DM: Logical Puzzles & Constraint-Based Reasoning

What Are Logical Puzzles?

Logical puzzle questions present a set of constraints or rules and ask you to determine a valid arrangement, sequence, or conclusion. These are among the most time-consuming DM questions but are highly learnable with practice.

Common Puzzle Types

1. Seating arrangements: “Five people are seated around a table. Alex is opposite Beth. Chris is next to Alex but not next to Dana…”
2. Scheduling: “Four meetings must be scheduled on Monday through Thursday, with the following constraints…”
3. Ordering/Sequencing: “Rank these items from highest to lowest given the following information…”
4. Matching: “Match each person to their profession given these clues…”

Systematic Approach

1. Read all constraints first before attempting to solve
2. Start with the most restrictive constraint — this limits possibilities the most
3. Use your noteboard — draw grids, tables, or diagrams. Do NOT try to solve these in your head
4. Work through constraints one at a time, eliminating possibilities as you go
5. Check your answer against ALL constraints before submitting

Noteboard Techniques

For seating arrangements: Draw the table/line and use initials. Mark confirmed positions with circles, possible positions with question marks.

For scheduling: Create a grid with time slots as columns and items as rows. Use ticks, crosses, and question marks.

For ordering: Write out a vertical list and place items using greater-than/less-than relationships (A > B > C).

Worked Example

Question: Four students — Ava, Ben, Cara, and Dan — each study a different subject: Biology, Chemistry, History, and Maths. Use the following clues to determine who studies what:

• Ava does not study Biology or Chemistry
• Ben does not study History
• Cara studies Biology
• Dan does not study Maths

Solution process:

1. From clue 3: Cara → Biology (definite)
2. From clue 1: Ava → History or Maths (not Bio, not Chem)
3. From clue 2: Ben → Biology, Chemistry, or Maths. Since Cara has Biology → Ben → Chemistry or Maths
4. From clue 4: Dan → Biology, Chemistry, or History. Since Cara has Biology → Dan → Chemistry or History
5. If Ben → Chemistry, then Dan → History, then Ava → Maths. Check: Ava not Bio/Chem ✓, Ben not History ✓, Dan not Maths ✓. Valid!

Answer: Ava–Maths, Ben–Chemistry, Cara–Biology, Dan–History