📆 Month Based Puzzles
Master month-based puzzles - month sequences, date combinations, 30/31 day constraints, and month + variable arrangements
Month Based Puzzles
Month-based puzzles use months of the year as the base for arrangement. They are similar to day-based puzzles but with 12 positions (or a subset), and often include date-specific conditions and days-per-month constraints.
Understanding the Base: Months
The 12 months of the year:
| Month | Number | Days |
|---|---|---|
| January | 1 | 31 |
| February | 2 | 28 (29 in leap year) |
| March | 3 | 31 |
| April | 4 | 30 |
| May | 5 | 31 |
| June | 6 | 30 |
| July | 7 | 31 |
| August | 8 | 31 |
| September | 9 | 30 |
| October | 10 | 31 |
| November | 11 | 30 |
| December | 12 | 31 |
Months with 30 days: April, June, September, November (4 months) Months with 31 days: Jan, Mar, May, Jul, Aug, Oct, Dec (7 months) February: 28 days (ordinary year) or 29 days (leap year)
Tip: Remember "30 days has September, April, June, and November. All the rest have 31, except February."
Types of Month Puzzles
Type 1: Only Months (6-9 persons)
Pro Content Locked
Upgrade to Pro to access this lesson and all other premium content.
Charged once for one year · ₹1188 total
Save ₹100/month vs ₹2388/year launch price
- All Agriculture & Banking Courses
- AI Lesson Questions (100/day)
- AI Doubt Solver (50/day)
- Glows & Grows Feedback (30/day)
- AI Section Quiz (20/day)
- 22-Language Translation (100/day)
- Recall Questions (20/day)
- AI Quiz (15/day)
- AI Quiz Paper Analysis (100/day)
- AI Step-by-Step Explanations (100/day)
- Spaced Repetition Recall (FSRS)
- AI Tutor
- Immersive Text Questions
- Audio Lessons — Hindi & English
- Mock Tests & Previous Year Papers
- Summary & Mind Maps
- XP, Levels, Leaderboard & Badges
- Generate New Classrooms
- Voice AI Teacher (AgriDots Live)
- AI Revision Assistant
- Knowledge Gap Analysis
- Interactive Revision (LangGraph)
🔒 Secure one-time yearly payment via Razorpay · No hidden fees
Month Based Puzzles
Month-based puzzles use months of the year as the base for arrangement. They are similar to day-based puzzles but with 12 positions (or a subset), and often include date-specific conditions and days-per-month constraints.
Understanding the Base: Months
The 12 months of the year:
| Month | Number | Days |
|---|---|---|
| January | 1 | 31 |
| February | 2 | 28 (29 in leap year) |
| March | 3 | 31 |
| April | 4 | 30 |
| May | 5 | 31 |
| June | 6 | 30 |
| July | 7 | 31 |
| August | 8 | 31 |
| September | 9 | 30 |
| October | 10 | 31 |
| November | 11 | 30 |
| December | 12 | 31 |
Months with 30 days: April, June, September, November (4 months) Months with 31 days: Jan, Mar, May, Jul, Aug, Oct, Dec (7 months) February: 28 days (ordinary year) or 29 days (leap year)
Tip: Remember "30 days has September, April, June, and November. All the rest have 31, except February."
Types of Month Puzzles
Type 1: Only Months (6-9 persons)
- 6 persons in 6 different months (e.g., May through October)
- Base = months in order, one person per month
Type 2: Month + Date
- Persons assigned to specific months AND specific dates (e.g., 5th, 12th, or 28th)
- Creates a 2D grid: months as rows, dates as columns
Type 3: Month + Variable
- Each person has a month AND a variable (laptop brand, car, city)
- Solve month order first, then assign variables
Key Terminology for Month Puzzles
| Exam Phrase | Meaning |
|---|---|
| "After one month" | The next month (Jan -> Feb) |
| "One month gap" | Skip one month (Jan -> Mar, one month gap = February skipped) |
| "After two months" | Two months later = one month gap (Jan + 2 = March) |
| "Before one month" | Previous month (March -> February) |
| "Two persons between A and B" | Two months separate them in sequence |
| "B went in the month having 30 days" | B is in Apr, Jun, Sep, or Nov |
| "X travelled in a month having only 30 days" | Same as above: Apr, Jun, Sep, Nov |
| "Born in a month with even number of days" | February (28), April (30), June (30), Sep (30), Nov (30) — all months with even day counts |
Gap Calculation for Months
Same formula as days: Gap = |Month number of A - Month number of B| - 1
Example: A in March(3), B in July(7): Gap = |3-7| - 1 = 3 months between them (Apr, May, Jun)
Days-Per-Month as a Constraint
This is unique to month puzzles and doesn't appear in day or floor puzzles:
- "A goes in a month having 30 days" — A is in April(4), June(6), September(9), or November(11)
- "B goes in a month having 31 days" — B is in Jan, Mar, May, Jul, Aug, Oct, or Dec
- "C goes in the shortest month" — C is in February
Even/Odd day count:
- Months with even number of days: Feb(28), Apr(30), Jun(30), Sep(30), Nov(30) — all have even day counts
- Months with odd number of days: Jan(31), Mar(31), May(31), Jul(31), Aug(31), Oct(31), Dec(31) — all have 31 days (odd)
Month + Date Grid (2D Puzzle)
Example: 9 persons born in 3 months (August, September, October) on dates 5th, 12th, or 28th.
| Date | August | September | October |
|---|---|---|---|
| 5th | |||
| 12th | |||
| 28th |
9 positions for 9 persons. Each cell gets exactly one person.
