Ordering Sequence

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Determining the rank order of items from comparison clues like higher-than, lower-than, and not-at-rank constraints.

Ordering sequence puzzles require arranging items in a ranked order from clues about their relative positions. Constraints include direct comparisons ('A is ranked higher than B'), exclusions ('A is not ranked 1st'), and sometimes transitive chains ('A > B and B > C implies A > C'). These puzzles test the ability to build a consistent ordering from partial information.

Given N items and comparison constraints: find total ordering consistent with all constraints

• 3 items ranked 1-3. Alice is ranked higher than Bob. Carol is not ranked 1st. What is Carol's rank?
• 4 items ranked 1-4. Alice is higher than Bob. Carol is lower than David. Bob is not ranked 3rd.
• 5 items ranked 1-5. Alice > Bob > Carol. David is not 1st or 5th. Emma > David.

How to recognize it

• Build a chain: if A > B and B > C, then A > C (transitivity)
• Use exclusion constraints to eliminate impossible positions
• Start with the longest chain of comparisons
• Count how many items must be above or below a given item to narrow its rank
• Try possible positions and check for contradictions

Common mistakes

• Forgetting to apply transitivity (if A > B and B > C, then A > C)
• Assuming a constraint means immediately adjacent ranks (A > B does not mean A is one rank above B)
• Not considering all possible orderings when constraints allow multiple valid arrangements

Practice guidance

Logical Deduction