Box puzzles for SBI PO

A box puzzle places boxes in a single stack, one above another. The frame is the same vertical line as a floor puzzle, but the wording is not. Boxes are "placed" or "kept", the gaps are counted in boxes, and the second variable is often a colour, a weight or the number of items inside. Many candidates who are comfortable with floor puzzles lose marks here only because they misread a phrase.

This guide covers the wording, the method, one fully worked SBI PO-level stack and a practice puzzle.

Reading the wording

The case-building method

1. Draw the stack with positions numbered from the bottom, and a column for each variable.
2. Place definite clues first, such as "E is at the bottom".
3. Branch on the first clue with two possibilities. Draw both cases side by side.
4. Test each new clue on every open case. A case that cannot fit a clue is crossed out at once.
5. Hold comparison clues ("R is heavier than Q") in a side list until the positions are fixed. They are best used last, to pick between the remaining options.
6. Check all clues against the final stack before answering.

An SBI PO-level puzzle: seven boxes, seven colours

Seven boxes, A, B, C, D, E, F and G, are placed one above another. Position 1 is the bottom and position 7 the top. Each box is a different colour: red, blue, green, yellow, white, black and orange.

1. Only one box is placed between box D and box A, and D is below A.
2. Box A is placed at an odd-numbered position above the middle of the stack.
3. Box G is placed immediately above box D.
4. Box A is blue, and the red box is placed immediately above it.
5. Only three boxes are placed between the red box and box B.
6. The orange box is placed immediately below box B.
7. Box E is placed below box B.
8. Box C is placed above the red box.
9. The black box is placed immediately above the yellow box.
10. Only one box is placed between the green box and the black box.

Step 1: branch on A. The middle of a seven-box stack is position 4, so clue 2 puts A at 5 or 7. Clue 1 puts D two positions below A, and clue 3 puts G immediately above D.

Step 2: test clue 4. The red box is immediately above A. In Case 2, A is at the top and nothing is above it. Case 2 fails. So A is at 5 and blue, the red box is at 6, G at 4 and D at 3.

Step 3: B, the orange box and E. Only three boxes lie between the red box (6) and B, so B is four positions away: position 2. The orange box is immediately below B, at 1. E is below B (clue 7), and the only position below 2 is 1, so E is at 1 and orange.

Step 4: C and F. Positions 6 and 7 are left for C and F. C is above the red box at 6, so C is at 7 and F is at 6, red.

Step 5: the last four colours. Green, yellow, white and black go to positions 2, 3, 4 and 7.

• Black is immediately above yellow (clue 9): yellow 2 and black 3, or yellow 3 and black 4. (Position 7 cannot hold black above yellow, because 6 is red.)
• If black is at 3, green must be at 1 or 5 (clue 10). Those are orange and blue. This fails.
• So black is at 4 and yellow at 3. Green is two away from black: position 2 or 6. Position 6 is red, so green is at 2, and white goes to 7.

Every other arrangement breaks at least one clue; this is the only solution.

Questions:

1. Which box is black?
2. How many boxes are placed between E and G?
3. Which box is at the top, and what colour is it?
4. What colour is box D?
5. How many boxes are placed above the green box?

Answers:

1. G.
2. Two: B and D.
3. C, white.
4. Yellow.
5. Five: D, G, A, F and C.

Weight and count variations

Mains box puzzles often replace colours with weights or with the number of items in each box. These clues are comparisons ("box R is heavier than box Q", "the lightest box is placed immediately above the 20 kg box"). Two habits help:

• Keep a sorted list of the values (for example 12, 15, 18, 20, 25, 30) beside the stack. "Heaviest" and "lightest" then point to a definite value.
• Use comparisons last. Fix positions with position clues first, then let the comparisons choose between the few assignments left.

Common traps

• Treating "above" as "immediately above".
• Counting the boxes themselves when asked how many are between them.
• Assuming position 1 is the top.
• Assuming a middle exists in a stack with an even number of boxes.

Practice puzzle

Six boxes, P, Q, R, S, T and U, are placed one above another. Position 1 is the bottom. Each weighs a different amount: 12, 15, 18, 20, 25 and 30 kg.

1. Only two boxes are placed between Q and U, and U is above Q.
2. U is the heaviest box.
3. The 25 kg box is placed immediately above the heaviest box.
4. P weighs 25 kg.
5. Only one box is placed between P and S.
6. T is placed immediately below S.
7. R is placed above U.
8. The lightest box is placed immediately above the 20 kg box.
9. R is heavier than Q.

Questions:

1. Which box weighs 12 kg?
2. How many boxes are placed between T and P?
3. What is the weight of the box at the top?
4. Which box is placed immediately below the heaviest box?

Answers:

1. S. U (30 kg) is at 4, 5 or 6, and P (25 kg) sits directly on it, so U is at 4 or 5. With U at 5: Q 2, P 6, S 4, T 3 and R 1, but R must be above U, so this fails. With U at 4: Q 1, P 5, S 3, T 2 and R 6. The 12 kg box sits directly on the 20 kg box: either T 20 and S 12, or Q 20 and T 12. The second leaves R with 15 or 18, lighter than Q, which breaks clue 9. So T is 20 kg and S 12 kg; then R is 18 kg and Q 15 kg.
2. Two: S and U.
3. 18 kg (R).
4. S.

Final stack from the top: R 18, P 25, U 30, S 12, T 20, Q 15.

What to do next

• Redo the seven-box puzzle from a blank page in under 6 minutes, drawing the case table.
• Solve five box puzzles with weights this week, using comparison clues only at the end.
• Revise floor puzzles, which share the frame, and then try scheduling puzzles.