How to Solve Arrangement Puzzles: Seats, Floors, Schedules and Rankings

The Professional level of the Civil Service Exam includes Analytical Ability, which the CSC describes as covering word association, identifying assumptions and conclusions, and logical reasoning. Arrangement puzzles are a classic way to practise that reasoning: you are given a few clues about people, offices or events, and you must find the one order that satisfies all of them. They look intimidating, but nearly all of them yield to the same five-step method.

The four common types

Type	What is ordered	Typical clue
Linear seating	people at desks or chairs in a row	“Eli sits immediately to the left of Ana.”
Floors	offices or people on floors of a building	“HR is directly above Records.”
Schedules	events across days or time slots	“Writing is held the day after Excel.”
Rankings	people by score, height or age	“Hana scored higher than Ivan but lower than Fe.”

The words differ, but each one is a single line of positions. Left and right, below and above, earlier and later, higher and lower are all the same idea.

The five-step method

1. Draw the line of positions. Write 1 2 3 4 5 (or Mon Tue Wed Thu). Decide which end is which: desk 1 on the left, floor 1 at the bottom, the highest score first.
2. Place the fixed clues first. “Cara sits at desk 3” goes straight onto your diagram.
3. Turn linked clues into blocks. “Eli immediately left of Ana” becomes the block E A. A block of two can only fit in a few places, so list them.
4. Test each possible case against the remaining clues. Cross out any case that breaks a clue. Usually only one survives.
5. Check every clue once more, then answer the questions from your finished diagram.

A worked example

Five clerks (Ana, Ben, Cara, Dan and Eli) sit at desks 1 to 5 from left to right. Cara sits at desk 3. Eli sits immediately to the left of Ana. Ben sits somewhere to the left of Dan. Dan does not sit at desk 5.

Step 1–2. Draw five desks and place Cara:

_ _ C _ _

Step 3. The block E A needs two neighbouring empty desks. With desk 3 taken, it fits only at desks 1–2 or desks 4–5.

Step 4. Test both cases.

• Case 1: E A C _ _. Ben and Dan take desks 4 and 5. Ben must be left of Dan, so Dan is at desk 5, but Dan cannot be at desk 5. Rejected.
• Case 2: _ _ C E A. Ben and Dan take desks 1 and 2. Ben is left of Dan, so Ben is at desk 1 and Dan at desk 2. Every clue is satisfied.

Step 5. Final order: Ben, Dan, Cara, Eli, Ana. Now any question is easy: Ana is at desk 5, Eli is immediately right of Cara, and two clerks (Cara and Eli) sit between Dan and Ana.

Notice that we did not try all 120 possible orders. Placing the fixed clue and the block cut the work to two cases.

Rankings: chain the clues

Ranking puzzles are even quicker if you write the clues as one chain. Take: Hana scored higher than Ivan but lower than Fe. Jo had the lowest score. Gil scored higher than Fe.

• Hana higher than Ivan, lower than Fe: Fe > Hana > Ivan
• Gil higher than Fe: Gil > Fe > Hana > Ivan
• Jo is lowest: Gil > Fe > Hana > Ivan > Jo

When the chain includes everyone, the ranking is complete. If two people are not connected in the chain, the puzzle may have more than one answer, and the question will usually ask what “must” or “could” be true.

Traps to avoid

• “Immediately” versus “somewhere”. Immediately to the left means next to; somewhere to the left means anywhere on that side.
• Left and right from whose view? In these puzzles, left and right are from the reader’s view of the row unless the puzzle says people face you.
• “Directly above”. It means the next floor up, not any higher floor.
• “Between”. “How many are between A and B” counts only the people strictly in between, not A and B.
• Stopping too early. If you have found an order that works, but you skipped testing other cases, check quickly that no second order also works.

Speed tips for the exam

• Spend a minute building the diagram before reading the questions in detail. Several questions usually share one puzzle, so a good diagram answers them all.
• Use initials (A, B, C) and short marks such as E A for blocks and ≠5 for “not at desk 5”.
• If a puzzle is taking too long, mark it and return later. One stubborn puzzle should not cost you easier items. Our guide on time management during the CSE explains how to pace yourself.

Practise

Try the method on our logic puzzles and arrangements set. Every puzzle there was checked by a script that tried every possible order and confirmed that exactly one fits. For the other parts of Analytical Ability, see our analytical ability guide.