Logical Puzzles

Logical Puzzles give you a set of rules and constraints about people, positions, schedules, or objects, and ask you to determine a specific fact (who sits where, what day something happens, which combination must be true). They have 4 options and are worth 1 mark.

These make up ~5-6 questions (~13.9% of DM). Target time: 60-90 seconds. They have the worst time-to-mark ratio in DM - a single 1-mark LP can take longer than a 2-mark Syllogism set.

The maths is brutal. Logical Puzzles: 1 mark, 60-120 seconds. Syllogisms: 2 marks, 45-90 seconds for 5 statements. LP gives you roughly half the marks per minute.

Strategy: ALWAYS attempt RA + Probability + Syllogisms + II first. Come to LP only with banked time.

That said, some LPs are straightforward - 3 variables, simple constraints. Those are worth attempting. The technique below makes them mechanical.

Step 1: Read the question first. Know what you need to find BEFORE parsing the rules. "Who is in position 6?" tells you to focus on position 6, not solve the entire puzzle.

Step 2: Identify the main variable. Which entity shows up most often? That goes down the middle of your table.

Step 3: Draw the table. Main variable as rows. Other categories as columns.

Step 4: Fill absolute facts first. "Fiona is in position 1" - write it in immediately. "Amir is in position 8" - same. These are free cells. Fill them before you touch any conditional rules.

Step 5: Extract hidden constraints. "A before B" means A can't be last AND B can't be first. "Not next to" means eliminate adjacent cells. Write these as X marks in your table.

Step 6: Look for forced cells. When a row or column has only one remaining option, it MUST be correct. Fill it and cascade.

Step 7: Stop when the answer emerges. You do NOT need to complete the entire table. Once you can answer the question, stop.

Stimulus:

"The photograph shows 8 new prefects in positions 1-8, alternating female, male, female, male. Fiona (F) is in position 1, Amir (M) is in position 8. Samantha (F) is centrally placed but nearer to Amir than Fiona. Luka (M) is to the left of Samantha. Rugby captain Max (M) sits next to Fiona. Max is five places from his sister Angie (F). Pierre (M) and Louise (F) fill the remaining spots."

Question: "Who is in position 6?"

Step 1: Goal = find who is in position 6.

Step 2: Main variable = positions (1-8).

Step 3: Draw the table with gender constraints (positions alternate F/M):

Step 4: Absolute facts filled (Fiona = 1, Amir = 8).

Step 5: Process rules one at a time.

Rule: "Samantha (F) is centrally placed, nearer to Amir than Fiona."
Centre of 8 = between 4 and 5. Nearer to Amir (pos 8) = position 5 (not 3, which is nearer to Fiona). Samantha is F; pos 5 is F. → Samantha = pos 5.

Rule: "Luka (M) is to the left of Samantha (pos 5)." → Luka is M; male positions left of 5 are pos 2 or pos 4. Hold.

Rule: "Max (M) sits next to Fiona (pos 1)." → Next to pos 1 = pos 2. → Max = pos 2.

Luka must be M and left of Samantha. Only pos 4 remains. → Luka = pos 4.

Rule: "Max is 5 places from Angie (F)." → Max is pos 2; five places away = pos 7 (F). → Angie = pos 7.

Remaining: Pierre (M) and Louise (F). Open slots: pos 3 (F) and pos 6 (M). → Louise = pos 3, Pierre = pos 6.

Answer: Pierre (A).

Time check: We could have stopped earlier - once Max went into pos 2, Luka was forced into pos 4, and the remaining M slot (pos 6) had to be Pierre. ~45 seconds.

Stimulus:

"Five students - Kai, Lena, Marco, Noor, and Priya - each study a different subject (Biology, Chemistry, History, Maths, Physics) and live on a different floor (1-5) of their hall. Kai studies neither Biology nor Chemistry. The Biology student lives on floor 3. Lena lives on a higher floor than the Chemistry student but lower than Marco. The Physics student lives on floor 1. Noor studies History. Priya lives on floor 4."

