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Figure Completion

Reasoning · Non-Verbal Reasoning

7 Part1 worked examples7 practice questions

Think of a carpet design with a torn corner. If the design follows a rule — the same on both sides, or repeated in every square — you can draw the torn piece without seeing it. Figure completion is exactly this: spot the rule of the pattern and build the missing part from it.

This chapter has four kinds of question:

KindRuleWhere
Symmetric pictureMirror line or half-turnPart 2
Pattern of cellsRepeat, turn, flip, Latin squarePart 3
The piece that fitsCounting cells and turningPart 4

How to use this chapter

  1. Read — each part explains the rule and how to test the options.
  2. Study the solved example — every example has the full solution open with its drawing.
  3. Try it yourself — the figure shows the unfinished picture (orange frame) on top and the options A–D below. Open the solution last.
AssuranceEvery question was checked by computer: the right option alone obeys the rule and each of the other three has something wrong. So every question has exactly one sure answer.
1

Foundation — the four checks

Symmetry? Repeat? Turn? Piece?

Four questions to ask of any unfinished figure and the order to test them.

What the rule of an unfinished figure is

Every complete figure hides a rule

The rule of a pattern, the idea of a “partner cell” and a first example.

The examiner first draws a complete figure that follows some rule and then rubs out a part. So the blank is never arbitrary — it is fixed by the rule. Your job has two halves: (1) find the rule, (2) get the shape of the blank from the rule and match it with an option.

A helpful idea is the partner cell: when the rule is symmetry, an empty cell has a partner cell that is in view. The partner’s colour is the empty cell’s colour.

?(A)(B)(C)(D)
Question figure and options
Example 1 · Basic
The picture above is symmetric खड़ी दर्पण-रेखा के दोनों ओर, but the orange empty space (?) has to be filled. Which patch placed there makes the picture fully symmetric? (The patches are shown enlarged.)
Solution, step by step
  1. 1The picture is symmetric खड़ी दर्पण-रेखा के दोनों ओर, so the colour of every empty cell is fixed by its partner cell.
  2. 2For example the top-left cell of the gap (row 2, column 1) has the partner cell in row 2, column 4, which is empty — so this cell must be empty.
  3. 3Checking all the partner cells gives the patch (row by row, ■ filled □ empty): □□ / ■■.
  4. 4That patch is option (C); the others differ in one or two cells and break the symmetry.
Answer Figure C
Find the partner of each empty cell and colour it the same.
?(A)(B)(C)(D)
Question figure and options
BasicTry it yourself first
The picture above is symmetric खड़ी दर्पण-रेखा के दोनों ओर, but the orange empty space (?) has to be filled. Which patch placed there makes the picture fully symmetric? (The patches are shown enlarged.)
?(A)(B)(C)(D)
Question figure and options
BasicTry it yourself first
The picture above is symmetric आड़ी दर्पण-रेखा के दोनों ओर, but the orange empty space (?) has to be filled. Which patch placed there makes the picture fully symmetric? (The patches are shown enlarged.)
?(A)(B)(C)(D)
Question figure and options
BasicTry it yourself first
One cell (?) of the pattern above is empty. Which figure belongs in it?

The four checks and their order

Easy questions first, harder later

Which rule to try first on seeing a figure.

The figure looks likeFirst testRule
A black-and-white picture divided in the middleSymmetryMirror line, half-turn, or diagonal
Many small cells, a small figure in eachRepeat / turnWhat changed from cell to cell
Different figures in each row and columnLatin squareEach figure once in every row and column
A hole shaped like a piece in a big figureCounting cells, then turningA mirror image never fits
The firm order for every question
Spot the kind of patternFind the ruleBuild the blankMatch the options
TrickDraw the blank’s shape yourself on paper before matching with the options. Hunting for the rule while looking at the options confuses the mind — all four options are built to look “nearly right”.
?(A)(B)(C)(D)
Question figure and options
BasicTry it yourself first
The picture above is symmetric खड़ी और आड़ी दोनों दर्पण-रेखाओं के बारे में, but the orange empty space (?) has to be filled. Which patch placed there makes the picture fully symmetric? (The patches are shown enlarged.)
?(A)(B)(C)(D)
Question figure and options
BasicTry it yourself first
One cell (?) of the pattern above is empty. Which figure belongs in it?
(A)(B)(C)(D)
Question figure and options
BasicTry it yourself first
Exactly one of the pieces fills the orange gap on the board above with no space left. A piece may be turned but not flipped over (no mirror image). Which piece?
?(A)(B)(C)(D)
Question figure and options
StandardTry it yourself first
One cell (?) of the pattern above is empty. Which figure belongs in it?
2

Completing symmetric pictures

Mirror lines and half-turns

Finding the patch for a gap in pictures with one or two mirror lines or a half-turn.

One mirror line

Alike on both sides of a vertical or horizontal line

Finding the partner cell and reading the gap row by row.

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Two lines, half-turn and the slanting line

Three new moves for the partner cell

The partner cell under both mirror lines, a half-turn about the centre and diagonal symmetry.

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3

Patterns of cells

Repeat, turn, flip and Latin square

In a pattern with one cell empty, find the rule and choose the figure.

Repeats and alternation

Alike, row-wise, column-wise or chessboard fashion

When the figure stays the same in every cell or changes in a fixed order.

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Turning and flipping

A turn at each step, or a mirror in every second cell

Recognising the direction and rate of turning.

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Latin squares and mixed rules

Each figure once in every row and every column

A Latin square of three figures and its mix with turning or flipping.

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4

The piece that fits

Count, then turn, never flip

Choosing the piece shaped like the hole in a board.

Which piece fits the hole

Number of cells → shape → turning

Jigsaw-like questions: the one of four pieces that exactly fills the blank.

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5

Strategy guide

The order of checks and the slips to avoid

The order of checks in any figure-completion question, common traps and time-savers.

The order of checks

Spot → rule → blank → match

A table to recognise the kind of pattern at first sight.

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Common traps and time-savers

The mistakes that keep happening

The commonest reasons for losing marks in figure completion.

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6

Mixed practice

All kinds mixed — first spot the kind

All kinds of question in three levels.

Basic practice

Small pictures, one rule

Symmetry, repeat, turning and small pieces.

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Standard practice

Bigger pictures, two-step rules

pictures, turn and flip, Latin squares and five-cell pieces.

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Advanced practice

Larger blanks, mixed rules

Bigger patches, mixed rules and six-cell pieces.

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7

Revision — cards

Flip each card and test yourself

Think of the answer yourself first, then flip.

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