Puzzles
Puzzles - Logic Puzzles, Seating Arrangement, Number Puzzles, Chessboard Puzzles, Calendar Puzzles
Learning Content
🧩 What are puzzles?
RiddlesThese are questions that analyze the given information and find the correct answer in a logical manner.
Puzzles are the most important section in TNPSC Exam!
📌 Types of puzzles
| No | Type | Explanation |
|---|---|---|
| 1 | Session arrangement | Sitting in a row / circle |
| 2 | Ranking puzzle | Height, Age, Weight Sort |
| 3 | Career conundrum | Who has what business? |
| 4 | Color puzzle | House, car, clothes colors |
| 5 | Number puzzle | Find the missing number |
| 6 | Chess board | Chess, number of squares |
| 7 | Calendar | Day, month, year account |
| 8 | Clock | Time, angle calculation |
🪑 1. Seating Arrangement
Categories:
• Single Row
Double Row
• Parallel Rows
• Opposite
• Inward
• Outward
• Hexagon session
• Square session
📊 2. Ranking Puzzle
• Height order (Height)
• Age
• Weight order
• Marks
Floor
Signs:
- Above / Higher than
- Below / Lower than
- Between
- in the middle
🎨 3. House / Color puzzle
5 houses, 5 colors, 5 professions, 5 drinks
Who in which house, what color, what occupation?
Solution Table:
| home | Color | profession | Drink |
|---|---|---|---|
| 1 | ? | ? | ? |
| 2 | ? | ? | ? |
🔢 4. Number Puzzles
Categories:
- Magic Square:The sum of line, column, diagonal is equal
- Sudoku:Numbers 1-9 in a 9×9 grid
- Kaguro:Addition of numbers puzzle
- Number Pyramid:Top-down addition
- Missing number:Missing number in sequence
♟️ 5. Chess board puzzle
Common Questions:
- Total number of squares =204
- Total rectangles =1296
- Horse movements
- King moves
- White/black grids = 32 each
📅 6. Calendar puzzles
• Ordinary year = 365 days = 52 weeks + 1 day
• Leap year = 366 days = 52 weeks + 2 days
• Leap year: divisible by 4 (centuries must be divisible by 400)
| month | days |
|---|---|
| January, March, May, July, August, October, December | 31 |
| April, June, September, November | 30 |
| February (Normal) | 28 |
| February (Leap) | 29 |
🕐 7. Clock puzzles
• Hour hand speed: 0.5° / min
• Minute spindle speed: 6° / min
• One revolution = 360°
• 12 hours = 360°
Angle of Joining of Pins:
Angle = |30H - 5.5M| (H=hour, M=minute)
💡 General steps to solve the puzzle
- Read the question carefully
- Mark the information in a graph/table
- Mark positive information first (✓).
- Mark negative information (X)
- Fill in the remaining spaces in a logical manner
- Check the answer options
🎯 Key codes
| Code | Meaning |
|---|---|
| ✓ | Assertive Information (Yes) |
| X | Misinformation (no) |
| ? | Unknown information |
| → | to the right |
| ← | to the left |
| ↑ | above |
| ↓ | below |
📐 Puzzles Formulas & Rules
All necessary formulas for TNPSC Exam!
