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mpt · CSS study notes

Sequencing & Ordering

Core Idea

Arrange people or items in a specific order (rank, queue, height, schedule) based on a set of clues. Convert every clue into a relationship first, then merge them into one single ordered list.

Strategy

  1. Convert words to symbols immediately — "A is older than B" → A > B
  2. Chain the relationships — combine all clues into a single ordered list before answering
  3. Don't assume order from how clues are listed — clues are rarely given in solved order; read all of them first
  4. Watch for relative-only clues (e.g. "B is somewhere between A and C") vs absolute position clues (e.g. "D is at the 3rd position")
  5. If ties/equal ranks are possible, check whether the question allows for them or assumes strict ordering

Worked Examples

  1. A is taller than B. C is shorter than B. D is taller than A. Who is the shortest?

    → D > A > B > C → C is the shortest

  2. In a queue: P is right behind Q. R is in front of Q. S is at the very back. Order the queue from front to back.

    → R, Q, P, S → R → Q → P → S

  3. Five friends A, B, C, D, E are ranked 1st to 5th. B is 2nd. D is not last. A is right after C. E is last.

    → E=5th (given). B=2nd (given). D ≠ 5th, so D is 1,3, or 4. "A right after C" means C,A are consecutive. Remaining positions for A,C,D: 1,3,4. Testing C=1,A=... wait A must be right after C, so if C=3,A=4, then D=1. → D, B, C, A, E

  4. X finished before Y. Y finished before Z. W finished after Z. Who finished last?

    → X < Y < Z < W → W finished last

Drill

  1. X is older than Y. Y is older than Z. Who is youngest? — Z
  2. If P > Q, Q > R, and R > S, who is the smallest? — S
  3. Six students ranked 1-6 in a race. A beat B. B beat C. D finished right after A. E finished last. F finished 2nd. Order? — A, D, F, B, C, E (working through: A beats B beats C establishes A<B<C in finish time terms as rank numbers; D right after A; F is 2nd; E is last — combine all constraints)
  4. In a height order, M is taller than N but shorter than O. P is the tallest. Order from tallest to shortest. — P, O, M, N

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