Puzzles — Advanced Exam Problems

🎯 Learning Objective

Solve two-variable floor puzzles, box-stack eliminations and person-city-day grids with the parallel-case method used in CBT-2.

💡 Concept

• Multi-variable puzzles = one frame + one grid: solve the FRAME variable (floor/position/day) first, then hang the second variable (post/city) on it
• Convert every counting clue to arithmetic instantly: 'two between' = difference of 3; 'immediately above' = difference of 1
• When a clue allows two placements, run BOTH cases in parallel columns — a later clue must kill one, otherwise re-read a clue
• Bridge clues ('the guard lives on the top floor') join the two variables — apply them AFTER the frame is fixed
• Finishing = rechecking: one pass over every clue against the final table catches the silent contradiction

🧮 Key Formulas

n people between = position difference of n + 1

>

Frame first (floors/days), second variable later (posts/cities)

>

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

✏️ Easy Example

Q. Mohit, Nidhi and Omprakash are from Lucknow, Madurai and Nagpur (one each), and one of them is a doctor. Nidhi is from Lucknow. The one from Nagpur is the doctor. Mohit is not the doctor. Who is the doctor?

1. Lock the direct clue first: Nidhi = Lucknow
2. Mohit is not the doctor, and the Nagpur person IS the doctor — so Mohit cannot be from Nagpur → Mohit = Madurai
3. Omprakash takes the leftover Nagpur, and the Nagpur person is the doctor → Omprakash

Answer: Omprakash

🇮🇳 Real-Life Example

A station master allotting quarters — post, floor and seniority all at once — runs exactly this cross-elimination: one confirmed allotment cancels a whole row of options.

📝 Exam-Level Example

Q. Amit, Bhaskar, Chirag, Deepa and Esha live on the five floors of a building (floor 1 lowest, floor 5 top) and hold five different posts — loco pilot, guard, TTE, station master and pointsman. Deepa lives on the lowest floor. Exactly two people live between Chirag and Bhaskar. Amit lives on an even-numbered floor. Chirag lives above Amit. The guard lives on the top floor. Bhaskar is the TTE. The loco pilot lives immediately above the station master. What is Deepa's post?

1. Lock the exact clue first: Deepa = floor 1, because every relative clue needs a fixed anchor
2. 'Two people between Chirag and Bhaskar' = a 3-floor gap; within floors 2-5 only (2,5) and (5,2) fit — hold both cases
3. Amit needs an even floor. In the Chirag=2 case Amit is forced to floor 4, but then Chirag(2) sits BELOW Amit(4), breaking 'Chirag above Amit' → that case dies; so Chirag=5, Bhaskar=2, Amit=4, and Esha takes the leftover floor 3
4. Now hang the posts on the finished frame: the guard lives on the top floor → Chirag is the guard; Bhaskar is the TTE (direct clue)
5. 'Loco pilot immediately above station master' needs two touching floors among the free people — Amit(4), Esha(3), Deepa(1); the only touching pair is 4-over-3 → Amit = loco pilot, Esha = station master
6. The last post goes to the last person: Deepa = pointsman

Answer: Pointsman

📝 Exam-Level Example

Q. Six boxes — G, H, J, K, L and M — are stacked one above another (position 1 at the bottom, 6 at the top). Exactly three boxes are kept between K and J, and K is above J. H is kept immediately above J. Exactly one box is kept between G and H, and G is above H. M is kept immediately above H. L is kept at the bottom of the stack. How many boxes are kept between M and L?

1. 'Three boxes between K and J' with K above = a position gap of 4 → (K, J) = (6, 2) or (5, 1); carry both cases in two columns
2. Chain the remaining clues onto J in each column: H = J+1, M = H+1 and G = H+2 — case A gives J2, H3, M4, G5 with K6; case B gives J1, H2, M3, G4 with K5. Note the one box between G and H is exactly M, so the clues agree
3. Both columns still fill legally — case A leaves L = 1, case B leaves L = 6 — so the frame is not decided yet; look for the killer clue
4. 'L at the bottom' murders case B, where L was forced to the TOP (position 6) → case A survives: bottom to top the stack is L, J, H, M, G, K
5. Count between M (position 4) and L (position 1): positions 2 and 3 → J and H → two boxes

Answer: Two boxes (J and H)

📝 Exam-Level Example

Q. Four friends — Om, Pihu, Raghav and Sana — each visit a different city (Agra, Bhopal, Chennai, Delhi) on a different day from Monday to Thursday. Pihu travels on Monday. Pihu travels on the day immediately before Om. Sana visits Bhopal. Om visits neither Bhopal nor Delhi. The Agra visit happens on Thursday. Who travels on Wednesday, and to which city?

1. Anchor the direct facts: Pihu = Monday, so Om = Tuesday (immediately after Pihu); Sana = Bhopal
2. Om avoids Bhopal and Delhi → Om is left with Agra or Chennai
3. Use the bridge clue: the AGRA trip happens on Thursday, whoever makes it — Om travels on Tuesday, so Om cannot be the Agra visitor → Om = Chennai
4. Agra and Delhi remain for Pihu and Raghav; Pihu travels on Monday, not Thursday → Pihu = Delhi, so Raghav = Agra, and the bridge clue fixes his day as Thursday
5. Only Wednesday and only Sana remain unpaired → Sana travels on Wednesday, to Bhopal

Answer: Sana — she travels on Wednesday, to Bhopal

🪄 Memory Trick

Give each case its own column on the rough sheet and note the clue numbers as you consume them. A case dies the moment it contradicts a clue — strike it out with one line, and the surviving column is your answer sheet.

⚠️ Common Mistakes

• ❌ Attaching a bridge clue to a person before the frame variable is fixed
• ❌ Reading 'two between' as a difference of 2 — it is 3
• ❌ Abandoning one case early without a clue that actually kills it

🏆 Exam Tips

• ✅ Solve the variable with more clues first — it is usually the frame (floors/days)
• ✅ Tick every clue as it is used; an unticked clue at the end is either your recheck or the examiner's trap
• ✅ Write stacks and floors bottom-to-top on paper exactly as the building stands — the visual match prevents inversion errors

📌 Summary

• Frame first, second variable later
• Counting words become arithmetic: n between = gap of n + 1
• Two live cases → parallel columns → the next clue kills one
• Bridge clues join the variables — apply them late and recheck every clue at the end