Logical Puzzles

Logical Puzzles are the second question type in the DM section. They give you a set of rules 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.

Logical Puzzles come in many permutations - scheduling, routing, resource exchanges, algebraic word puzzles - but on most papers the two dominant families are rules-about-people (matching characteristics to individuals) and ordering (placing people or things into a sequence). The technique below targets those two families directly; the rarer variants are covered in the When the table doesn't fit section.

These make up roughly 5-6 questions (~14% of DM). Format: 4 options, 1 mark.

Target time and triage

Logical Puzzles have the worst time-to-mark ratio in DM - a single 1-mark puzzle can take 60-120 seconds, the same time as a 2-mark Syllogism set.

Default strategy: skip and flag. Come back only with banked time. The exception is straightforward 3-variable, simple-constraint puzzles, where the technique below makes them mechanical.

Most Logical Puzzles you see will fall into one of two families. Recognising which one you're on shapes the table you draw.

1. Two-variable matching questions. A group of people (or objects) each have two characteristics that need matching up - e.g. five workmates each with a different car colour AND a different leave time. You match each person to one of each. Use a two-way table.
2. Ordering / positioning questions. People in a line, around a table, on numbered floors, or in a sequence of days. You only need to track one variable per entity (their position). Use a one-way table - effectively a single row of slots.

Ordering questions are the simpler form, so we'll cover the harder two-variable case first; the technique reduces cleanly when there's only one variable.

Six steps. Stick to them - the table works for the vast majority of these questions.

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.

2. Identify the main variable. This is the set that appears most often in the clues - usually the people. They go in the leftmost column of your table.

3. Draw the right type of table.

• Two-variable matching → two-way table: people as rows, attribute A as columns on one side, attribute B as columns on the other side.
• Ordering → one-way table: a single row of positions.

4. Fill in absolute facts and hidden constraints. "James drives a red car" goes in immediately. "James leaves before Kathy" has a hidden constraint (see below) - fill those crosses in too.

5. Look for forced cells. When a row or column has only one option remaining, it MUST be correct. Fill it and let the consequences cascade.

6. Stop the moment the answer emerges. Don't waste time completing the table. The most common time-sink in logical puzzles is finishing the grid out of habit. Once you can answer the question, move on.

Every clue has an explicit meaning AND a hidden constraint that you can fill in immediately:

Spot the hidden constraint and add the eliminations to your table before working any further. This is what separates a 30-second puzzle from a two-minute one.

Three small marks make the table dramatically easier to work with:

Single-letter abbreviations. Under time pressure, use first letters everywhere: H for Harriet, R for red, etc. The table needs to be readable at a glance, not pretty.

Dotted arrow → for ordering. When a clue tells you "Maggie leaves before James," draw a dotted arrow from Maggie's row to James's row. The arrow is a permanent reminder that this ordering constraint is in play.

Solid arrow ⇒ for biconditional links. When a clue couples two attributes - e.g. "The person who drives the silver car leaves at 5:30" - draw a solid arrow between the silver column and the 5:30 column. Then: whatever you write into one of those cells, carbon-copy to the linked cell. This is one of the highest-yield moves in LP.

Five workmates - Harriet, James, Kathy, Leo, and Maggie - each drive a different colour car (red, silver, black, white, blue) and leave the office at different times (5:00, 5:15, 5:30, 5:45, 6:00).

James drives a red car. James leaves before Kathy. The person who drives the silver car leaves at 5:30. Harriet does not drive the black or white car. Leo leaves last. Maggie's car is white. Maggie leaves before James. Leo does not drive a black car.

Question: What colour car does Kathy drive?

Step 1 - Read the question.

Goal: Kathy's car colour. Stop the moment this is forced.

Step 2 - Main variable.

The workmates. They go down the left column.

Step 3 - Draw the table.

Two-way table: names down the left, colours as the first block of columns, times as the second block.

        |  R  |  S  |  B  |  W  |  U  ||  5:00 | 5:15 | 5:30 | 5:45 | 6:00
   H    |     |     |     |     |     ||       |      |      |      |
   J    |     |     |     |     |     ||       |      |      |      |
   K    |     |     |     |     |     ||       |      |      |      |
   L    |     |     |     |     |     ||       |      |      |      |
   M    |     |     |     |     |     ||       |      |      |      |

Step 4 - Fill facts and hidden constraints.

"James drives a red car." - tick J/R. Cross out the rest of J's row in the colour block, and the rest of the R column.

"Maggie's car is white." - tick M/W. Cross the rest of M's row and W column.

"Harriet does not drive the black or white car." - cross H/B and H/W.

"Leo leaves last." - tick L/6:00.

"James leaves before Kathy." - dotted arrow J ⇢ K. Hidden constraint: J ≠ 6:00 and K ≠ 5:00.

"Maggie leaves before James." - dotted arrow M ⇢ J. Hidden constraint: M ≠ 6:00 (already true via Leo) and J ≠ 5:00. Combined with the J ⇢ K arrow: M comes before J which comes before K.

"The person who drives the silver car leaves at 5:30." - solid arrow between the S column and the 5:30 column. Anything that gets ticked in one carbon-copies to the other.

"Leo does not drive a black car." - cross L/B.

Step 5 - Forced cells.

Look at the B column. Only K is left (H, J, L crossed; M is white). → K = black.

Look at the U column. Available: H, K, L. K is now black. H must be silver or blue (not red/black/white). The solid arrow says silver-driver leaves at 5:30 - but Leo leaves at 6:00, so Leo ≠ silver → Leo = blue. → L/U ticked.