🪑 Session arrangement formulas
| Type | formula | Explanation |
|---|---|---|
| Queue session | n! | Ways to arrange n people in a queue |
| Round Session | (n-1)! | Ways to arrange n numbers in a circle |
| evening type | (n-1)!/2 | Hopefully, we can see both ways |
| parallel sequence | n! × 2ⁿ | Opposite / same side |
📊 Ranking formulas
| situation | formula |
|---|---|
| Total | Up + Down - 1 |
| Those above | Total - Down + 1 |
| Those below | Total - Above + 1 |
| Those in between | Large space - Small space - 1 |
🔢 Number puzzle formulas
1. Magic Square (3×3):
For 3×3: 3(9+1)/2 =15
2. Rules of Sudoku:
- 1-9 only once in each line
- 1-9 only once in each programme
- 1-9 only once in each 3×3 box
3. Missing number:
Missing number = Expected - Actual sum
♟️ Chess board formulas
| question | formula | For an 8×8 board |
|---|---|---|
| Number of squares | n(n+1)(2n+1)/6 | 8×9×17/6 = 204 |
| Number of rectangles | n²(n+1)²/4 | 64×81/4 = 1296 |
| Diagonal squares | 2n-1 | 2×8-1 = 15 |
📅 Calendar formulas
1. Odd Days:
• Leap year = 2 odd days
• 100 years = 5 odd days
• 200 years = 3 odd days
• 300 years = 1 single day
• 400 years = 0 odd days
2. Weekday Symbols:
| Sunday = 0 | Monday = 1 | Mars = 2 |
| Wednesday = 3 | Jupiter = 4 | Silver = 5 |
| Saturn = 6 | ||
3. To find leap year:
• Century is divisible by 400
• 2000 = leap (divided by 400)
• 1900 = not a leap (not divisible by 400)
🕐 Clock formulas
1. Speed of Pins:
| bell pin | 0.5° / min | 30° / hour |
| Minute hand | 6° / min | 360° / hour |
| Second hand | 6° / second | 360° / min |
2. Angle calculation:
(H = hour, M = minute)
Example: 3:15
Angle = |30(3) - 5.5(15)| = |90 - 82.5| =7.5°
3. Timing of pins joining:
(Only 1 time between 12 PM and 11 PM)
Joining interval = 12/11 hrs = 65 5/11 min
🎲 General puzzle rules
| statement | Meaning |
|---|---|
| A is to the right of B | B _ A sequence |
| A is next to B | A B or B A |
| A is between B and C | B A C or C A B |
| A is above B | ahead of A rank |
| A is opposite to B | Opposite in circle |
🔄 Combination Formulas
| situation | formula |
|---|---|
| Order is important | ⁿPᵣ = n!/(n-r)! |
| The order is not important | ⁿCᵣ = n!/[r!(n-r)!] |
| Allow re-examination | nʳ |
💡 Solution strategies
- Mark positive information first
- Mark X for negative information
- Only one ✓ per line/program
- Fill in the rest in a logical manner
- Method of deleting options
📚 Solved puzzle questions
Model Questions Asked in TNPSC Exam with Explanation!
Question 1: Session arrangement
6 persons A, B, C, D, E, F are sitting in a row.
- A sits next to B
- C is not at the end of the sequence
- D sits to the left of E
- F is between C and A
Who is sitting next to B?
Solution:
Step 1:A, B successively → AB or BA
Step 2:F, between C and A → CFA or AFC
Step 3:Add AB → CFAB or AFCB
Step 4:D is to the left of E → DE
Step 5:Full lineup:C F A B D E
Question 2: Ranking puzzle
Rahul is ranked 15th from the top and 21st from the bottom in a class. How many students are there in total in the class?
Solution:
Formula:Total = Above + Below - 1
Given:
- Space from top = 15
- Place from bottom = 21
Calculation:
Total = 15 + 21 - 1 =35 students
Question 3: Circle session
6 people sit at a round table facing inwards.
- A is sitting opposite to F
- B is to the right of A
- C is between B and D
- E is to the right of D
Who is to the left of F?
Solution:
Step 1:A opposite F → A _ _ _ F _ circle
Step 2:B is to the right of A → A B _ F _ _
Step 3:C between B and D → A B C D F _
Step 4:E is to the right of D → D E
Step 5:Circular Structure:
A E B F C D
Question 4: Calendar question
If 1 January 2020 is Wednesday, then what day is 15 August 2020?
Solution:
Step 1:Calculation of number of days
| January | 31 - 1 = 30 days |
| February | 29 days (2020 Leap) |
| March | 31 days |
| April | 30 days |
| May | 31 days |
| June | 30 days |
| July | 31 days |
| August | 15 days |
| Total | 227 days |
Step 2:Odd days = 227 ÷ 7 = 32 weeks + 3 days
Step 3:Mercury + 3 =Saturday
Question 5: Clock angle
What is the angle between the hour hand and the minute hand at 3:15?
