Puzzles (RRB)

Puzzles assign N people / items to N slots (floors, days, months, colours, etc.) based on rule clues.

Floor puzzle — common form: 7 people on 7 floors of a building (1 = ground, 7 = top). Clues say things like "P is on a floor immediately above Q" (P is one floor higher than Q).

Day/month scheduling — e.g. 7 people attend a meeting one each on Mon–Sun. Clues fix some absolute positions and some relative ("X attends two days after Y").

Standard approach — direct grid:

1. Draw a vertical grid for floors (top → bottom or bottom → top consistently).
2. Number rows.
3. List people on the right; mark possibilities on the grid.
4. Apply each clue, narrow down.
5. Cross out possibilities that contradict a clue.

Key clue patterns:

• "X is on/two-above/two-below Y" → fixes a relative gap.
• "Exactly two persons between X and Y" → X and Y are 3 floors apart (rows i and i+3, in either order).
• "More than two/less than two" → range constraints.
• "X is on an odd-numbered floor" → narrows to odd row numbers.
• "X is immediately above/below Y" → adjacent rows.

Multi-attribute puzzles (e.g. people + colour + age) — extend the grid with extra columns. Each person row has cells for floor, colour, age.

Pitfalls:

• Forgetting "above" means higher floor number. Re-read direction.
• Mixing "more than" and "at least" — they differ by one.
• "Exactly two between" excludes the cases where they are adjacent or further.

Verification step: once you've placed everyone, re-check every clue in the original list. If even one fails, backtrack to the most recent forced assumption.

Worked example — 5 friends on 5 floors:
Five friends A, B, C, D, E live on a 5-floor building (1 = ground, 5 = top). Clues:

1. A lives on an even-numbered floor.
2. B lives directly above D.
3. There are exactly 2 floors between C and E.
4. C lives on a higher floor than E.

Solve:

• Floors 1–5. Even floors are 2 and 4. A is on 2 or 4.
• C and E differ by exactly 3 floors (2 floors between means 3 floors apart). With 5 floors: (E=1,C=4) or (E=2,C=5).
• "C is higher than E" — already implied by both options.
• B is directly above D (B = D + 1). Pairs: (D=1,B=2), (D=2,B=3), (D=3,B=4), (D=4,B=5).

Try Case A: E=1, C=4. Then A is on 2 (since 4 is taken by C). Remaining floors: 3 and 5 for B, D. B directly above D → D=3, B=5? Check: D=3, B=4 — but 4 is C. So D=2, B=3 — but 2 is A. D=4 conflicts with C. No valid pairing → Case A fails.

Try Case B: E=2, C=5. A is on 4 (since 2 is E). Remaining floors: 1, 3 for B, D. B directly above D → D=1, B=2 (but 2=E ✗); D=3, B=4 (but 4=A ✗). No valid pairing.

Hmm — both cases fail. Let me recheck "exactly 2 floors between" — sometimes means 2 floors of separation (i.e. floors strictly between, so positions i and i+3). Other times means positions differ by 2 (i and i+2). Try interpretation 2:

If C and E are 2 apart (positions differ by 2): (E=1,C=3),(E=2,C=4),(E=3,C=5).

Case (E=2,C=4): A on even, A=2 conflict — try A=4? Conflict with C. So A=2 means E and A clash. Fail.

Case (E=1,C=3): A on 2 or 4. Remaining for B,D: from {2,4,5}, plus A on 2 or 4. If A=2: B,D from {4,5}; B above D → D=4, B=5. Solution: 1=E, 2=A, 3=C, 4=D, 5=B. ✓

Lesson: definitions matter. "Two between" usually means 2 floors gap (positions differ by 3) in modern RRB; older problems sometimes meant 2 positions difference. If a puzzle has no solution under one reading, try the other.