📅 Days Based Puzzles - Advanced
Advanced day puzzles with non-standard weeks, multiple variables, time slots, holidays, and Mains-level multi-entity puzzles
Days Based Puzzles - Advanced
Advanced day puzzles feature non-standard week ranges, multiple variables, time slots, and complex multi-entity arrangements that appear in Mains exams.
Non-Standard Week Start
Some puzzles change the start day of the week:
Tuesday to Monday (7 days):
Sunday to Saturday (7 days):
Critical: When the week starts from Tuesday, "after 3 days of Tuesday" means Friday (not Thursday). Always re-number days according to the given start.
Days + Cities/Countries
In these puzzles, each person goes on a specific day AND travels to a specific city:
| Day | Person | City |
|---|---|---|
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday | ||
| Saturday | ||
| Sunday | ||
| Monday |
Example: 7 persons (B, N, P, C, D, A, M) go to 7 world cities (Tokyo, Singapore, London, Paris, Malaysia, Rome, New York) on different days (Tue-Mon).
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Days Based Puzzles - Advanced
Advanced day puzzles feature non-standard week ranges, multiple variables, time slots, and complex multi-entity arrangements that appear in Mains exams.
Non-Standard Week Start
Some puzzles change the start day of the week:
Tuesday to Monday (7 days):
Sunday to Saturday (7 days):
Critical: When the week starts from Tuesday, "after 3 days of Tuesday" means Friday (not Thursday). Always re-number days according to the given start.
Days + Cities/Countries
In these puzzles, each person goes on a specific day AND travels to a specific city:
| Day | Person | City |
|---|---|---|
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday | ||
| Saturday | ||
| Sunday | ||
| Monday |
Example: 7 persons (B, N, P, C, D, A, M) go to 7 world cities (Tokyo, Singapore, London, Paris, Malaysia, Rome, New York) on different days (Tue-Mon).
Conditions mix both variables:
- "D goes to Singapore on Saturday" — direct: D = Sat, city = Singapore
- "B goes to Paris but before M" — B's city = Paris, B's day < M's day
- "The one who goes to Rome goes just before P" — Rome person's day = P's day - 1
Holiday Within the Week
Some puzzles include a rest day/holiday:
- "There is one holiday except Saturday" — the holiday is not Saturday but is one of the other 6 days
- "R goes on the next day of the holiday" — R goes on the day immediately after the holiday
- "The one who goes just after the holiday belongs to Delhi" — links the holiday to a city variable
Effect: With 7 days and 1 holiday, only 6 persons are placed. The holiday creates an empty slot.
Strategy: Treat the holiday as a "vacant" day (like vacant floors in floor puzzles). Try different holiday positions and see which is consistent.
Two Time Slots (3D Arrangement)
Pattern: 10 students, 5 days (Mon-Fri), 2 time slots (8 AM and 11 AM)
| Day | 8:00 AM | 11:00 AM |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday |
This is identical to Floor + Flat puzzles:
- Days = Floors
- Time slots = Flat-A and Flat-B
- "Between F and J" means between their day positions (not between time slots)
Key terminology for two-slot puzzles:
- "I has exam on Tuesday at 8 AM" — direct: I = Tue, 8AM slot
- "H does not have exam at 11 AM" — H is in the 8AM slot
- "The one who has exam at 8 AM is immediately before J" — the 8AM person's day is one day before J's day
Mains-Level: Sports Meet Puzzle
The most complex day puzzle involves multiple entities across days and time slots:
Example: 12 teams play 16 games across 4 days (Mon, Wed, Fri, Sun) with 3 time slots (8AM, 12PM, 3PM).
| Day | 8:00 AM | 12:00 PM | 3:00 PM |
|---|---|---|---|
| Monday | |||
| Wednesday | |||
| Friday | |||
| Sunday |
- 12 positions = 4 days x 3 slots
- 12 teams play different games in these slots
- Conditions involve which team plays which game at what time on what day
Approach:
- This is a 4-variable puzzle: Day, Time slot, Team, Game
- Fix the grid with days as rows and time slots as columns
- Start with definite placements ("Team D plays Y at 12PM")
- Use "before/after" conditions for sequencing
- The ordering is: Mon 8AM < Mon 12PM < Mon 3PM < Wed 8AM < Wed 12PM < ...
