Directions: Read the information and answer the given questions. Six persons,…

Concept: This is a linear-order (chronological arrangement) puzzle. A group of entities is placed into a single ordered sequence of time-based slots built by combining two or more calendar attributes, while a separate, independent attribute (here, a set of distinct qualities) is assigned to each entity. Two clue types drive the solution: relative clues ("two persons after", "immediately before", "three persons before") translate into arithmetic differences between slot numbers in the fixed chronological order, while absolute clues (a parity or count-based property of a calendar unit) anchor specific entities to specific slots without needing any other clue. The standard method is to anchor first with the absolute clues, convert every relative clue into a position equation, test any branch that yields more than one possibility until it collapses to one (rejecting any branch that produces a contradiction), resolve the independent attribute last by elimination, and finally verify the completed grid against every clue.

Step-by-step derivation:

1. Number the six slots in chronological order: 1 = March 9, 2 = March 16, 3 = June 9, 4 = June 16, 5 = August 9, 6 = August 16 (months run March to June to August, and within a month 9 precedes 16).

2. "A showcases in the month that has an even number of days": among March (31), June (30), and August (31), only June has an even day count, so A occupies slot 3 or slot 4.

3. "A showcases two persons after the one who likes Red": position(A) = position(Red) + 2. If A = 3, Red sits at slot 1; if A = 4, Red sits at slot 2.

4. "F showcases on an odd-numbered date, but after A": the only odd-dated slot after slot 3 or slot 4 is slot 5 (August 9) - slot 4 (June 16) and slot 6 (August 16) are both even-dated - so F = slot 5 under either value of A.

5. "C does not showcase on an even-numbered date": C occupies slot 1, 3, or 5; slot 5 already belongs to F, so C = slot 1 or slot 3 (slot 3 is only free when A = 4).

6. Test A = 3: then C must take slot 1, which is also the Red slot from step 3, so C would like Red. "C showcases three persons before the one who showcases immediately after the one who likes Black" gives position(Black) = position(C) + 2 = slot 3 - but slot 3 is A's own slot, and A does not like Black - a direct contradiction, so A cannot equal 3.

7. So A = 4 (June 16), and by step 3 the Red-liker sits at slot 2 (March 16). By step 5, C = slot 1 or slot 3 (slot 4 is taken by A).

8. Test C = 3 (June 9): then the Black-liker sits at position(C) + 2 = slot 5, so F would like Black. "The one who likes Yellow showcases immediately before D" needs D among the remaining slots {1, 2, 6}: D cannot be slot 1 itself, and D = slot 6 would put the Yellow-liker at slot 5 = F, clashing with F already being Black; so D = slot 2, with the Yellow-liker at slot 1, and D itself takes the Red slot established earlier (slot 2). The remaining slots {1, 6} then go to B and E; since neither C nor B may like Yellow, and slot 1 is the Yellow slot, B cannot be slot 1, so E = slot 1 (Yellow) and B = slot 6. But "the one who likes Green showcases in the same month as E" now needs a March slot for Green (E's month), and both March slots are already taken - slot 1 by Yellow and slot 2 by Red - leaving no slot for Green. So C cannot equal 3.

9. Hence C = slot 1 (March 9), and by the clue in step 6's form, the Black-liker sits at position(C) + 2 = slot 3 (June 9).

10. Remaining slots {2, 3, 6} go to B, D, and E. "The one who likes Yellow showcases immediately before D": if D = 2, Yellow would sit at slot 1 = C, but neither C nor B may like Yellow or White; if D = 3, Yellow would sit at slot 2, which is already the Red slot - a clash. So D = slot 6, with the Yellow-liker at slot 5 = F.

11. Slots {2, 3} remain for B and E. "E likes neither Red nor Green" rules out E at slot 2 (the Red slot), so B = slot 2 (Red) and E = slot 3 (Black, from step 9).

12. Colors fixed so far: slot 2 = Red (B), slot 3 = Black (E), slot 5 = Yellow (F). Remaining colors Green, Blue, White go to C (slot 1), A (slot 4), and D (slot 6). Neither C nor B may like White, so C is barred from White. "The one who likes Green showcases in the same month as E": E's month is June (slot 3), and the only other June slot is slot 4 = A, so A likes Green. C is then left with Blue (White being barred), and D takes the remaining color, White.

13. Final grid: slot 1 = C, March 9, Blue; slot 2 = B, March 16, Red; slot 3 = E, June 9, Black; slot 4 = A, June 16, Green; slot 5 = F, August 9, Yellow; slot 6 = D, August 16, White.

Cross-check against every clue:

• Yellow (F, slot 5) sits immediately before D (slot 6). Matches.

• E likes Black, not Red or Green. Matches.

• A is in June, the only even-day-count month among the three. Matches.

• Red (B, slot 2) plus two slots gives slot 4 = A. Matches.

• F's date is 9 (odd) and slot 5 is after A's slot 4. Matches.

• The slot immediately after the Black-liker (E, slot 3) is slot 4 (A), and C (slot 1) sits exactly three slots before slot 4. Matches.

• C's date is 9, an odd number. Matches.

• A likes Green, not Black. Matches.

• Green (A, slot 4, June) is in the same month as E (slot 3, June). Matches.

• Neither C (Blue) nor B (Red) likes Yellow or White. Matches.

Conclusion: F showcases on 9 August.