Conditions may include:
- "V and L have 2 persons born between them" — in the linear sequence (Aug5, Aug12, Aug28, Sep5, Sep12, Sep28, Oct5, Oct12, Oct28)
- "N was born immediately before A and immediately after V" — V, N, A are consecutive
- "G was born on an odd-numbered date" — date is 5th (odd)
- "Z was born immediately before D" — Z just before D in the sequence
Linear ordering for month+date:
Solved Example: 6 Persons, 6 Months + Laptop Brands
Question: Six persons A, B, C, D, E, F went shopping in different months: May, June, July, August, September, October. Each bought a different laptop: HP, Redmi, Sony, Panasonic, Lenovo, Samsung.
Conditions:
- B went in a month having 30 days
- 3 persons between the Redmi buyer and B
- A does not buy Redmi
- Only 1 person between C and the Redmi buyer
- As many after C as before the Sony buyer
- D went immediately after the HP buyer
- F went immediately before B, who bought Panasonic
- As many after the Panasonic buyer as before A
- F does not buy Samsung
Solution:
Months in order: May(1), Jun(2), Jul(3), Aug(4), Sep(5), Oct(6)
From (1): B in a 30-day month. From {May(31), Jun(30), Jul(31), Aug(31), Sep(30), Oct(31)}: B = June(2) or September(5)
From (7): F immediately before B, B buys Panasonic.
- If B = June(2), F = May(1)
- If B = September(5), F = August(4)
From (2): 3 persons between Redmi buyer and B.
- If B = June(2): Redmi is at 2+4=6 (Oct) or 2-4=-2 (impossible). Redmi buyer in October(6).
- If B = Sep(5): Redmi at 5+4=9 (impossible) or 5-4=1. Redmi buyer in May(1).
Case 1: B=Jun(2), F=May(1), Redmi=Oct(6) From (3): A doesn't buy Redmi. So A is not in October. From (4): 1 person between C and Redmi(Oct/6). C = Aug(4) or impossible position 8. C = August(4).
From (5): persons after C(4) = persons before Sony buyer. After C: Sep(5), Oct(6) = 2 persons. Before Sony buyer = 2, so Sony buyer = position 3 = July(3).
Remaining: A, D, E in Jul(3), Sep(5), and one more... wait, positions filled: F=May(1), B=Jun(2), C=Aug(4), Redmi person=Oct(6). Remaining persons: A, D, E for Jul(3), Sep(5), Oct(6). But Oct has the Redmi buyer. A doesn't buy Redmi, so A is not Oct. D and E could be at Oct.
From (6): D immediately after HP buyer. So HP buyer's month + 1 = D's month. From (8): persons after Panasonic buyer (B/Jun=2) = persons before A. After B: Jul, Aug, Sep, Oct = 4 persons. Before A = 4, so A = position 5 = September(5).
Then D and E at Jul(3) and Oct(6). From (6): D immediately after HP buyer. If D = Jul(3), HP buyer = Jun(2) = B. B buys Panasonic, not HP. Contradiction. If D = Oct(6), HP buyer = Sep(5) = A. A buys HP.
So D = October(6) (buys Redmi), E = July(3) (buys Sony). A = Sep(5) buys HP. F = May(1), B = Jun(2) buys Panasonic, C = Aug(4).
Remaining laptops: Lenovo, Samsung for F and C. From (9): F doesn't buy Samsung. F buys Lenovo, C buys Samsung.
Final:
| Month | Person | Laptop |
|---|---|---|
| May | F | Lenovo |
| June | B | Panasonic |
| July | E | Sony |
| August | C | Samsung |
| September | A | HP |
| October | D | Redmi |
Strategy for Month Puzzles
- List the months in order with their numbers and day counts
- Apply 30/31 day constraints first — they narrow down positions immediately
- Use gap calculations with month numbers
- For month+date puzzles, linearize the grid into a single sequence
- Assign variables after fixing month positions
Speed Tips
- Memorize which months have 30 days: April, June, September, November (think "AJSN")
- For 6-month puzzles (May-Oct), immediately note: Jun(30) and Sep(30) are the only 30-day months
- In month+date puzzles, convert the 2D grid to a linear sequence numbered 1 to 9 (or whatever total)
- "Month having even days" includes February (28 is even) — don't forget this
- Pre-calculate all possible gap positions before diving into Part B solving