Floor and flat puzzles for SBI PO

In a floor puzzle, each person lives on a different floor of one building, usually with a second attribute: a city, a fruit, a colour, a profession. Floor puzzles are a staple of bank PO reasoning because they test exactly what the section is built to test: reading clues precisely and keeping two or three possibilities open without losing track.

The good news is that the frame never changes. It is a single vertical line. Once your method is fixed, a floor puzzle is mostly bookkeeping.

Reading the clues

The case-building method

1. Draw the frame. One row per floor, top floor at the top, with a column for each variable.
2. Place definite clues first. "L lives on the lowest floor" goes straight in.
3. Use clues that link to a placed person. "O lives immediately above M" is useless until M is placed.
4. Branch on the first clue with two options. Draw Case 1 and Case 2 side by side and carry both forward.
5. Test every open case against each new clue. Cross out a case the moment it breaks.
6. Keep attribute clues in a side list ("the person from Delhi lives immediately above the person from Jaipur") until enough floors are fixed to use them.
7. Check all the clues against the final grid before you answer.

Warm-up: a six-floor puzzle

Six people, J, K, L, M, N and O, live on six floors of a building, one per floor. Floor 1 is the bottom and floor 6 the top. Each likes a different fruit: apple, banana, grape, mango, orange and pear.

1. L lives on the lowest floor and likes orange.
2. J lives on an even-numbered floor, immediately below the person who likes apple.
3. Only one person lives between J and M, and M lives below J.
4. O likes pear and lives immediately above M.
5. The person who likes grape lives on the top floor.
6. K lives above N.
7. The person who likes banana lives immediately below the person who likes pear.

Solving:

• L is on floor 1 (clue 1).
• J is on an even floor with someone above, so 2 or 4. M is two floors below J (clue 3). J on 2 would put M on floor 0, so J is on 4 and M on 2, and apple is on floor 5.
• O is immediately above M: O on 3, liking pear.
• K and N take floors 5 and 6, with K above N: K on 6, N on 5. N likes apple; K, on the top floor, likes grape.
• Banana is immediately below pear (floor 3), so on floor 2: M likes banana. That leaves mango for J.

Who likes mango? J. How many people live between L and J? Two (M and O).

An SBI PO-level puzzle: eight floors, two variables

Eight people, P, Q, R, S, T, U, V and W, live on eight floors of a building, one per floor. Floor 1 is the bottom and floor 8 the top. Each is from a different city: Delhi, Mumbai, Pune, Jaipur, Kochi, Patna, Surat and Indore.

1. S lives on an odd-numbered floor above floor 4.
2. Only two people live between S and the person from Mumbai.
3. P lives immediately above the person from Mumbai and immediately below the person from Pune.
4. W lives immediately above S.
5. The person on the top floor is from Kochi, and W is not from Kochi.
6. Only one person lives between V and W.
7. Q lives immediately below T.
8. Only one person lives between R and P.
9. The person from Delhi lives immediately above the person from Jaipur.
10. Only one person lives between the person from Surat and the person from Jaipur, and the person from Surat lives lower.
11. The person from Indore lives below the person from Patna.

Step 1: branch on S. Clue 1 allows floor 5 or 7.

• Case 1: S on 5. Case 2: S on 7.

Step 2: place W and test the cases. W is immediately above S (clue 4).

• Case 1: W on 6. Case 2: W on 8.
• Clue 5: the person on floor 8 is from Kochi, and that is not W. Case 2 fails. So S is on 5 and W on 6.

Step 3: Mumbai, P and Pune. Only two people live between S (floor 5) and the Mumbai person, so Mumbai is on 2 or 8. Floor 8 is Kochi, so Mumbai is on 2. By clue 3, P is on 3 and Pune is on 4.

Step 4: R. Only one person lives between R and P (floor 3), so R is on 1 or 5. S holds 5, so R is on 1.

Step 5: V, Q, T and U. The floors left are 2, 4, 7 and 8. V is two floors from W (floor 6), so on 4 or 8.

• If V is on 8, the floors left for Q, T and U are 2, 4 and 7. Q must be immediately below T (clue 7), and no two of these are adjacent. This fails.
• So V is on 4. Q and T take the adjacent pair 7 and 8: Q on 7, T on 8. U is on 2.

Step 6: the cities. Floors 2 (Mumbai), 4 (Pune) and 8 (Kochi) are taken. The rest go on floors 1, 3, 5, 6 and 7.

• Delhi is immediately above Jaipur (clue 9), and Surat is two floors below Jaipur (clue 10).
• Jaipur on 5 gives Delhi 6 and Surat 3: all free. Jaipur on 6 would need Surat on 4, which is Pune. Jaipur on 3 would need Delhi on 4, also Pune. Jaipur on 7 would put Delhi on 8, which is Kochi, and Jaipur on 1 leaves no floor for Surat.
• So Jaipur 5, Delhi 6, Surat 3. Patna and Indore take 1 and 7, with Indore lower: Indore 1, Patna 7.

Checked by testing every possible arrangement: this is the only one that fits all eleven clues.

Questions:

1. Who is from Patna?
2. How many people live between U and W?
3. On which floor does the person from Surat live?
4. Who lives immediately above the person from Jaipur?
5. How many people live above the person from Pune?

Answers:

1. Q.
2. Three: P, V and S.
3. Floor 3 (P).
4. W, who is from Delhi.
5. Four: S, W, Q and T.

Flat puzzles

Some puzzles add flats: for example, flat A and flat B on each floor, with flat A to the west of flat B. Draw two columns per floor and treat each flat as a separate cell. Clues such as "lives in the same flat type as" or "lives to the east of" then refer to the column. The method is unchanged; only the frame is wider.

Common mistakes

• Treating "above" as "immediately above".
• Counting the end people when a clue says how many live between.
• Forgetting a negative clue ("W is not from Kochi"). Mark it on the grid with a cross as soon as you read it.
• Dropping a case too early. Cross a case out only when a clue actually breaks it.

Practice puzzle

Seven people, A, B, C, D, E, F and G, live on seven floors, one per floor. Floor 1 is the bottom. Each likes a different colour: red, green, blue, white, black, yellow and pink.

1. A lives on an even-numbered floor below floor 6.
2. Only two people live between A and the person who likes red, who lives above A.
3. G likes blue and lives immediately above A.
4. B likes green and lives immediately below the person who likes red.
5. F lives immediately below A.
6. D lives on the lowest floor, and C lives immediately above D.
7. The person who likes white lives immediately above F.
8. Only one person lives between the people who like pink and black.
9. The person who likes black lives above the person who likes yellow.

Questions:

1. Who likes yellow?
2. Which colour does E like?
3. How many people live between D and G?
4. On which floor does F live, and which colour does F like?

Answers:

1. C. A is on 2 or 4. If A were on 2, F would be on 1, but D is on 1. So A is on 4, F on 3, G on 5, red on 7, B on 6 and C on 2, leaving E on 7. White is on 4. Pink and black take floors 1 and 3, with yellow on 2; black is above yellow, so black is on 3 and pink on 1.
2. Red (floor 7).
3. Three: C, F and A.
4. Floor 3, black.

What to do next

• Solve the eight-floor puzzle again from a blank page, without looking, in under 7 minutes.
• Do two floor puzzles a day for a week, drawing every case.
• Move on to box puzzles, which use the same vertical frame with different wording, and see the reasoning plan for where this fits.