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Floor Puzzle Reasoning: Drawing the Floor Grid and Placing Fixed Clues First

Floor 1 is the bottom • Fixed floors first • Branch on 'between' and 'above' clues • A second column for colours or cities • Counting floors

Banking 📅 Last updated: 2026-10-23

A floor puzzle places a group of people on the floors of a building, one person per floor, and gives clues about who lives where. Seven people can be placed on seven floors in 7! = 5040 ways, so the clues must be used in an order that removes possibilities fast.

Start by drawing the building as a column of boxes and numbering the floors. Unless the question says otherwise, floor 1 is the bottom floor and the numbers rise upwards. Write the numbers on the left so that "above" always means a larger number and "below" a smaller one.

Sort the clues before placing anyone:

  1. Fixed clues name a floor: "T lives on the middle floor", "S lives on the lowest floor".
  2. Linked clues tie someone to an already placed person: "P lives immediately below T".
  3. Branching clues allow two floors: "one person lives between T and Q". Draw both cases side by side.
  4. Negative clues rule something out: "E does not live on floor 1". Use them last, to settle what is still open.
Clue wordingFloor arithmetic
X lives immediately above YX = Y + 1
X lives above YX > Y, any gap
Two people live between X and Ythe floors differ by 3
X lives on the middle floor of 7X = (7 + 1) ÷ 2 = 4

Worked example 1: seven floors

P, Q, R, S, T, U and V live on the seven floors of a building, one on each floor. Floor 1 is the bottom floor.

  1. T lives on the middle floor.
  2. S lives on the lowest floor.
  3. P lives immediately below T.
  4. One person lives between T and Q.
  5. U lives immediately above Q.
  6. V lives below R.

Solution. The fixed clues come first. Clue 1 puts T on floor 4 and clue 2 puts S on floor 1. Clue 3 links P to T, so P is on floor 3. Clue 4 branches: Q is on floor 2 or floor 6. If Q were on floor 2, clue 5 would put U on floor 3, which is P's, so that case fails. Q is on floor 6 and U on floor 7. Floors 2 and 5 remain for R and V, and clue 6 puts V on floor 2 and R on floor 5.

From the bottom: S, V, P, T, R, Q, U.

Check clue 4 on the answer: T is on floor 4 and Q on floor 6, so 6 − 4 − 1 = 1 person lives between them.

Questions often ask for counts too: above R, on floor 5, there are 7 − 5 = 2 people, Q and U.

Harder puzzles give each person a second attribute, such as a favourite colour, a city or a job. Draw a table with one row per floor and one column per attribute. Five people and five colours give 5! × 5! = 14400 combinations, so the table matters even more here. Some clues tie a colour to a floor without naming the person; write the colour in its column and fill in the name later.

Worked example 2: five floors and five colours

A, B, C, D and E live on floors 1 to 5, one per floor. Each likes a different colour: Red, Blue, Green, Yellow or White.

  1. The person who likes Red lives on floor 3.
  2. B lives immediately above the person who likes Red.
  3. D lives on the top floor and does not like White.
  4. The person who likes Green lives on the lowest floor.
  5. A lives immediately above the person who likes Green.
  6. E does not live on floor 1.
  7. B likes Yellow.

Solution. Clue 1 writes Red against floor 3, and clue 2 puts B on floor 4. Clue 3 puts D on floor 5. Clue 4 writes Green against floor 1, and clue 5 puts A on floor 2. C and E share floors 1 and 3, and clue 6 puts E on floor 3 and C on floor 1. B likes Yellow. White and Blue remain for A and D, and D does not like White, so D likes Blue and A likes White.

FloorPersonColour
5DBlue
4BYellow
3ERed
2AWhite
1CGreen
  • ✘ Reading "above" as "immediately above".
  • ✘ Numbering from the top when the question numbers from the bottom.
  • ✘ Forgetting the ground floor when floors start at 0.
  • ✘ Following only one branch of a "between" clue without checking the other.

The same fixed-first method works for rows in linear seating arrangement and for tables in circular seating arrangement. The full list of reasoning topics is in the study hub.

Q1. In puzzle 1 on this page (P to V on floors 1 to 7), who lives between P and R? easy

✅ Answer: (d) T

💡 Explanation: From the bottom the floors are S, V, P, T, R, Q, U. P is on floor 3 and R on floor 5, so the only person between them is T on floor 4.

Q2. In puzzle 1 on this page, who lives immediately above V? medium

✅ Answer: (b) P

💡 Explanation: V lives on floor 2, because V must be below R and floors 2 and 5 were the only ones left. Floor 3, immediately above, belongs to P.

Q3. In puzzle 2 on this page (A to E and five colours), which colour does A like? medium

✅ Answer: (a) White

💡 Explanation: A lives on floor 2, immediately above the Green lover on floor 1. Only White and Blue are left for A and D, and D does not like White, so A likes White.

Q4. In puzzle 2 on this page, who likes Red? hard

✅ Answer: (c) E

💡 Explanation: Red is on floor 3. B is on floor 4, A on floor 2 and D on floor 5. E cannot be on floor 1, so E takes floor 3 and likes Red, leaving floor 1 for C.

Q5. A building has 8 floors, numbered 1 at the bottom to 8 at the top. M lives on floor 3 and N lives four floors above M. How many floors are above N's floor? easy

✅ Answer: (d) 1

💡 Explanation: N lives on floor 3 + 4 = 7. The only floor above floor 7 is floor 8, so 8 − 7 = 1 floor is above N.

Q6. A building's floors are numbered from 0 for the ground floor up to 6 for the top floor. How many floors does the building have? easy

✅ Answer: (b) 7

💡 Explanation: Counting from 0 to 6 includes both ends, so the number of floors is 6 − 0 + 1 = 7. Answering 6 forgets the ground floor.

Is the ground floor floor 0 or floor 1?

It depends on the question, so read the first line carefully. Most bank puzzles say the bottom floor is numbered 1 and the floor above it 2. When a question says ground floor is 0, every floor number shifts down by one.

What does 'above' mean without 'immediately'?

'Above' alone means anywhere higher, not necessarily the next floor. Only 'immediately above' or 'just above' means the very next floor. Treating plain 'above' as 'immediately above' is a common source of wrong arrangements.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 7 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveenkumar on 2026-10-23 against the sources listed above.

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