Study the following information carefully and answer the questions given…

Concept

In a linear month-and-date ordering puzzle, six people occupy six fixed chronological slots built from the calendar (9 April, 26 April, 9 July, 26 July, 9 September, 26 September), and six colours are distributed one per slot. “Immediately before/after” fixes two adjacent slots. A gap stated as “N persons between X and Y” counts the people strictly in between, so X and Y sit N+1 slots apart; a gap stated as “N persons before/after” is a direct offset of N slots in the stated direction — the two phrasings are different and must not be mixed up. Fixing the six people on the timeline first (from the adjacency and date/month clues), then fixing the six colours on that same timeline (from the colour-gap clues), pins down the whole grid; checking that every remaining branch breaks at least one clue is what confirms the surviving branch is unique.

Application

Place the six people on the timeline first:

1. D is immediately before F, D's own date is odd (a 9th), and D's own month has an even number of days — April and September both have 30 days, July has 31, so July is ruled out for D. So the (D, F) adjacent pair is either (9 April, 26 April) or (9 September, 26 September).

2. E is immediately before C, and E's own date is even (a 26th). The only slots where an even date is immediately followed by another slot are 26 April→9 July and 26 July→9 September (26 September has no slot after it). So the (E, C) adjacent pair is either (26 April, 9 July) or (26 July, 9 September).

3. The (D, F) pair and the (E, C) pair cannot overlap. If (D, F) = (9 April, 26 April), then (E, C) cannot use 26 April, so (E, C) = (26 July, 9 September); the two leftover slots, 9 July and 26 September, go to A and B. If instead (D, F) = (9 September, 26 September), then (E, C) cannot use 9 September, so (E, C) = (26 April, 9 July); the two leftover slots, 9 April and 26 July, go to A and B.

4. Each of these two branches now needs the colour clues checked against it before either can be accepted.

Test the first branch — D = 9 April, F = 26 April, E = 26 July, C = 9 September, with 9 July and 26 September left for A and B:

1. “Pink is two persons before C” is a direct 2-slot offset, so Pink sits 2 slots before C (9 September), i.e. at 9 July.

2. “Two persons between Pink and Blue” is a between-count, so Blue sits 3 slots from Pink (9 July), i.e. at 26 September.

3. So the two leftover slots, 9 July and 26 September, are exactly the Pink slot and the Blue slot — A and B take these two slots in one of two orders. “A is two persons after the one who likes Yellow” is a direct 2-slot offset, so A's slot minus Yellow's slot equals 2. If A sits at 9 July, Yellow would have to sit 2 slots earlier, at 9 April (D) — that is consistent. If A sits at 26 September instead, Yellow would have to sit at 9 July, which is already the Pink slot in this branch — impossible. So A is at 9 July (Pink) and B is at 26 September (Blue), and Yellow sits at 9 April (D).

4. “Two persons between F and the one who likes Red” is a between-count, so Red sits 3 slots from F (26 April), i.e. at 9 September (C).

5. Two colours remain, White and Green, for the two remaining slots, 26 April (F) and 26 July (E). “A was born before the one who likes Green” means Green's slot must come after A's slot (9 July); 26 July (E) qualifies and 26 April (F) does not (it is earlier than 9 July), so Green sits at 26 July (E) and White sits at 26 April (F). E doesn't like Yellow — E likes Green here, so that clue holds too. Every clue is satisfied by this branch.

The second branch — D = 9 September, F = 26 September, E = 26 April, C = 9 July, with 9 April and 26 July left for A and B — fails at the same colour-gap clue: “Pink is two persons before C” puts Pink 2 slots before 9 July, i.e. at 9 April; “A is two persons after Yellow” then forces Yellow onto 26 April, which is E's slot — making E the Yellow-liker and directly breaking the clue “E doesn't like Yellow.” This branch cannot survive, confirming the first branch is the only valid one.

Final arrangement

Cross-check

Check all seven clues against this grid: D (9 Apr) is immediately before F (26 Apr) on an odd date in a 30-day month; E (26 Jul) is immediately before C (9 Sep) on an even date; Pink (9 Jul, A) sits exactly 2 slots before C (9 Sep); two people (E, C) sit between Pink (9 Jul) and Blue (26 Sep); A (9 Jul) sits exactly 2 slots after Yellow (9 Apr, D) and before Green (26 Jul, E); two people (A, E) sit between F (26 Apr) and Red (9 Sep, C); Green (26 Jul) comes after A (9 Jul); and E likes Green, not Yellow. Every clue holds, so the pairing “F – White, 26 April” is the one that is correct.