Rule: Every figure can be drawn in one stroke, without lifting the pen and without going over any line twice. Which set of figures follows this rule?

Set D. A figure can be drawn in one stroke only if it is connected and has no more than two junctions where an odd number of lines meet. Each other set contains a figure with four or more such junctions. The set that follows the rule is option D.

Rule: Each figure keeps all the lines of the figure before it and adds exactly one more line. Which set of figures follows this rule?

Set A. Only one set grows by exactly one new line at every step without losing or moving any line; each other set adds two lines at once, moves a line, or gets simpler at some step. The set that follows the rule is option A.

Rule: At each step the closed outer figure loses one side and the open inner figure gains one side. Which set of figures follows this rule?

Set C. In the right set the outer figure has 6, 5, 4, 3 sides and the inner figure 1, 2, 3, 4: one fewer and one more at every step. Every other set breaks this at some step. The set that follows the rule is option C.

Rule: The figure turns 45° clockwise at every step. Which set of figures follows this rule?

Set D. Only one set turns by exactly 45° clockwise from each box to the next; the others turn the wrong way, by the wrong amount, or skip a step somewhere. The set that follows the rule is option D.

Rule: Every figure can be drawn in one stroke, without lifting the pen and without going over any line twice. Which set of figures follows this rule?

Set A. A figure can be drawn in one stroke only if it is connected and has no more than two junctions where an odd number of lines meet. Each other set contains a figure with four or more such junctions. The set that follows the rule is option A.

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Non Verbal Reasoning · Series, Matrices & Rules

Rule Detection — Questions & Answers

Rule detection questions state a rule and give four sets of figures; exactly one set follows the rule in every step. Check the rule on each box of a set, not just the first.

5 solved questions
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How to approach

A figure can be drawn in one stroke only if at most two junctions have an odd number of lines.
Check the rule from each box to the next — a set fails if one step breaks it.
Count sides or lines carefully when a rule says a figure gains or loses one.

5 solved Rule Detection questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
Rule: Every figure can be drawn in one stroke, without lifting the pen and without going over any line twice.

Which set of figures follows this rule?
4 steps · reveal one at a time
1. Step 1: Understand the Rule
  A figure can be drawn in one continuous stroke if it is connected and has no more than two junctions where an odd number of lines meet. This is a key principle in graph theory.
2. Step 2: Count Odd Junctions
  To apply the rule, you need to count how many lines meet at each junction. If a junction has $1$ , $3$ , $5$ , etc., lines meeting, it's an odd junction. The rule allows at most two such junctions.
3. Step 3: Apply the Condition
  The solution establishes that other sets contain at least one figure with four or more odd junctions. Such figures cannot be drawn in one stroke. Therefore, these sets do not follow the rule.
4. Step 4: The answer
  So the answer is (D) Set D. This set is the only one where all figures meet the condition of having no more than two junctions with an odd number of lines meeting.
02
Rule: Each figure keeps all the lines of the figure before it and adds exactly one more line.

Which set of figures follows this rule?
4 steps · reveal one at a time
1. Step 1: Understand the Rule
  The rule has two important parts. Each figure must keep all the lines of the figure before it. Additionally, it must add exactly one more line. This means the total number of lines should increase by one at each step.
2. Step 2: Check for Consistency
  We need to find a set where the figures always follow this exact pattern. This means no lines are removed or moved, and the count of new lines is always $1$ for each step. Other sets might add more than one line, move existing lines, or even reduce the number of lines.
3. Step 3: Identify the Correct Set
  Only one set consistently adds exactly one new line at every step, without losing or moving any existing lines. All other sets either add more than one line, move lines, or become simpler at some point, failing the rule.
4. Step 4: The answer
  So the answer is (A) Set A. This set is the only one where each figure keeps all previous lines and adds exactly one new line, following the rule perfectly.
03
Rule: At each step the closed outer figure loses one side and the open inner figure gains one side.

Which set of figures follows this rule?
4 steps · reveal one at a time
1. Step 1: Understand the Rule
  The rule states that at each step, the closed outer figure loses one side and the open inner figure gains one side. We need to find the set of figures that consistently follows this transformation.
2. Step 2: Examine Side Counts
  The correct set of figures shows the outer figure having $6$ , $5$ , $4$ , and $3$ sides in sequence. For the inner figure, the side counts are $1$ , $2$ , $3$ , and $4$ in sequence. These are the specific side counts that follow the rule.
3. Step 3: Verify the Rule
  Let's check this sequence against the rule. The outer figure goes from $6$ to $5$ , then $5$ to $4$ , then $4$ to $3$ . This means it loses one side at every step. The inner figure goes from $1$ to $2$ , then $2$ to $3$ , then $3$ to $4$ . This means it gains one side at every step. This set perfectly matches the rule.
4. Step 4: The answer
  So the answer is (C) Set C. This set is the only one where the outer figure consistently loses one side and the inner figure consistently gains one side at each step, as specified by the rule.
04
Rule: The figure turns 45° clockwise at every step.

Which set of figures follows this rule?
4 steps · reveal one at a time
1. Step 1: Understand the Rule
  The core rule for this question is that a figure rotates by exactly $45^\circ$ in a clockwise direction at each step. We need to find the set of figures where every figure in the sequence follows this specific rotation.
2. Step 2: Verify Rotation Amount
  Next, for each set, check if the figure is turning by the exact amount of $45^\circ$ from one step to the next. Some sets might turn by a different angle, like $90^\circ$ , or even skip a rotation.
3. Step 3: Identify Correct Set
  Only one set of figures consistently follows both parts of the rule: turning clockwise and rotating by precisely $45^\circ$ at every single step. All other sets will fail one or both of these conditions.
4. Step 4: The answer
  So the answer is (D) Set D. This set is the only one where the figure turns by exactly $45^\circ$ clockwise from each box to the next, while other sets either turn the wrong way, by the wrong amount, or skip a step.
05
Rule: Every figure can be drawn in one stroke, without lifting the pen and without going over any line twice.

Which set of figures follows this rule?
4 steps · reveal one at a time
1. Step 1: Understand the Rule
  The rule describes figures that can be drawn in one continuous stroke. This means you can draw the entire figure without lifting your pen and without going over any line twice.
2. Step 2: Identify Key Condition
  To follow this rule, a figure must be connected. Additionally, it must have no more than two junctions where an odd number of lines meet. These are often called 'odd degree' vertices.
3. Step 3: Apply the Condition
  We need to examine each set of figures. For a set to follow the rule, every figure within that set must meet the condition of having at most two odd junctions. If any figure has four or more odd junctions, its set does not follow the rule.
4. Step 4: The answer
  So the answer is (A) Set A. This set contains figures that are connected and have no more than two junctions where an odd number of lines meet, unlike the other sets.

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