Solved Example: 7 Persons + 7 Countries
Question: Seven persons A, B, C, D, E, F, G go abroad on different days (Mon-Sun) to different countries (Canada, USA, Pakistan, Finland, Russia, Iran, Hong Kong).
Conditions:
- A goes on Friday
- The person going to USA goes on Wednesday
- Only one person goes between Hong Kong person and USA person
- B goes immediately after the Hong Kong person
- Only one person between B and Iran person
- Two persons between Iran and C
- F goes one day before G
- E goes to Pakistan
- F is not going to Russia
Solution:
From (1): A = Friday(5) From (2): USA person = Wednesday(3)
From (3): 1 person between Hong Kong and USA(Wed). Hong Kong = Mon(1) or Fri(5). A = Friday. If Hong Kong = Friday, A goes to Hong Kong. Let's explore both.
Case 1: Hong Kong = Monday(1) From (4): B immediately after Hong Kong(Mon). B = Tuesday(2).
From (5): 1 person between B(Tue/2) and Iran. Iran = Thu(4) or Sun(7)... wait: |2 - Iran| - 1 = 1, so |2 - Iran| = 2. Iran = Sat(4)? No: day 4 = Thu. Iran = Thursday(4) or Sunday(0, impossible) — actually Mon = 1, so Iran person at day 4 (Thu) or day 0 (impossible). Iran = Thursday(4).
From (6): 2 persons between Iran(Thu/4) and C. |4 - C| - 1 = 2, |4 - C| = 3. C = 7(Sun) or 1(Mon). Mon = Hong Kong person. If C = Mon, C goes to Hong Kong. If C = Sun, C goes on Sunday.
From (7): F goes one day before G. F and G are consecutive, F first.
Remaining days: Wed(3), Sat(6), Sun(7) for C, D, E, F, G (A=Fri, B=Tue, Hong Kong person=Mon).
Wait — who is the Hong Kong person on Monday? It's not A(Fri) or B(Tue). Could be C, D, E, F, or G.
If C = Sunday(7): Remaining Mon for one of D, E, F, G (Hong Kong person).
From (7): F-G consecutive pair. Available consecutive pairs from {Mon(1), Wed(3), Sat(6)}: (Mon, ?) — no one after Mon that's available. Wait, remaining days: Mon, Wed, Sat, Sun for D, E, F, G. But C = Sun. So remaining: Mon, Wed, Sat for D, E, F, G — that's only 3 days for 4 persons. Contradiction.
So C = Monday(1), C goes to Hong Kong.
Remaining days: Wed(3), Sat(6), Sun(7) for D, E, F, G (4 persons, 3 days). Contradiction again!
We need to reconsider. Actually there should be 7 persons on 7 days. Let me recount: A=Fri(5), B=Tue(2), C=Mon(1). Used days: 1, 2, 5. Remaining: Wed(3), Thu(4), Sat(6), Sun(7) for D, E, F, G. That's 4 days, 4 persons. Good.
Iran = Thursday(4). From (7): F one day before G. From remaining {3,4,6,7}: F=3,G=4 or F=6,G=7.
From (8): E goes to Pakistan. From (9): F not going to Russia.
If F=3(Wed),G=4(Thu): F goes to USA (Wed=USA). G goes on Thu (Iran person). So G goes to Iran. D and E at Sat(6) and Sun(7).
If F=6(Sat),G=7(Sun): remaining D and E at Wed(3) and Thu(4). Wed person goes to USA. Thu person goes to Iran.
Both cases are possible. Additional conditions would narrow it down in a full exam question.
Strategy for Advanced Day Puzzles
- Identify the day range — is it Mon-Sun, Tue-Mon, or specific days only?
- Number the days starting from 1 for quick calculation
- Handle holidays as vacant positions
- For multi-slot puzzles, set up a 2D grid (days x slots)
- For multi-entity puzzles, identify all variables and use a systematic grid
Speed Tips
- For non-standard weeks, immediately re-number the days (Tue=1, Wed=2, etc.)
- Holidays: try the most constrained holiday position first (the one that satisfies the most conditions)
- For two-slot puzzles, use the Floor-Flat approach directly
- For Mains-level puzzles with 3 time slots, think of it as a 3-column grid per day
- Practice converting phrases like "goes just before P" to mathematical form: day = P_day - 1