Note 28

Embedded Figures and Non-Verbal Reasoning

Complete notes for SSC Combined Graduate Level examinations

Hidden

Scan

Trace

Match

Series

Odd One

Transform

Recall

1The Big Picture — Graphic Mind Map

Embedded Figure

Locate every segment, turn and junction of a simple target inside a busy host. Extra host lines are allowed; missing or bent target lines are not.

Figure Counting

Partition the diagram into families and sizes. Use an inventory, not random recounting. Shared sides do not merge two distinct closed paths.

Series & Classification

Track what changes—shape, position, count, fill, size or direction—and what stays fixed. The odd figure violates the shared rule.

Visual Memory

Encode a figure as a feature bundle: outer frame, element count, relative locations, orientation, shading and special marks—then compare.

Observe
whole figure

➜

Decompose
anchors & paths

➜

Transform
only if allowed

➜

Verify
every feature

Master principle: do not match the “look.” Match the structure—connectivity, order of turns, relative positions and invariant features.

2The Foundation — From First Look to Exact Match

1. Target vs Host

The target is the simple figure to be found. The host is the complex figure. Trace the target as one continuous route whenever its segments are connected.

Every target edge must exist.
Intersections may add irrelevant lines.
Target scale may change unless stated otherwise.

2. Anchor Points

Start from a rare landmark: sharp apex, fork, enclosed loop, unequal arm, dot or distinctive intersection. Then follow neighbouring segments in order.

Rare anchor first → fewer candidate paths → faster rejection.

3. Connectivity & Turn Order

An exact path preserves adjacency and the order of turns. Two drawings may contain the same number of lines but join them differently.

Path signature: \(P=(e_1,v_1,e_2,v_2,\ldots,e_n)\)

Transformations: what may change?

Translation

Only location changes. Direction, chirality and connections remain identical.

Rotation

The entire figure turns through angle \(\theta\). Cyclic order around each junction remains the same.

Reflection

A mirror reverses handedness. A feature on the target’s left appears on the right; rotation alone cannot do this.

Scaling

Lengths change in one ratio \(k\), while angles, relative positions and connectivity remain unchanged.

Feature	Exact / identical form	Rotated form	Mirror form	Useful rejection
Number of segments / components	Same	Same	Same	Different count rejects immediately
Connectivity and degree of junctions	Same	Same	Same	A fork cannot become a crossing
Clockwise cyclic order	Same	Same	Reversed	Detect mirror disguised as rotation
Absolute position	May move	May move	May move	Usually not decisive
Angles / proportions	Same	Same	Same	Stretching one arm invalidates match
Shading / dots / arrows	Same relative place	Turn together	Reverse side	Never rotate only the outline

Figure Counting Method

Name the basic units or cells.
Count smallest figures systematically from left to right.
Count combinations of \(2,3,\ldots\) units.
Add inverted, overlapping and whole-figure cases.
Use a table so no family is repeated.

\(N_{\text{total}}=N_{\text{small}}+N_{\text{medium}}+N_{\text{large}}+N_{\text{composite}}\)

Visual Memory: Chunk, Do Not Photograph

Convert the stimulus into a verbal-spatial code:

Frame: square / circle / open outline.
Count: number of elements.
Position: top-left, centre, outside, touching.
Orientation: arrow, opening, slope.
Detail: fill, dot, notch, crossing.

Figural Series — Rule Bank

Movement / Rotation

Element moves by fixed positions or turns through \(\theta,2\theta,3\theta,\ldots\). Check clockwise and anticlockwise separately.

Add / Subtract

Line, dot, side or component count may follow \(+1,-1,+2\), alternation, or two interlaced sequences.

Superposition / Cancellation

Combine corresponding lines. In XOR-type rules a line appearing twice cancels; in union-type rules all lines remain.

Terminology distinction: an embedded figure asks whether a target path exists inside a host. Figure counting asks how many valid paths/shapes exist. Figure completion asks which option restores a missing region. Do not apply one task’s rules to another.

3Short Tricks & Magic Visual Methods

Anchor–Trace–Verify

A: select rare junction. T: trace one branch at a time. V: confirm last endpoint, turn direction and attachments. Reject as soon as one compulsory segment fails.

