Reasoning

Non-Verbal Reasoning — Mirror, Water Image, Paper Folding & Cubes

Non-verbal reasoning tests visual pattern recognition — mirror images, water images, paper folding, paper cutting, embedded figures and cube/dice analysis. SSC, RRB, Police and Defence exams give 4–8 marks for these and they are the easiest of all reasoning types if you visualise the figure step-by-step.

Exam relevance: SSC CGL/CHSL Tier-I: 4–6 questions. RRB Group D / NTPC: 3–5 questions. Defence (CDS/AFCAT): 6–10 questions. State Police exams: 5–8 questions.

In-Depth Tutorial

A formal, accessible 800–1000 word walkthrough of this topic, written for the serious aspirant. Switch to हिन्दी using the toggle on the right.

What Non-Verbal Reasoning Measures and Why It Matters

Non-verbal reasoning consists of questions in which the entire information is presented through figures, patterns, dice, cubes or paper-folding diagrams rather than through words. The candidate must identify a hidden pattern, predict a missing figure, or visualise a three-dimensional object from a two-dimensional drawing. This skill is treated as fundamental in defence, railway and police recruitment because the operational duties in those services routinely require map reading, situation visualisation and rapid spatial judgement under stress.

Non-verbal reasoning typically contributes five to twelve marks in Staff Selection Commission examinations, six to ten marks in Railway Recruitment Board papers, and a substantial share in National Defence Academy and Combined Defence Services papers. The questions are short, language-independent and culturally neutral, which is why they appear consistently across both English and Hindi medium tests.

Mirror and Water Image — Two Different Reflections

A mirror image reverses the figure horizontally, as if a vertical mirror were placed to the right of the original figure. The left side becomes the right side, the right side becomes the left, but top remains top and bottom remains bottom. A water image, by contrast, reverses the figure vertically, as if a horizontal water surface were placed below the original figure. Top becomes bottom, bottom becomes top, but left and right remain unchanged.

The professional method begins by writing the alphabet in three rows on the rough sheet at the start of the paper: the first row contains the original letters, the second contains their mirror images, and the third contains their water images. Letters with vertical symmetry — A, H, I, M, O, T, U, V, W, X, Y — look identical in a mirror image. Letters with horizontal symmetry — B, C, D, E, H, I, K, O, X — look identical in a water image. With these two short lists memorised, every mirror or water image question becomes a routine letter-substitution.

Paper Folding and Paper Cutting

Paper-folding questions show a square sheet folded one or more times along marked dotted lines, after which one or more cuts are made through the folded sheet. The candidate must visualise the unfolded sheet and select the correct option showing the holes or removed shapes. The reliable method is to undo the folds in reverse order. Each fold, when reversed, doubles the number of holes by reflecting them across the fold line. After two folds and one cut, four holes appear in mirror-symmetric positions; after three folds and one cut, eight holes appear.

The professional discipline is to lightly draw each unfolding stage on the rough sheet. The candidate must not attempt three folds entirely in the head — even experienced solvers make symmetry errors when bypassing this step. With practice, the entire visualisation takes thirty to forty seconds per question, well within the time budget for any examination.

Cubes — Counting, Painting and Arrangement

Cube questions take three standard forms. In the first form, a large cube is painted on all six faces and then sliced into smaller unit cubes; the candidate must count how many small cubes have three painted faces, two painted faces, one painted face, or no painted face. The standard formulas are: small cubes with three painted faces are always eight (the corners); with two painted faces are 12(n−2), where n is the number of cubes per edge; with one painted face are 6(n−2)²; and with no painted face are (n−2)³.

In the second form, the candidate is shown an unfolded net of a cube and asked which face is opposite which after folding. The reliable method is to identify two adjacent faces from the net and use the rule that opposite faces never share an edge. In the third form, two views of a single cube are given and the candidate must identify the bottom or hidden face. The professional approach is to mark each visible face with a temporary label and use the property that any two visible faces in a single view are adjacent — never opposite.

