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Logical Reasoning · one of four sections

Logical Reasoning for the maths olympiad

The section that catches children who are good at arithmetic. Nothing here needs a method you were taught in class, which is exactly why practice on it moves a score more than another hour of long division.

We have written 400 Logical Reasoning questions by hand across classes 3 to 8.

Quick answer

How many Logical Reasoning questions are in the SOF IMO?

Logical Reasoning is Section 1 of the SOF International Mathematics Olympiad (IMO) paper. SOF's pattern gives it 10 questions in classes 1 to 4 and 15 questions in classes 5 to 10, at 1 mark each, out of 35 and 50 questions on the whole paper. In class 3, for example, SOF's syllabus lists patterns, analogy and classification, coding-decoding, ranking, mirror images, and clock and calendar.

Source: Science Olympiad Foundation: IMO syllabus and paper pattern · Updated

Try two of them

One from a class 4 paper and one from class 7, so you can see how the same section grows. Have a go before opening the answer.

4 pointsClass 4Question 6

Ria says: I am thinking of a shape that has 4 sides. Sam may ask questions to work out exactly which shape it is. Which of these questions would be LEAST useful to Sam?

Show the answer and how to see it

Answer: Does it have 4 sides?

A useful question is one whose answer could still go either way. Ria has already said the shape has 4 sides, so asking that again is certain to get yes and rules nothing out. The other questions all split the four-sided shapes into two groups.

Why a child picks Are all 4 of its sides the same length?: This one helps: a square and a rhombus say yes, a rectangle and a kite say no.

Sit the whole paper this came from
4 pointsClass 7Question 1

A park has five gates: A, B, C, D and E. Paths join A to B, A to C, B to C, B to D, C to D, C to E, and D to E. A sweeper wants to sweep every path exactly once, never going along the same path twice. From how many of the five gates could she START and still manage it?

Show the answer and how to see it

Answer: 2

Count the paths meeting at each gate. Every gate she passes THROUGH uses up two paths, one in and one out, so a gate with an odd number of paths can only be where she starts or where she finishes. Exactly two gates here have an odd number.

Why a child picks 5: Every gate is reachable from every other, but being connected is not enough. Where she starts still matters.

Sit the whole paper this came from

What this section actually tests

  • 1Reading a rule off a sequence of shapes or numbers and carrying it forward, rather than recognising a sequence you have seen before.
  • 2Holding several statements at once and working out what they force to be true, the way a seating puzzle or a who-owns-what grid does.
  • 3Direction, turning and position: which way something faces after a sequence of turns, and where it ends up.
  • 4Coding and decoding, where a word or number is rewritten by a rule you have to reverse.
  • 5Odd-one-out, where four things share a property and one does not, and the property is never the obvious one.

The method, in order

Worth saying out loud the first few times. The order matters more than the speed.

  1. 1. Say what changes, not what you see

    Describe the difference between one step and the next out loud. A rule you can say is a rule you can carry forward; a picture you can only look at is not.

  2. 2. Write the facts down as short lines

    For a puzzle with several statements, put each one on its own line in shorthand. Most wrong answers here come from trying to hold four facts in your head at once.

  3. 3. Test the rule on the step you already have

    Before using a rule to find the answer, run it on a step you can see. If it does not reproduce that step, it is the wrong rule.

  4. 4. Check the option you rejected first

    The distractors are built from real half-rules. If two options both fit, your rule is not specific enough yet.

The four ways children lose marks here

These are not guesses. Each one is a wrong option we deliberately built into real questions, which is why every one of them feels reasonable at the time.

Spotting the first pattern and stopping

The fix: Two rules often run at once, one on shape and one on count. Check the second before you choose.

Counting the turns instead of tracking the facing

The fix: Draw the arrow after every turn. Four right turns is not the same as one, unless you finish where you started.

Reading "some" as "all"

The fix: In statement puzzles, "some A are B" never lets you conclude anything about every A. Underline the quantity word.

Choosing the odd one out on looks

The fix: The property is usually structural: number of sides, whether it is symmetrical, whether it can be folded. Not colour or size.

How many Logical Reasoning questions are on the paper

ClassLogical Reasoning questionsMarks eachQuestions on the paper
Class 310135 (40 marks)
Class 410135 (40 marks)
Class 515150 (60 marks)
Class 615150 (60 marks)
Class 715150 (60 marks)
Class 815150 (60 marks)

Section names and the shape of the paper follow the Science Olympiad Foundation olympiad blueprint. We are not affiliated with them, these questions are our own, and the official pattern is theirs to confirm. Source: SOF IMO syllabus and paper pattern, checked October 21, 2026.

Questions parents ask

How many marks is Logical Reasoning worth?

In our papers it is 10 of 35 questions for classes 3 and 4, and 15 of 50 for classes 5 to 8. It is the section most often left unpractised, because it is not on the school syllabus, which is why it is the fastest place to gain marks.

Can Logical Reasoning actually be practised, or is it just ability?

It can be practised, because the question types repeat. There are perhaps a dozen shapes of question, and a child who has met each one several times recognises the shape and starts on the right foot instead of staring at it.

Is it the same as the reasoning in CogAT or NNAT?

It overlaps. Figure series, matrices and odd-one-out appear in both. The difference is that olympiad logical reasoning also uses number rules and statement puzzles, which the ability tests mostly do not.

My child is strong at maths but weak here. Is that normal?

It is the most common pattern we see. School maths rewards knowing a method; this section rewards finding one. They are different skills and the second improves with exposure.

Practise it inside a whole paper

One section at a time is how you fix a weakness. A full timed paper is how you find out whether it is fixed.

Sit a full paperSOF IMO preparation
The other three sections: Mathematical Reasoning, Everyday Mathematics, Achievers Section.