Solution:
Formula:Angle = |30H - 5.5M|
Given:
- H = 3 hrs
- M = 15 min
Calculation:
Angle = |30(3) - 5.5(15)|
= |90 - 82.5|
=7.5°
Question 6: Chess board
How many squares are there in total in a 4×4 chess board?
Solution:
Formula:n(n+1)(2n+1)/6
Given:n = 4
Calculation:
= 4(4+1)(2×4+1)/6
= 4 × 5 × 9 / 6
= 180 / 6
=30 squares
Description:
- 1×1 squares = 4² = 16
- 2×2 squares = 3² = 9
- 3×3 squares = 2² = 4
- 4×4 squares = 1² = 1
- Total = 30
Question 7: Color puzzle
Four houses are of different colors. Find the color of each house according to the given information:
- The red house is next to the blue house
- The green house is at the end of the row
- The yellow house is to the left of the red house
- The blue house, not in the first place
Solution:
Step 1:Green house at the end → _ _ _ green
Step 2:Red, blue successively → blue red or red blue
Step 3:Yellow, to the left of red → yellow is red
Step 4:Blue is not first → Yellow Blue Red Green
- Yellow
- Blue
- Red
- Green
Question 8: Career conundrum
Raj, Ravi and Ramesh are doctors, engineers and teachers (in no particular order).
- Raj and the engineer are university friends
- Ramesh is younger than the teacher
- Ravi and the teacher live in the same flat
Whose profession is that?
Solution:
| Name | Doctor | Engineer | Teacher |
|---|---|---|---|
| Raj | ✗ | ||
| Ravi | ✗ | ||
| Ramesh | ✗ |
Step 1:Raj is not an engineer (as a friend).
Step 2:Ravi is not a teacher (as he lives in a flat).
Step 3:Ramesh is not a teacher (younger in age).
Step 4:Raj should be a teacher
Step 5:Ravi or Ramesh Engineer/Doctor
- Raj = Teacher
- Ravi = Engineer
- Ramesh = Doctor
Question 9: Number Puzzle
One of the numbers 1 to 50 is missing. The total sum is 1200. What is the missing number?
Solution:
Formula:Sum from 1 to n = n(n+1)/2
Step 1:Expectation from 1 to 50
= 50 × 51 / 2
=1275
Step 2:Missing number = Expected - Actual
= 1275 - 1200
=75
So 75 > 50, given information is wrong!
Correct calculation (if sum is 1200):
Missing number = 1275 - 1200 =75(not possible)
Question 10: Sequence puzzle
5 people stand in order of height. Find the sequence given the given information:
- A is taller than C
- B is shorter than D
- C is taller than E
- D is shorter than A
- E is not very short
Who is the tallest?
Solution:
Step 1:Comparison of information
- A > C → A high
- D > B → D high
- C > E → C high
- A > D → A high
Step 2:Writing together
A > C > E and A > D > B
Step 3:E is not very short → B is short
Step 4:Full lineup:
A > D > C > E > B
Row (Height):A > D > C > E > B
🎯 Practice Tips:
- Solve at least 10 questions for each puzzle type
- Remember the solution method
- Manage time (2-3 min for puzzles)
- The habit of drawing and solving pictures
- Use the deselect method
⚡ Quick Solving Techniques
Special methods to solve puzzles in less time!
🎯 Session arrangement speed modes
1. Fixed Position Method:
Eg:Place A first and set B, C, D
2. Method of negative elimination:
• Then mark the positive statements ✓
• The rest will be filled automatically
3. Conjoined Pairs:
4. Round Session Shortcut:
• Keep 1 person stable and set up others
• Divide by 2 in evening terms
📊 Ranking speed shortcuts
| being asked | Instant formula |
|---|---|
| Find the total | Up + Down - 1 |
| Those in between | Large space - Small space - 1 |
| Place of nth person | Total - n + 1 (from bottom) |
| Same place in both directions | Total = 2 × Place – 1 |
🕐 Clockwise angular velocity cross paths
The three main cross-roads are:
3:00, 9:00 only (exactly)
Otherwise: 2:27, 3:33, 8:27, 9:33 etc. about 90°
Only 6:00 exactly
Others: 5:11, 6:16, 7:22 etc are about 180°
12:00, 1:05, 2:11, 3:16, 4:22, 5:27, 6:33, 7:38, 8:44, 9:49, 10:55
Speed calculation:
| Hourly place | H × 30° | (multiply the number by 30) |
| Minute place | M × 6° | (multiply the minute by 6) |
| Hour adjustment | M × 0.5° | (Divide the minute by 2) |
📅 Calendar speed modes
1. To find leap year immediately:
• If 00 is possible → is it divisible by 400?