Dice — Position and Opposite-Face Logic

Dice questions ask the candidate to determine which number lies opposite which on a standard die, given two or three views of the die in different orientations. Two key rules unlock every dice question. First, on a standard die the opposite faces sum to seven, so the pairs are 1 and 6, 2 and 5, and 3 and 4. Second, when two views of the same die share one common visible face, the orientation of the other faces relative to that common face determines the rest of the configuration.

The professional method is to mark the common face from both views and then trace the rotation of the die between the two views — typically a quarter turn around one axis. Each quarter turn shifts the visible faces in a predictable cycle, which the candidate should rehearse on a real die or a small paper cube during preparation. Five minutes spent rotating a paper cube establishes more spatial intuition than fifty solved questions on paper.

Series, Analogy and Embedded-Figure Patterns

Non-verbal series and analogy questions present figures whose components — line segments, dots, arrows or shaded regions — change according to a hidden rule. The professional method is to focus on one component at a time. The candidate should ask: how does the line rotate, how does the dot move, how does the shading shift? Once each component's rule is identified separately, the next figure is constructed by applying every rule simultaneously.

Embedded-figure questions show a complex shape and ask which simpler shape is hidden within it. The reliable method is to scan the complex shape systematically — top to bottom, left to right — and to mentally subtract each line of the simpler shape from the complex one. With consistent practice across all five non-verbal categories, an aspirant can secure ten to twelve high-accuracy marks in every defence and railway examination, with no requirement of language skills and minimal calculation.

1Mirror Image & Water Image

A mirror image flips a figure left-right (lateral inversion). A water image flips a figure top-bottom (vertical inversion).

Mirror image rule: the image's left becomes the original's right and vice versa. Letters that look the same in a mirror (vertically symmetric): A, H, I, M, O, T, U, V, W, X, Y. Water image rule: the image flips top-bottom. Letters that look the same in a water image (horizontally symmetric): B, C, D, E, H, I, K, O, X. Numbers: 0, 1, 8 are mirror-symmetric; 0, 1, 8 are also water-image-symmetric.

Examples
  • Mirror image of HELLO → reverse the letters and flip each: O-L-L-E-H with each letter mirrored.
  • Mirror image of 1234 → 4321 with each digit mirrored.
  • Water image of 'CODE' → letters flipped vertically (e.g. C → upside-down C, D → upside-down D).
  • Mirror image of word 'BOY' → flipped 'YOB' with each letter laterally inverted.
Exam tip: Mirror image = horizontal flip (left-right swap). Water image = vertical flip (top-bottom swap). They are NOT the same — students often confuse them.

2Paper Folding & Paper Cutting

Paper folding shows a square piece of paper folded one or more times and a hole/cut made; you must identify the figure when the paper is unfolded.

Each fold creates a line of symmetry across which any subsequent hole is mirrored. Two folds → 4 holes. Three folds → 8 holes (one in each of 8 quadrants). When unfolding, mirror the holes/cuts across each fold-line in REVERSE order of folding (last fold = first to unfold).

Examples
  • Square folded once horizontally + one circular hole punched at the centre of the bottom edge → unfolded shows 2 holes (top and bottom mid-edges).
  • Square folded twice (horizontally + vertically) + 1 hole at centre → unfolded shows 4 holes (one at each quadrant centre).
  • Square folded once diagonally + a triangular cut at the corner → unfolded shows two symmetric triangular cuts on either side of the diagonal.
  • Square folded thrice (along both axes + diagonal) → 1 cut becomes 8 symmetric cuts.
Exam tip: Always unfold in REVERSE order of folding. Mirroring is across the LAST fold-line first, then the previous, and so on.

3Cubes & Dice

Cube and dice problems involve a solid cube (often painted) cut into smaller cubes, or a die showing numbers/symbols on its faces.

Cube painted on all faces and cut into n³ smaller cubes: cubes painted on 3 faces = 8 (corners); 2 faces = 12(n−2) (edges); 1 face = 6(n−2)² (centres of faces); 0 faces = (n−2)³ (interior). For dice: opposite faces of a standard die sum to 7 (1+6, 2+5, 3+4). Use two views of the same die to identify the position of any face by elimination.