That leaves silver for Harriet. → H = silver. Solid arrow: H leaves at 5:30.

Stop.

Question is answered: Kathy drives a black car.

For completeness (not required in the exam), the rest falls out: times remaining are 5:00, 5:15, 5:45 for M, J, K. Ordering M before J before K → M = 5:00, J = 5:15, K = 5:45.

For pure ordering questions, the table is just a single row of positions. The same hidden-constraint rules apply. Build the table incrementally, one clue at a time, and watch each clue narrow what can sit in each cell.

Five people - Anna, Ben, Cara, Dan, Eve - finish a race in some order. Eve finishes last. Anna finishes before Ben. Cara finishes immediately after Dan. Dan does not finish first.

Question: In what position does Cara finish?

Start with an empty row.

   pos 1   |   pos 2   |   pos 3   |   pos 4   |   pos 5
   ?       |   ?       |   ?       |   ?       |   ?

Clue 1: "Eve finishes last." Drop E into pos 5 and eliminate E from every other cell.

   pos 1   |   pos 2   |   pos 3   |   pos 4   |   pos 5
   ¬E      |   ¬E      |   ¬E      |   ¬E      |   E

Clue 2: "Anna finishes before Ben." Hidden constraint: A cannot be last (already E anyway) and B cannot be first. Add B's elimination.

   pos 1   |   pos 2   |   pos 3   |   pos 4   |   pos 5
   ¬E ¬B   |   ¬E      |   ¬E      |   ¬E      |   E

Clue 3: "Cara immediately after Dan." D and C sit in adjacent positions with D first, and neither can be in pos 5 (E is there). Hidden constraint on C: C cannot be in pos 1 (because D would have to be in pos 0). Hidden constraint on D: D cannot be in pos 4 (because C would have to be in pos 5, but E is there).

   pos 1   |   pos 2   |   pos 3   |   pos 4   |   pos 5
   ¬E ¬B   |   ¬E      |   ¬E      |   ¬E      |   E
   ¬C      |           |           |   ¬D      |

Clue 4: "Dan does not finish first." Add D's elimination from pos 1.

   pos 1   |   pos 2   |   pos 3   |   pos 4   |   pos 5
   ¬E ¬B   |   ¬E      |   ¬E      |   ¬E      |   E
   ¬C ¬D   |           |           |   ¬D      |

Now look at pos 1. It can't be E, B, C, or D. Only A remains. Force it.

   pos 1   |   pos 2   |   pos 3   |   pos 4   |   pos 5
   A       |   ?       |   ?       |   ?       |   E

Where can the (D, C) pair sit? D must come immediately before C, and D can't be in pos 1 or pos 4. So (D, C) is either (pos 2, pos 3) or (pos 3, pos 4). In both cases Cara is in pos 3 or pos 4 - not yet forced.

Try each:

• (D, C) = (2, 3): leaves pos 4 for B. Check "A before B": A=1, B=4 ✓.
• (D, C) = (3, 4): leaves pos 2 for B. Check "A before B": A=1, B=2 ✓.

Both orderings satisfy every clue. Cara is in pos 3 or pos 4 - the puzzle as stated doesn't force a single answer.

Rarely a puzzle involves spatial layouts, network connections, or chains of barter exchanges that don't fit a table. Fallback moves:

1. Plug each option into the constraints. Whichever one doesn't violate a rule is your answer.
2. Process of elimination. Ruling out three options forces the fourth.

These are fallbacks, not your default. The table works for the majority of logical puzzles.

Read the stimulus. Count the variables and rules.
    |
    ├── 3-4 people/items, 3-4 simple rules
    │   → Attempt. Should solve in 60-90s.
    │
    ├── 5+ people/items OR 4+ complex rules
    │   (conditional chains, "if X then Y but only if Z")
    │   → Flag immediately. Guess from options.
    │     Return only with 2+ minutes banked.
    │
    └── Algebraic puzzle (symbols and equations)
        → Attempt if equations are simple.
          Flag if more than 2 unknowns.

The maths is brutal: 1 mark in 90 seconds versus 2 marks per syllogism set in the same time. Always do Recognising Assumptions, Probability, Syllogisms, and Interpreting Information first. Come to Logical Puzzles only with banked time.

1. Trying to solve the entire puzzle. Stop the moment you can answer the question.
2. Missing hidden constraints. "A before B" means A isn't last AND B isn't first - both go on the table immediately.
3. Working in your head. Logical puzzles overload working memory fast. Use the table; let the paper do the thinking.
4. Spending 2+ minutes on one question. If you're stuck at 90s, guess and move on. The mark isn't worth it.
5. Drawing ovals or circles instead of a proper grid. The two-way table needs straight rows and columns so you can scan a column for the only remaining option. Sketchy diagrams hide forced cells.

Logical Puzzles test six skills:

• B1: Constraint Satisfaction / Elimination - systematic elimination using multiple constraints. The core skill - handled by the two-way table.
• B2: Sequential / Temporal Ordering - chronological order from relative information. One-way table + dotted arrows.
• B3: Scheduling / Route Planning with Time Calculations - combining time arithmetic with logical reasoning about connections and delays.
• B4: Positional / Spatial Reasoning - directional and relational clues in seating, floors, or positions.
• B5: Algebraic / Numerical Deduction - solving equations or numerical relationships expressed in words.
• B6: Resource Exchange / Equivalence Reasoning - tracking chains of equivalent value through barter 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.