Seating Arrangement

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Determining positions of people in a row based on constraint clues like adjacency, relative order, and fixed positions.

Seating arrangement puzzles require you to determine the positions of people (or objects) in a linear sequence based on a set of constraints. Constraints can include relative positioning ('A sits to the left of B'), adjacency ('A sits next to B'), non-adjacency ('A is not next to B'), end positions ('A sits at an end'), and fixed positions ('A sits in position 3'). The goal is to find the arrangement that satisfies all constraints simultaneously.

Given N items and a set of constraints C1, C2, ..., Ck: find permutation P of items such that all Ci are satisfied

• 3 people sit in a row. Alice sits to the left of Bob. Carol sits at an end. Who sits in the middle?
• 4 people sit in a row. David is not next to Emma. Frank sits in position 1. Alice sits next to Frank. Where does Bob sit?
• 5 people sit in a row. Alice sits at an end. Bob sits to the left of Carol. David is not next to Emma. Emma sits in position 3.

How to recognize it

• Start with the most restrictive constraints (fixed positions, end positions)
• Use process of elimination to narrow down possibilities
• Draw a diagram: number the positions and fill in what you know
• Test remaining arrangements against all constraints
• If stuck, try assuming a position and check for contradictions

Common mistakes

• Forgetting that 'to the left of' means anywhere to the left, not immediately adjacent
• Confusing 'next to' (adjacent) with 'to the left/right of' (relative order)
• Not checking all constraints against the final arrangement

Practice guidance

Logical Deduction