Eg:2024 → 24÷4 = 6 ✓ Leap!
2. Single Days Reminder:
| Period | single days | Reminder |
|---|---|---|
| 100 years | 5 | "One hundred = five" |
| 200 years | 3 | "Two hundred = three" |
| 300 years | 1 | "Three hundred = one" |
| 400 years | 0 | "Four hundred = swirl" |
3. Weekday Speed Pattern:
Total days ÷ 7 = Remainder (odd days)
Start day + odd days = end day
♟️ Chessboard Speed Shortcuts
Things to remember:
| Size | Squares | Speed reminder |
|---|---|---|
| 2×2 | 5 | Step by step Add: 1, 4, 9, 16... classes |
| 3×3 | 14 | |
| 4×4 | 30 | |
| 5×5 | 55 |
Diagonal velocity cross-section:
Eg:8×8 → 2(8) - 1 = 15 squares
🎨 Color & Career Puzzle Speed Modes
1. Table Method:
| Name | Option 1 | Option 2 | Option 3 |
|---|---|---|---|
| A | ✓/✗ | ✓/✗ | ✓/✗ |
| B | ✓/✗ | ✓/✗ | ✓/✗ |
2. Negative First:
• “B does not like Y” → mark X immediately
• The rest is self-explanatory
3. Chain of communication:
Keep A constant and solve for the others
🔢 Number puzzle speed shortcuts
1. Missing number:
1-10 to → 55
1-20 to → 210
From 1-50 → 1275
From 1-100 → 5050 (Remember!)
2. Magic square instant method:
4×4 → magic number =34
5×5 → magic number =65
3. Queue Filling:
• Multiply Order → Find Multiplicative Number
• Square order → 1, 4, 9, 16, 25...
• Cubic order → 1, 8, 27, 64, 125...
⏱️ General techniques to save time
| strategy | Explanation | Time left |
|---|---|---|
| Optional deletion | Delete the wrong options first | 30-40 seconds |
| Drawing a picture | Solve the session by drawing a circle | 20-30 seconds |
| tabular method | Use X and ✓ symbols | 40-50 seconds |
| Sutra mnemonic | Memorization of common formulas | 60+ seconds |
🎯 Exam practice tips too
✅ Things to do:
- Solve simple puzzles first
- Use the blank space to draw the picture
- Underline the given information
- Practice time management (2-3 min/puzzle)
- Recall formulas quickly
❌ Avoid:
- Don't waste time on difficult puzzles
- Don't base it on assumptions
- Don't miss out on information
- Don't rush
- Don't forget to check
🏆 Master Tips
1. Numbers to Memorize:
- Sum of 1-10 = 55
- Sum of 1-100 = 5050
- 3×3 magic = 15
- 8×8 squares = 204
- 100 years = 5 odd days
- Round session = (n-1)!
2. Speed Reminder Words:
- "Next" = Conduct in pairs
- "Opposite" = 180° or the exact opposite
- "Between" = leave a space
- "total" = sum - 1
- "Order" = order is important (P)
- "Choice" = Order Doesn't Matter (C)
💡 Final advice:
- Practice Daily:Solve at least 10 puzzles
- Time Record:Mark the average time for each category
- Weaknesses:Additional training in difficult categories
- Previous Questions:Solve TNPSC Past Questions
- Mock Test:Write a weekly mock test
📌 Important note
Puzzles practice is the way to mastery!
Speed + Accuracy = Success 🏆
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