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

Concept: In a multi-variable arrangement puzzle, the entities (here, six people) are placed along a fixed timeline of positions (here, the six date-month slots in chronological order), and each clue is one of three kinds: an absolute fact that fixes one entity directly, a relative fact that fixes the gap between two entities' positions, or a matching fact that links two different attributes (date/month and colour) to the same entity or slot.

The standard method is: (1) use every absolute clue first to fix positions or months directly; (2) chain the relative clues ("immediately before", "two after", "three before the one after X") onto those fixed points to pin down the remaining positions; (3) only once positions are settled, overlay the attribute-matching clues (colour, month-parity, etc.) onto the fixed timeline; (4) finally verify every original clue against the completed table.

Application:

1. Fix the month with an even number of days: among March (31), June (30) and August (31), only June has an even count, so A, who shows in the month with an even number of days, shows in June -- position 3 (June 9) or position 4 (June 16).

2. Use the Red-gap clue (A shows two positions after the Red-liker) together with the odd-date clue for F (F shows on the 9th, after A) to test both June positions for A. If A were at position 3, the Red-liker would sit at position 1, and F (an odd date after position 3) would have to be position 5. The remaining positions {1, 2, 4, 6} go to B, C, D, E; C must also sit on an odd date (position 1, since positions 3 and 5 are taken), so C = 1. The Black-gap clue then fixes the Black-liker at position 3 (two ahead of C) -- but position 3 is A, and A does not like Black. This is a contradiction, so A cannot be at position 3. Hence A is at position 4 (June 16), which places the Red-liker at position 2 (March 16) and, since F must be on an odd date after position 4, F lands at position 5 (August 9).

3. Use the odd-date clue for C (C does not show on an even date) together with the Black-gap clue (C sits two positions before the Black-liker) to place C. With A=4 and F=5 already fixed, the only odd positions left for C are 1 or 3. If C were at position 3: the Black-liker would sit at position 5, i.e. F. The remaining positions {1, 2, 6} go to B, D, E. Testing D=6 puts the Yellow-liker at position 5 -- but F already likes Black there, a direct colour clash. Testing D=2 puts the Yellow-liker at position 1; since position 2 is always the Red-liker's slot, whichever of B or E sits at position 1 exhausts both March slots (Yellow at 1, Red at 2) -- but the Green-liker must share E's month, and if E itself sits at position 1 its month is March, leaving no free March slot for Green; if B sits at position 1 instead, B would like Yellow, which the clue 'neither C nor B likes Yellow' forbids. Testing D=1 fails outright, since Yellow would need a non-existent position 0. Every branch under C=3 fails, so C cannot be at position 3. Hence C is at position 1 (March 9), which fixes the Black-liker at position 3 (two positions ahead of C).

4. Use the Yellow-immediately-before-D clue on the remaining open positions (2, 3, 6 for B, D, E). If D were at position 2, the Yellow-liker would have to be at position 1 (C) -- but C is barred from liking Yellow. If D were at position 3, the Yellow-liker would have to be at position 2 -- but position 2 is already fixed as the Red-liker's slot, so the same person cannot like both colours. Both cases fail, so D must be at position 6 (August 16), with the Yellow-liker one slot earlier at position 5 -- meaning F likes Yellow.

5. Since E cannot like Red and the Red-liker sits at position 2, E cannot be at position 2; so B takes position 2 (March 16, Red) and E takes the remaining position 3 (June 9) -- exactly the slot already fixed as the Black-liker's position, so E likes Black.

6. Match the Green clue: the Green-liker shows in the same month as E (June). The only two June slots are position 3 (E, already Black) and position 4 (A), so A must like Green.

7. The two colours left, Blue and White, go to C and D. Since neither C nor B may like White, White must go to D, leaving Blue for C.

Final arrangement:

Cross-check:

• Yellow-before-D: Yellow-liker at position 5, D at position 6 -- immediately before. Holds.

• A's month: A is at position 4 = June, the even-day month. Holds.

• Red-gap: Red-liker at position 2, A at position 4 -- exactly two after. Holds.

• F's date and order: F is at position 5 = August 9 (odd date) and 5 > 4 = A's position. Holds.

• Black-gap: Black-liker at position 3; the slot immediately after is position 4; three before position 4 is position 1 = C. Holds.

• C's date: C is at position 1 = March 9, an odd date. Holds.

• A not Black: A likes Green, not Black. Holds.

• Green/E same month: Green-liker (A) and E are both in June. Holds.

• Neither C nor B likes Yellow or White: C likes Blue, B likes Red. Holds.

The completed timeline places D at position 6, i.e. 16 August, so the person who showcases on 16 August is D.