Examples
  • A cube of side 5 painted and cut into 125 small cubes: 3-face = 8; 2-face = 12×3 = 36; 1-face = 6×9 = 54; 0-face = 27. Total = 125. ✓
  • Two dice show: face 6 with 1, 2, 3 visible. Face opposite 1 = 6; opposite 2 = 5; opposite 3 = 4.
  • Cube of side 4 painted: 1-face cubes = 6 × (4−2)² = 24.
  • If 6 small cubes are painted on 3 faces in a 3×3×3 cube, then total cubes painted on 3 faces = 8 (corners always 8 in any cube).
Exam tip: In any painted cube divided into n³ small cubes, the count painted on EXACTLY 3 faces is always 8 (the 8 corners) regardless of n.

4Series & Analogy of Figures (Pattern Recognition)

A figure series shows 3–4 figures changing according to a rule; you must pick the next figure. A figure analogy shows two figure pairs and asks which pair has the same rule.

Common rules: rotation (90°, 180°, 270°), addition/removal of a line/dot, change in shape, reflection. Always note the rule that connects fig-1 to fig-2 (rotation degree, addition of element, colour change). Apply the SAME rule from fig-3 to choose fig-4.

Examples
  • Square with a dot in top-left → square with dot in top-right → square with dot in bottom-right → ? → square with dot in bottom-left (clockwise rotation).
  • Triangle with one line → triangle with two lines → triangle with three lines → ? → triangle with four lines (line addition).
  • Arrow up → arrow right → arrow down → ? → arrow left (90° clockwise rotation).
  • Pair (Circle, Square) :: Pair (Pentagon, ?) → next regular polygon → Hexagon.
Exam tip: Try rotation first (most common), then line/element addition, then reflection. Cross-check by applying the rule to ALL frames of the series — not just the last two.

Short Tricks & Shortcuts

Use these speed tricks in the exam. Each trick is followed by a worked example so you can verify the shortcut yourself.

Trick 1Mirror-image symmetric letter set

Memorise the 11 letters that look the same in a mirror image: A, H, I, M, O, T, U, V, W, X, Y. Any other letter changes shape.

Example: Mirror image of MOM = MOM (all 3 letters are mirror-symmetric).
Trick 2Water-image symmetric letters

Memorise: B, C, D, E, H, I, K, O, X look the same when reflected top-to-bottom. Digits 0, 1, 8 are also water-image-symmetric.

Example: Water image of 'CODE' = CODE (all 4 letters are water-image-symmetric).
Trick 3Painted-cube quick formulas

n³ small cubes from one painted cube: 3-face = 8; 2-face = 12(n−2); 1-face = 6(n−2)²; 0-face = (n−2)³.

Example: n=4: 3-face = 8; 2-face = 24; 1-face = 24; 0-face = 8 → total = 64. ✓
Trick 4Opposite faces of a die sum to 7

On a standard die, opposite faces always sum to 7: (1, 6), (2, 5), (3, 4). Use this to identify a hidden face from any visible face.

Example: If top of a die shows 2, bottom shows 7 − 2 = 5.
Trick 5Rotation-first heuristic for figure series

Most figure series follow rotation by 45°, 90° or 180°. Always test rotation BEFORE line additions or reflections. Verify with the previous frame.

Example: Arrow up → right → down → left (90° clockwise each time).

Quick Revision Facts

  • 8 corner cubes are painted on 3 faces in ANY n×n×n painted cube.
  • Mirror image flips left-right; water image flips top-bottom — they are NOT the same.
  • Each fold of a square paper doubles the number of holes/cuts when unfolded.
  • Opposite faces of a standard die sum to 7.

Frequently Asked Questions

A mirror image is a horizontal (left-right) flip — like seeing yourself in a wall mirror. A water image is a vertical (top-bottom) flip — like seeing your reflection in a still pool. Letters/figures that are symmetric in one direction may not be symmetric in the other.

Use the formula 12(n−2) where n is the number of small cubes per side. The factor 12 is the count of edges of a cube; (n−2) is the count of small cubes per edge that are NOT corners.