Solving Strategy & Mixed Puzzles

🎯 Learning Objective

Build a reliable method — fixed clues first, two-case elimination — and apply it to tougher mixed and double-row puzzles.

💡 Concept

• Step 1: read ALL clues once and separate FIXED clues (exact seat/end) from FLOATING clues (relative)
• Step 2: draw the frame — a numbered row or a circle of dots with the facing direction marked
• Step 3: place fixed clues, then convert pair clues into blocks and slide them into gaps
• Step 4: if a clue allows two positions, draw BOTH cases and cancel one using a later clue
• Double row: two rows face each other, so each person faces exactly one person opposite
• Double-row face-to-face rule: MY right = YOUR left (think of a handshake)
• Step 5: recheck the finished arrangement against every clue before answering

🧮 Key Formulas

Two-case method: draw both, eliminate with the next clue

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Double row, face to face: my RIGHT = your LEFT

✏️ Easy Example

Q. Four people W, X, Y and Z sit in a row facing north. W is not at either end. X sits at the extreme right end. Y sits to the immediate left of W. Z does not sit at the extreme left end. Who sits at the extreme left end?

1. X = seat 4 (extreme right); W is not at an end → W = seat 2 or seat 3
2. Case W = 3: Y = seat 2, Z = seat 1 → but Z cannot be at extreme left (seat 1). Rejected
3. Case W = 2: Y = seat 1, Z = seat 3 → Z is not at seat 1, all clues fit
4. Extreme left end = seat 1 = Y

Answer: Y

🇮🇳 Real-Life Example

Facing seats in a Vande Bharat coach — the passenger opposite you sees everything flipped: the window on your right is on their left. That single fact solves every double-row puzzle.

📝 Exam-Level Example

Q. Aman, Bina and Cira sit in row 1 facing north. Esha, Dev and Farhan sit in row 2 facing south, and the two rows face each other so each person faces exactly one person of the other row. Dev sits in the middle of row 2. Bina faces Dev. Cira sits to the immediate right of Bina. Farhan sits diagonally opposite Aman. Who faces Aman, and who sits to the immediate left of Dev?

1. Dev = middle of row 2; Bina faces Dev → Bina = middle of row 1
2. Bina faces north, so her right = east → Cira sits at the east seat of row 1; Aman takes the west seat
3. Farhan is diagonally opposite Aman (row-1 west) → Farhan = east seat of row 2; Esha = west seat of row 2
4. Facing pairs: Aman↔Esha, so Esha faces Aman. Dev faces south, so his left = east → the immediate left of Dev is Farhan

Answer: Esha faces Aman; Farhan is to the immediate left of Dev

📝 Exam-Level Example

Q. Eight people sit around a circular table facing the centre. If Gopal sits third to the left of Harish, how many people sit between Gopal and Harish when counted along Harish's right side?

1. Facing centre: left = clockwise, right = anti-clockwise
2. Gopal is 3rd to Harish's left → 3 seats clockwise from Harish (2 people sit between them on that side)
3. The other way round (Harish's right side) covers the remaining seats: 8 total − 2 endpoints = 6 people split as 2 and 4
4. Along Harish's right side: 8 − 3 − 1 = 4 people between them

Answer: 4 people

🪄 Memory Trick

For every arrangement write your rough sheet in this order: frame → fixed clues → blocks → two-case split → recheck. Following the same 5 steps every time makes even 'hard' puzzles routine.

⚠️ Common Mistakes

• ❌ Jumping to floating clues before locking the fixed ones
• ❌ Using page-left/right for the south-facing row without flipping
• ❌ Answering without rechecking — one missed clue changes the whole seat map

🏆 Exam Tips

• ✅ When two cases survive, keep both mini-diagrams side by side and test the next clue on each
• ✅ In double rows, mark a small arrow beside each row showing where it faces

📌 Summary

• Fixed clues first, blocks next, two-case split when stuck
• Double row: each person faces exactly one opposite; my right = your left
• Flip left/right for the south-facing row
• Always recheck the final arrangement against every clue