Figure series, mirrors, embedded shapes and paper folding.
About Rule Detection
A rule detection question states a rule and gives four sets of figures. Exactly one set obeys the rule; the others each break it somewhere. Nothing has to be discovered, because the rule is given - the work is to check four sets against it carefully rather than to guess what the setter had in mind.
What you need to understand
A rule of this kind names one or two properties of a figure: how many sides it has, how large it is, how many marks are inside it, or which way up it is.
The rule has to hold across every figure in the set, not only between the first two. A set where the step is right twice and wrong once is wrong.
One figure breaking the rule is enough to reject the whole set, so an option can be dismissed part way through and the time spent on the next.
The wrong options are near misses. They keep the step the rule describes everywhere except in one figure, which is why they have to be checked rather than glanced at.
The order of the figures matters. A set with the right figures in the wrong order does not show a regular step.
Only the properties the rule mentions are being tested. The other properties of the figures - their colour, their position on the page - are noise.
How to work through these questions
Read the rule and write down the properties it mentions, which is usually one or two of sides, size, marks and direction.
Take the first option and check the property between the first figure and the second. If the step is wrong, reject the option immediately and move on.
If the first step is right, check the same property between the second figure and the third. A set that is right once and wrong once is not regular.
If the rule mentions two properties, both have to hold at every step. One holding and the other not is not the answer.
Repeat for the remaining options, rejecting early and never going back to one already rejected.
When one option has survived every step, that is the answer. Do not keep looking for a set that fits better.
Mistakes that cost marks
Checking only the first two figures of a set and assuming the third follows.
Reading "increases" as "increases by one" when the rule says only that it increases, or the other way round.
Rejecting an option on a property the rule does not mention, such as the size of the figures when the rule is about the marks.
Losing count of the sides in a figure with many of them, which is where a near miss is designed to catch the reader.
Assuming the option that looks most regular is the answer rather than testing it.
Forgetting that the rule can be about direction, and checking only the counts.
Worked example
The rule is that the number of sides increases by one from figure to figure, and the figure gets smaller each time. Four sets of three figures are offered; in three of them one figure breaks the rule.
Write down the two properties the rule mentions: the number of sides, and the size.
Take the first option. Its figures have 4, 5 and 6 sides, so the sides step is right.
Now the size. The figures get smaller from the first to the second and again from the second to the third, so this option obeys both parts of the rule.
Take the second option. Its figures have 4, 6 and 7 sides. The step from the first to the second jumps by two, so the option is rejected at once and no further checking is needed.
Take the third and fourth options in the same way. Each breaks the rule in one place, which leaves the first option.
The answer is the option whose sides step by one and whose figures shrink at every step.
Answer: The set in which the sides go up by one and the figures shrink each time.
Practice questions with answers
A few Rule Detection questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
The first figure of the correct set is shown below. In which of these sets of three figures does the number of sides increases by one and the number of marks inside increases by one, from figure to figure? Read each set from left to right.
A
B
C
D
Answer: Option D — with explanation
The rule is that the number of sides increases by one and the number of marks inside increases by one, from figure to figure, and the set starts from the figure given in the question.
Take the options one at a time and check the property the rule mentions across all three figures, starting from that first figure. The right option keeps the step the rule describes; in each of the others one figure breaks it, so the sequence is no longer regular.
Common mistakes
- in this option the second figure breaks the run of marks
- in this option the second figure breaks the run of sides
- in this option the third figure breaks the run of sides
Question 2
Which of these sets of three figures begins with the figure shown below and follows the rule that the number of sides increases by one and the number of marks inside increases by one, from figure to figure?
A
B
C
D
Answer: Option B — with explanation
The rule is that the number of sides increases by one and the number of marks inside increases by one, from figure to figure, and the set starts from the figure given in the question.
Take the options one at a time and check the property the rule mentions across all three figures, starting from that first figure. The right option keeps the step the rule describes; in each of the others one figure breaks it, so the sequence is no longer regular.
Common mistakes
- in this option the third figure breaks the run of sides
- in this option the third figure breaks the run of marks
- in this option the second figure breaks the run of marks
Question 3
Which of these sets of three figures begins with the figure shown below and follows the rule that the number of sides increases by one and the number of marks inside increases by one, from figure to figure?
A
B
C
D
Answer: Option C — with explanation
The rule is that the number of sides increases by one and the number of marks inside increases by one, from figure to figure, and the set starts from the figure given in the question.
Take the options one at a time and check the property the rule mentions across all three figures, starting from that first figure. The right option keeps the step the rule describes; in each of the others one figure breaks it, so the sequence is no longer regular.
Common mistakes
- in this option the second figure breaks the run of marks
- in this option the third figure breaks the run of marks
- in this option the second figure breaks the run of sides
Question 4
The correct set of three figures begins with the figure shown below. Which of these sets follows the rule that the number of sides increases by one and the number of marks inside increases by one, from figure to figure? Read each set from left to right.
A
B
C
D
Answer: Option B — with explanation
The rule is that the number of sides increases by one and the number of marks inside increases by one, from figure to figure, and the set starts from the figure given in the question.
Take the options one at a time and check the property the rule mentions across all three figures, starting from that first figure. The right option keeps the step the rule describes; in each of the others one figure breaks it, so the sequence is no longer regular.
Common mistakes
- in this option the second figure breaks the run of marks
- in this option the third figure breaks the run of marks
- in this option the third figure breaks the run of sides
Question 5
The first figure of the correct set is shown below. In which of these sets of three figures does the number of sides increases by one and the number of marks inside increases by one, from figure to figure? Read each set from left to right.
A
B
C
D
Answer: Option A — with explanation
The rule is that the number of sides increases by one and the number of marks inside increases by one, from figure to figure, and the set starts from the figure given in the question.
Take the options one at a time and check the property the rule mentions across all three figures, starting from that first figure. The right option keeps the step the rule describes; in each of the others one figure breaks it, so the sequence is no longer regular.
Common mistakes
- in this option the third figure breaks the run of sides
- in this option the third figure breaks the run of marks
- in this option the second figure breaks the run of sides
Frequently asked questions
Where do I start?
Write down the properties the rule mentions before looking at any option. Then you are checking two things at each step instead of trying to hold the whole rule in mind while reading four sets of figures.
Do all the figures have to follow the rule?
Yes, every step between consecutive figures. A set where the first step is right and the second is wrong is not a regular sequence, and that is exactly what the near-miss options rely on.
Can I reject an option without checking the last figure?
Yes, and you should. As soon as a step is wrong the option is out. The last figure only needs checking once every earlier step has held.
What if two options both seem to follow the rule?
Go back and count again on the property the rule names. One of the two will have a figure that breaks the step, usually by one, and it is easier to see when you count the sides or the marks rather than glance at the shapes.
Take the Rule Detection test
Two timed papers on the same syllabus — sit the foundation paper first,
then the advanced one. Both use the real exam paper format with a full
step-by-step review of every question once you submit.
