Floor and box puzzles for IBPS PO

Floor and box puzzles are the gentlest way into IBPS PO puzzles, and they still decide marks. The frame is a single vertical line, so there is no left and right to confuse. What the puzzle tests is whether you read each clue exactly and whether you can carry two possibilities forward without losing track.

In a floor puzzle, each person lives on a different floor, often with a second variable such as a colour, a city or a profession. In a box puzzle, boxes are stacked one on top of another, often holding different numbers of items. The method is the same for both.

Reading the clues exactly

The case-building method

1. Draw the frame. Floors from the top (highest number) down to 1, with a column for each variable.
2. Find the anchors. A definite clue ("the one who likes Green lives on the top floor") goes in at once.
3. Build cases. When a clue allows two positions, draw Case 1 and Case 2 side by side. Do not choose one in your head.
4. Push every case forward with each new clue. A case dies the moment any clue cannot be satisfied.
5. Use negative clues last. "S does not like Blue" often decides the final two slots.
6. Check every clue against the final table before answering.

Why cases beat guessing: a guess that turns out wrong forces you to start over. Written cases let you keep every deduction you have already made; only the dead case is thrown away.

Worked set 1: floors and colours

Seven people, P, Q, R, S, T, U and V, live on seven floors of a building, one on each floor. The bottom floor is numbered 1 and the top floor 7. Each likes a different colour: Red, Blue, Green, Yellow, White, Black and Pink.

1. P lives on an odd-numbered floor, but not on the top or the bottom floor.
2. Only two people live between P and U.
3. U likes Black.
4. S lives on a floor below U.
5. Only one person lives between U and the one who likes Red.
6. T likes Red.
7. The one who likes Pink lives immediately below T.
8. The one who likes Green lives on the top floor.
9. The one who likes White lives on an odd-numbered floor above T.
10. V lives immediately above the one who likes White.
11. R lives on a floor above V.
12. S does not like Blue.

Building the cases

• Clue 1: P is on floor 3 or 5.
• Clue 2: If P = 5, U = 2 (floor 8 does not exist). If P = 3, U = 6 (floor 0 does not exist). So Case 1: P = 5, U = 2 and Case 2: P = 3, U = 6. U likes Black in both (clue 3).
• Clues 5 and 6: T is two floors from U. Case 1: T = 4. Case 2: T = 4 as well (floor 8 does not exist).
• Clue 7: Pink is on floor 3. In Case 2, that is P.
• Clue 8: Green is on floor 7.
• Clue 9: White is on an odd floor above 4, so floor 5 or 7. Floor 7 is Green, so White = floor 5.
• Clue 10: V is immediately above White, so V = 6. In Case 2, floor 6 is U. Case 2 fails.

Finishing Case 1

• P (floor 5) likes White. V = 6.
• Clue 4: S is below U (floor 2), so S = 1.
• Floors 3 and 7 remain for Q and R. Clue 11: R is above V, so R = 7 and Q = 3. Q likes Pink.
• Blue and Yellow remain for V and S. Clue 12: S likes Yellow, V likes Blue.

Questions

1. Who likes Blue? V.
2. How many people live between S and the one who likes White? Three (U, Q and T).
3. Which colour does the person immediately above T like? White (P).
4. Who lives immediately below the one who likes Green? V.
5. If the seven moved so that P is on floor 1, Q on 2, and so on up to V on 7, how many would stay on their present floor? None.

Worked set 2: boxes and items

Six boxes, J, K, L, M, N and O, are stacked one above another. Position 1 is at the bottom and position 6 at the top. Each box holds a different number of items: 12, 15, 18, 20, 24 or 30.

1. Only three boxes are kept between K and L.
2. L holds 15 items.
3. The box with 24 items is kept immediately above L.
4. O is kept immediately below K.
5. The box with 20 items is kept immediately below O.
6. The box with 12 items is kept immediately above J.
7. J is kept below M.
8. K holds more items than M.

Building the cases

• Clue 1: K and L are at positions 1 and 5, or 2 and 6, in some order.
• Clue 3: something sits above L, so L is not at 6. Clue 4: something sits below K, so K is not at 1.
• That leaves Case 1: L = 1, K = 5 and Case 2: L = 2, K = 6.
• Clues 3, 4 and 5: Case 1 has 24 at position 2, O at 4 and 20 at 3. Case 2 has 24 at 3, O at 5 and 20 at 4.
• Clue 6 in Case 2: J can be at 1, 3 or 4. At 1, the box above is L with 15. At 3, the box above holds 20. At 4, the box above is O, so O holds 12. Then M and N take positions 1 and 3, both below J, which breaks clue 7. Case 2 fails.
• Clue 6 in Case 1: J can be at 2, 3 or 6. At 2, the box above holds 20, not 12. At 6, nothing is above. So J = 3 with 20 items, and O holds 12.
• Clue 7: M is above J, so M = 6 and N = 2 with 24 items.
• Clue 8: K and M share 18 and 30; K holds more, so K has 30 and M has 18.

Questions

1. Which box is at the top? M.
2. How many items are in the box immediately below K? 12 (O).
3. How many boxes are kept between N and M? Three (J, O and K).
4. What is the total number of items in the boxes above J? 60 (12 + 30 + 18).
5. Which box holds 24 items? N.

Common mistakes

• Reading "above" as "immediately above". Mark "immediately" clues with a different symbol in your notes.
• Taking only one direction from a "between" clue. Write both, then let the frame's size kill one.
• Forgetting the attribute clues once the people are placed. In set 1, the colours need their own column from the start.
• Dropping a case too early. A case dies only when a clue fails, not when it "looks less likely".
• Skipping the final check. One misread clue costs all five answers.

Practice puzzle

Eight people, A, B, C, D, E, F, G and H, live on eight floors of a building, one on each floor. The bottom floor is 1 and the top floor 8.

1. B lives on an even-numbered floor below floor 6.
2. A lives above B, with only one person between them.
3. H lives immediately below A.
4. F lives below H, with only one person between them.
5. F lives on an odd-numbered floor, above E.
6. C lives immediately above E.
7. G lives on an odd-numbered floor.

Questions

1. Who lives on the top floor?
2. How many people live between C and H?
3. Who lives immediately above B?
4. On which floor does G live?
5. How many people live above A?

Answers

B is on floor 2 or 4. If B = 2, then A = 4, H = 3 and F = 1, but F must be above E, so this case fails. So B = 4, A = 6, H = 5 and F = 3. E is below F and C is immediately above E, so E = 1 and C = 2. Floors 7 and 8 remain; G is odd, so G = 7 and D = 8.

1. D.
2. Two (F and B).
3. H.
4. Floor 7.
5. Two (G and D).

What to do next

• Solve two floor or box puzzles a day for a week, writing cases side by side every time.
• Time yourself: aim for set 1 above in under six minutes on a fresh attempt next week.
• Move on to scheduling puzzles, which use the same method on a timeline, and see the reasoning plan for where puzzles fit in your week.