Unit 16
Positional Constraint Deduction
About this unit
Assign items, people, or objects to specific positions or slots by satisfying a set of explicit placement rules. Unlike general ordering, these questions give hard constraints: "must be directly adjacent", "must be in position 1", "must be exactly 2 apart" — and you must find the unique valid configuration.
What types of questions will you face?
- 1Assign 4-6 coloured boxes/bags in a row where specific pairs must be adjacent or a set distance apart
- 2Stack 5 ingredients in a sandwich/lunchbox where each layer is constrained relative to others
- 3Assign people to car seats (driver, passenger, back left, back right) under strict constraints
- 4Identify which locker or position holds the prize using adjacency and distance clues
- 5Seat 6+ people at a rectangular table with row, column, and opposite-seat rules
- 6Assign departments to building floors under a full set of ordering and adjacency constraints
Skills you will build
- Applying hard adjacency constraints ("only next to", "directly above/below")
- Handling absolute constraints ("must be in position 1 or 2") alongside relative ones
- Building up valid assignments incrementally — start with the most constrained element
- Eliminating invalid arrangements quickly using a single violated constraint
- Tracking "exactly N positions away" constraints on a numbered row
- Applying both linear and 2D grid positional rules simultaneously
By the end of this unit, you will be able to
- Solve any hard-constraint placement puzzle by starting from the most restricted element
- Find the unique valid configuration when every position is tightly constrained
- Assign seats, layers, or positions efficiently without checking every possibility
- Distinguish solvable from unsolvable configurations when given partial constraints
Difficulty profile
The hardest unit in the course (avg 3.92). Simple 4-element row problems are Medium; 6-element rows with multiple adjacency, distance, and direction constraints plus table-seating problems are Very Difficult. This unit rewards systematic, patient work.
Exam tip: Positional Constraint Deduction
Always start with the element that has the most explicit constraints (e.g. "must be in position 1", "only adjacent to X"). Place it first, then use each constraint to narrow what the remaining positions can contain. Never guess — build the solution one forced step at a time.
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