Junction-Degree Fingerprint

Count incident arms at key vertices. A target with one 4-way crossing and two 3-way forks cannot match a path with only corners. The multiset \(D=\{d(v_1),d(v_2),\ldots\}\) is rotation-proof.

Chirality Test

Choose an asymmetric mark and walk around the outline. If the order of neighbouring features reverses, the option is a mirror, not a rotation.

Size Ledger

For counting, write columns S–M–L–C (small, medium, large, composite). Complete one orientation before moving to another; never mix sizes mentally.

Overlay Ledger

For A + B series, examine each location separately: present in neither, A only, B only, or both. Determine whether the operation is union, common-only, or cancellation.

Split Alternating Series

If one rule seems irregular, separate odd terms \((1,3,5,\ldots)\) and even terms \((2,4,6,\ldots)\). Each often follows a simple movement or count rule.

Option-First Elimination

Reject wrong component count.
Reject wrong junction type.
Reject impossible relative position.
Then trace the surviving one or two options fully.

Three-Pass Visual Memory

Pass 1: outer frame and count. Pass 2: orientation and relative position. Pass 3: one diagnostic detail. This produces a compact code instead of an unreliable photographic impression.

Question signal	Fastest first test	Second test	Do not waste time on
Find target in complex figure	Rarest junction / endpoint	Turn sequence	Tracing every line of host
Identical figure	Component and junction count	Relative marker positions	Absolute page orientation
Rotated figure	Clockwise feature order	Rotate one anchor mentally	Mirror options
Odd figure	List common invariants	Find single violated invariant	Inventing a rule for each option
Figural series	Make feature ledger by term	Test alternation	Guessing from last two only
Visual memory	Chunk into 3–5 features	Verify diagnostic detail	Remembering overall “look”

4The SSC / TCS Traps — Red Flags

Trap 1: “Almost” Embedded

The option shares most target lines, but one endpoint continues from the wrong junction or one arm is missing. Extra host lines are harmless; a missing target segment is fatal.

Trap 2: Mirror as Rotation

A symmetric outline hides a reversed dot/notch. Rotation preserves clockwise order; reflection reverses it. Track one asymmetric marker.

Trap 3: Duplicate Counting

A composite figure is often rediscovered from a different starting vertex. Record its boundary or unit span; different tracing direction does not create a new figure.

Trap 4: Multiple Valid Rules

An attractive local pattern may fit two terms. Prefer the rule that explains all transitions and all features with the fewest arbitrary exceptions.

Trap 5: Wrong Overlay Operation

Do not assume “combine” always means union. TCS-style matrices may retain common lines, remove common lines, or transfer only shaded parts. Infer operation from a complete row/column.

Trap 6: Memory by Gist

“Square with a dot” is too coarse. The answer options exploit corner, inside/outside, contact, count and orientation. Encode one diagnostic detail before the stimulus disappears.

Red-flag wording: “exactly similar” normally permits change of position and may permit rotation, but not reflection unless the task or options imply it. “Same as” requires every relevant mark. Read the instruction line before applying a transformation.

5Memory Hooks & Mnemonics

ATV

Anchor → Trace → Verify. Like riding an ATV through a crowded line jungle: choose the landmark, follow the track, check the destination.

R.O.S.

Rotation: Order Stays. Clockwise neighbour order is preserved. If left/right feature order reverses, shout “mirror!”

SMLC Drawers

Put counted figures into four drawers: Small, Medium, Large, Composite. Empty every drawer before totaling.

FCPOD

Visual-memory code: Frame, Count, Position, Orientation, Detail.

Hidden-Figure Chant

“Extra is okay; missing is no way.” Host clutter may cross the target, but it cannot supply a bent, disconnected or absent target segment.

Series Sentence

Say one sentence per feature: “shape cycles, dot moves clockwise, count rises by one.” A complete sentence exposes an option that satisfies only part of the rule.

Three Questions

Ask: What stays? What changes? By how much / in what order? These three questions unlock most non-verbal series and classification items.

Final recall line: See the skeleton, not the decoration — anchor the rare point, preserve connectivity, track transformation, and verify every invariant.