sat(6)
Note: Some questions start the week from Sunday or even Tuesday. Always read the question setup carefully.
Key Terminology
This is the most critical section. Misinterpreting a single phrase can lead to a completely wrong answer.
| Exam Phrase | Meaning | Example |
|---|---|---|
| "After one day" / "Next day" | The very next day | After Thursday = Friday |
| "Before one day" / "Previous day" | The day immediately before | Before Thursday = Wednesday |
| "One day gap" / "After two days" | Skip one day (2 positions apart) | Two days after Monday = Wednesday |
| "One day after Thursday" | The day right after Thursday | = Friday |
| "Any day after Thursday" | Any day from Fri to Sun | Could be Fri, Sat, or Sun |
| "On the day before" / "One day prior" | Previous day | Before Friday = Thursday |
| "Immediately followed by" | The very next day | A on Wed, immediately followed by B = B on Thu |
| "Immediately preceded by" | The day right before | A on Wed, immediately preceded by B = B on Tue |
| "Followed by" (without "immediately") | After, but not necessarily next day | A on Wed, followed by B = B is on Thu, Fri, Sat, or Sun |
| "Preceded by" (without "immediately") | Before, but not necessarily previous day | A on Wed, preceded by B = B is on Mon or Tue |
Gap Calculation for Days
Gap = |Day number of A - Day number of B| - 1
Examples:
- A on Monday(1), B on Thursday(4): Gap = |1-4| - 1 = 2 days between them (Tue and Wed)
- A on Wednesday(3), B on Friday(5): Gap = |3-5| - 1 = 1 day between them (Thursday)
- A on Monday(1), B on Tuesday(2): Gap = |1-2| - 1 = 0 days (adjacent, no gap)
Two-Slot Day Puzzles
In some puzzles, each day has two time slots (e.g., 10 AM and 5 PM), accommodating more persons than days.
Example: 5 days (Mon-Fri) with 10 persons — 2 per day.
| Day | 10 AM Slot | 5 PM Slot |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday |
This is similar to the Floor + Flat concept: days = floors, time slots = flats.
Solved Example 1: 7 Persons, 7 Days
Question: Seven persons A, B, C, D, E, F, G watch movies on different days of the week (Monday to Sunday), not necessarily in this order.
Conditions:
- B watches on Tuesday
- F watches on the day adjacent to B (Monday or Wednesday)
- There are 3 days gap between F and A
- G watches just after D
- As many persons watch between A and G as between D and C
- C watches before D but not just before
Solution:
Part A:
From (1): B = Tuesday (day 2) From (2): F = Monday(1) or Wednesday(3)
Case 1: F = Monday (day 1) From (3): 3 days gap between F(1) and A. |1 - A| - 1 = 3, so |1 - A| = 4. A = 5 (Friday) or A = -3 (impossible). A = Friday (day 5)
From (4): G is just after D. G = D + 1 (consecutive days).
From (6): C before D, not just before. So at least 1 day between C and D.
From (5): Persons between A(5) and G = Persons between D and C.
Remaining days: Wed(3), Thu(4), Sat(6), Sun(7) for C, D, E, G. G = D + 1. Possible: D=3,G=4 or D=4,G=? — but 5 is taken. D=6,G=7 or D=3,G=4.
Try D = 3 (Wed), G = 4 (Thu): Between A(5) and G(4): |5-4| - 1 = 0 persons between them. Between D(3) and C: should also be 0. So |3 - C| - 1 = 0, meaning C = 2 or 4. B=2, G=4. Both taken. Dead end.
Try D = 6 (Sat), G = 7 (Sun): Between A(5) and G(7): |5-7| - 1 = 1 person between them (day 6 = D). Between D(6) and C: should also be 1. |6 - C| - 1 = 1, so |6 - C| = 2. C = 4 or 8. C = 4 (Thursday).
From (6): C(4) before D(6), gap = |6-4| - 1 = 1. "Not just before" means gap >= 1. Gap = 1, which means there IS one day between them. C is not immediately before D (Thu before Sat with Fri between). This satisfies "not just before."
E is on the remaining day: Wednesday (3)
Final arrangement:
| Day | Person |
|---|---|
| Monday | F |
| Tuesday | B |
| Wednesday | E |
| Thursday | C |
| Friday | A |
| Saturday | D |
| Sunday | G |
Days with Variables (Cities)
In some puzzles, each person not only goes on a specific day but also belongs to a city.
Example: 6 persons go to college on different days (Mon-Sun, one rest day). Each belongs to a different city.
Conditions typically include:
- "The person who goes on Tuesday belongs to Lucknow"
- "A belongs to Delhi and goes after Wednesday"
- These link days to variables, adding a second dimension
Holiday/Rest Day Concept
Some day puzzles include a holiday or rest day where nobody goes:
- "One day is a holiday (except Saturday)" — Saturday is not the holiday, but one other day is
- "The person who goes just after the holiday belongs to Delhi" — first working day after the off day
Strategy: The holiday creates a gap. If holiday = Thursday, then the schedule has positions on Mon, Tue, Wed, Fri, Sat, Sun.
Common Traps
- "After two days" vs "two days after" — both mean skip 1 day (2 days gap in some interpretations). Always count: Monday + 2 = Wednesday.
- "Adjacent day" means immediately before OR after — not just after
- "Followed by" is NOT "immediately followed by" — "followed by" allows any later day
- Week starting day — some puzzles start from Sunday or Tuesday. Re-number accordingly.
- Same day, different slots — in two-slot puzzles, two persons CAN be on the same day
Speed Tips
- Write days horizontally: Mon | Tue | Wed | Thu | Fri | Sat | Sun
- Number them 1-7 for quick gap calculations
- Place the definite day assignments first (like "B watches on Tuesday")
- For "adjacent day" conditions, immediately mark the 2 possible days
- For gap conditions, calculate both directions and check which is valid
- Practice the terminology table until you can instantly translate exam phrases to positions