Logical Puzzles: Ordering and Sequencing

Ordering and sequencing puzzles are among the most common logical puzzle types in the UCAT Decision Making subtest. They require you to determine the correct order of items, people, or events based on a set of clues. This lesson provides a systematic method for solving these puzzles accurately and quickly, with fully worked examples that demonstrate the approach.

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What Are Ordering and Sequencing Puzzles?

These puzzles present a set of items (typically 4–6) that must be placed in a linear sequence (first to last, shortest to tallest, earliest to latest, etc.) based on comparative clues.

Typical Clue Types

Clue type	Example	What it tells you
Direct position	"A is first"	A is fixed in position 1
Relative order	"B is before C"	B is somewhere earlier than C (not necessarily immediately)
Immediately before/after	"D is immediately before E"	D and E are adjacent, with D first
Not in a position	"F is not last"	F can be in any position except the last
Gap constraints	"There is exactly one item between G and H"	G and H have one item separating them
Endpoint constraints	"I is either first or last"	I is at one end of the sequence

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The Systematic Method

Step 1: Set Up Empty Slots

Draw a row of empty slots numbered 1 through N (where N is the number of items).

1	2	3	4	5
_	_	_	_	_

Step 2: Place Fixed Items

If any item has a defined position, write it in immediately.

Step 3: Identify Constrained Pairs

Look for "immediately before/after" clues — these create blocks that must stay together. Treat the block as a single unit when considering positions.

Step 4: Apply Relative Order Clues

For "A is before B" clues, write A...B to remind yourself of the direction, and eliminate any arrangement where B appears before A.

Step 5: Eliminate Using "Not" Constraints

Cross out impossible positions for items with "not in position X" clues.

Step 6: Combine Constraints to Deduce Positions

Often, combining two or more constraints will force an item into a single position. Look for these forced placements.

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Worked Example 1: Five Items in Order

Five patients — Ahmed, Bola, Chen, Deepa, and Ella — arrive at a clinic at five different times. The following information is known:

• Bola arrives before Deepa
• Chen arrives immediately after Ahmed
• Ella arrives first
• Ahmed does not arrive last

Question: In what position does Deepa arrive?

Step 1: Set up slots.

1	2	3	4	5
_	_	_	_	_

Step 2: Ella arrives first.

1	2	3	4	5
Ella	_	_	_	_

Step 3: Chen arrives immediately after Ahmed → they form a block [Ahmed, Chen]. This block needs two consecutive slots from positions 2–5.

Possible positions for the [Ahmed, Chen] block: (2,3), (3,4), or (4,5).

Step 4: Ahmed does not arrive last. If the block were at (4,5), Ahmed would be 4th and Chen 5th — Ahmed is not last, so this is allowed. Actually, "Ahmed does not arrive last" means Ahmed ≠ position 5. In the (4,5) block, Ahmed = 4, Chen = 5 — fine. All three positions work so far.

Step 5: Bola arrives before Deepa. The remaining people after placing Ella and the [Ahmed, Chen] block are Bola and Deepa, and Bola must come first.

Let's try each position for the [Ahmed, Chen] block:

Case 1: [Ahmed, Chen] at (2,3). Remaining slots: 4, 5 for Bola and Deepa. Bola before Deepa → Bola = 4, Deepa = 5.

1	2	3	4	5
Ella	Ahmed	Chen	Bola	Deepa

All constraints satisfied? Ella first ✓, Chen immediately after Ahmed ✓, Bola (4) before Deepa (5) ✓, Ahmed (2) not last ✓. Valid.

Case 2: [Ahmed, Chen] at (3,4). Remaining slots: 2, 5 for Bola and Deepa. Bola before Deepa → Bola = 2, Deepa = 5.

1	2	3	4	5
Ella	Bola	Ahmed	Chen	Deepa

All constraints satisfied? ✓ Valid.

Case 3: [Ahmed, Chen] at (4,5). Remaining slots: 2, 3 for Bola and Deepa. Bola before Deepa → Bola = 2, Deepa = 3.

1	2	3	4	5
Ella	Bola	Deepa	Ahmed	Chen

All constraints satisfied? Ahmed (4) not last ✓. All good. Valid.

Three valid arrangements exist. Deepa is in position 5, 5, or 3 respectively.