Question: "Which floor does Kai live on?"

Step 1: Goal = find Kai's floor.

Step 2: Three variables to track: student, subject, floor. Build a grid.

Step 3: Start with absolute facts:

• Noor → History
• Priya → Floor 4
• Biology student → Floor 3
• Physics student → Floor 1

Step 4: Apply constraints:

• Kai studies neither Biology nor Chemistry; Noor studies History → Kai studies Maths or Physics.
• Physics student lives on Floor 1 - but we don't yet know if Kai is Physics. Hold.
• Lena lives higher than Chemistry student, lower than Marco → Marco is above Lena.

Step 5: Start eliminating.

Who is on Floor 3? The Biology student. Kai doesn't study Biology, and Noor studies History - so Floor 3 = Lena or Marco (studying Biology).

Test: can Marco be on Floor 3? Then Lena must be below Marco (Floor 1 or 2) and above the Chemistry student. Lena = Floor 2 → Chemistry = Floor 1, but Floor 1 = Physics. Contradiction. Lena = Floor 1 → nobody below her for Chemistry. Contradiction.

→ Marco is not on Floor 3. Lena = Floor 3 (Biology). Marco must be above Lena, and Priya holds Floor 4 → Marco = Floor 5.

Lena (Floor 3) is higher than the Chemistry student → Chemistry is on Floor 1 or 2. Floor 1 = Physics → Chemistry student is on Floor 2.

Kai doesn't study Chemistry → Kai is not on Floor 2 → Kai = Floor 1 (Physics), Noor = Floor 2 (Chemistry).

Answer: Floor 1.

Time check: This one is harder - 3 interlinked variables and one proof-by-contradiction step. ~90 seconds. The key was the contradiction: placing Marco on Floor 3 forces Chemistry into an impossible spot. If you hit this in the exam and weren't making progress after 60 seconds, guessing and flagging would be reasonable.

Every rule has an explicit meaning AND a hidden constraint:

LP questions test six skills from the DM taxonomy:

• B1: Constraint Satisfaction / Elimination - systematic elimination using multiple constraints until forced conclusions emerge. This is the core LP skill.
• B2: Sequential / Temporal Ordering - determining chronological order from relative temporal information (before, after, dates).
• B3: Scheduling / Route Planning with Time Calculations - combining time arithmetic with logical reasoning about connections and delays.
• B4: Positional / Spatial Reasoning - using directional and relational clues in seating arrangements, floors, or positions.
• B5: Algebraic / Numerical Deduction - solving equations or numerical relationships expressed with symbols or words.
• B6: Resource Exchange / Equivalence Reasoning - tracking chains of equivalent value through barter/exchange rates.

The Two-Way Table handles B1, B2, and B4 directly. B3 needs time arithmetic on top. B5 and B6 sometimes need a different approach - working backwards from options or setting up simple equations.

Rarely, a puzzle won't fit neatly into a table - maybe it involves spatial layouts, network connections, or multi-step exchanges. When that happens:

1. Work backwards from the options. Try plugging each answer choice into the constraints. The first one that doesn't violate any rule is your answer. Often 3 of 4 options violate a rule quickly.
2. Process of elimination. If you can rule out 3 choices, the remaining one must be correct - even if you can't fully solve the puzzle.

This is a fallback, not your default. The table works for the vast majority of LP questions.

Remember: Guessing on a 1-mark LP and spending that 90 seconds on a 2-mark Syllogism set is almost always the better trade.

1. Trying to solve the entire puzzle - You only need to answer the specific question asked. Stop the moment you have enough information.
2. Missing hidden constraints - "A before B" means A isn't last and B isn't first. Write these eliminations down immediately.
3. Working in your head - LPs overload working memory fast. Use the table. Write X marks for eliminated cells. Let the paper do the thinking.
4. Spending 2+ minutes on a single question - If you're stuck after 90 seconds, guess and move on. The mark isn't worth the time.

Next lesson: 2.7 Triage & Technique Map