Logical Puzzles

Logical puzzles are one of the most common question types in the UCAT Decision Making subtest. These questions present a set of constraints (rules or conditions) and ask you to determine what must be true, what could be true, or what arrangement is valid. This lesson teaches you a systematic approach to solving them efficiently under time pressure.

---

What Are Logical Puzzles in the UCAT?

Logical puzzles in the DM subtest typically involve:

• Scheduling problems — arranging events, appointments, or activities in a sequence
• Seating arrangements — placing people around a table or in a row according to rules
• Ordering problems — determining the correct sequence of items based on comparative clues
• Allocation problems — assigning people to teams, rooms, or tasks based on constraints
• Matching problems — pairing items from two or more categories (e.g., matching people to hobbies and locations)

These questions usually provide 4-6 constraints and ask you to determine which arrangement satisfies all of them, or to identify which single statement must be true.

---

The Systematic Approach

The key to solving logical puzzles under time pressure is to follow a structured, repeatable method rather than trying to reason through the problem in your head.

Step 1: Read All Constraints Before Starting

Read every constraint carefully. Do not start placing items until you understand all the rules. This prevents you from setting up a framework that you later need to scrap.

Step 2: Identify the Framework

Decide what kind of structure you need:

Problem Type	Framework
Linear ordering (1st, 2nd, 3rd...)	Number line or slots
Seating around a table	Circular diagram
Two-category matching	Grid or table
Three-category matching	Multi-row table
Scheduling across time slots	Time grid

Step 3: Place the Most Constrained Items First

Look for items that have the most restrictions or items that are fixed in position. Place these first, as they reduce the possibilities for everything else.

Step 4: Apply Remaining Constraints

Work through the remaining constraints one by one, eliminating impossible arrangements at each step.

Step 5: Check Your Answer Against All Constraints

Before selecting an answer, verify that your arrangement satisfies every single constraint. A common error is satisfying most constraints but violating one.

---

Worked Example 1: Linear Ordering

Scenario:

Five friends — Amara, Ben, Chloe, Daniel, and Elena — finish a race in five distinct positions (1st through 5th). The following information is known:

• Amara finishes 1st
• Ben finishes immediately before Chloe
• Elena finishes 3rd
• Daniel does not finish last

Question: Who finishes 2nd?

Solution

Step 1: Set up five slots and place the fixed items:

1st	2nd	3rd	4th	5th
Amara	?	Elena	?	?

Step 2: Ben finishes immediately before Chloe. They form a consecutive pair. Available slots are 2nd, 4th, and 5th. The possible consecutive pairs are: (2nd, 3rd) — but 3rd is Elena, so no. (4th, 5th) — this works.

1st	2nd	3rd	4th	5th
Amara	?	Elena	Ben	Chloe

Step 3: Daniel is the only person remaining. The only open slot is 2nd. Check: Daniel does not finish last — 2nd is not last. ✓

1st	2nd	3rd	4th	5th
Amara	Daniel	Elena	Ben	Chloe

Step 4: Verify all constraints:

• Amara finishes 1st ✓
• Ben (4th) is immediately before Chloe (5th) ✓
• Elena finishes 3rd ✓
• Daniel (2nd) does not finish last ✓

Answer: Daniel finishes 2nd.

Key Learning Point: Always set up a grid, place fixed items first, then work through constraints systematically. Verify every constraint before selecting your answer.

---

Worked Example 2: Seating Arrangement

Scenario:

Six doctors — A, B, C, D, E, and F — sit around a circular table with six seats. The following rules apply:

• A sits directly opposite D
• B sits next to A
• C does not sit next to E

Question: Who sits directly opposite B?

Solution

Step 1: Draw a circular table with six positions (1–6). In a 6-seat circle, position 1 is opposite position 4, position 2 is opposite position 5, position 3 is opposite position 6.

Step 2: Place A and D opposite each other. Let A = position 1, D = position 4.

Step 3: B sits next to A. A is at position 1, so B is at position 2 or position 6.

Case 1: B at position 2. B is opposite position 5. Remaining: C, E, F for positions 3, 5, 6.

• C does not sit next to E. Position 3 is next to positions 2 and 4. Position 5 is next to positions 4 and 6. Position 6 is next to positions 5 and 1.
• If C = 3 and E = 5: are they next to each other? No (positions 3 and 5 are not adjacent). ✓ F = 6.
• Check: C(3) neighbours are B(2) and D(4). E(5) neighbours are D(4) and F(6). C and E are not adjacent. ✓

Answer: The person opposite B (position 2) is whoever sits at position 5, which is E.