Example 1
"Every number that ends in 4 divides by 4." True or false?
- Try a few: 4 yes, 24 yes, 14: 14 ÷ 4 = 3.5, no.
- One counter-example is enough.
Answer: False (14 is a counter-example)
🏅 Olympiad maths · session 4 of 49 · 60 minutes · ⭐ Plus
Logic puzzles: knights, knaves and grids
Logical reasoning questions reward careful thinking, not speed. Learn to test every case, rule things out with a grid and spot a contradiction, using the famous knights and knaves puzzles.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up4 min
- True or false8 min
- Knights and knaves9 min
- Grids7 min
- Contradiction7 min
- Activity 17 min
- Activity 27 min
- Activity 36 min
- Quiz4 min
- Set the project1 min
By the end you can
- Decide whether a statement is true or false
- Solve knights-and-knaves puzzles by testing every case
- Use a grid to rule out possibilities
- Find an answer by assuming something and reaching a contradiction
Before you start
- None: just careful reading
Have ready
- Paper and pencil
- A ruler for drawing grids
Classes 4 to 7 · ages 9 to 13
Warm-up · think first
On an island, knights always tell the truth and knaves always lie. You meet someone who says: "I am a knave." What can you say about them?
Show the answer
Nobody on the island can say it. A knight would be lying (impossible), and a knave would be telling the truth (also impossible). So the speaker cannot be from the island! Testing both cases is today's big tool.
Teacher tip: Ask the learner to try each case out loud: "Suppose they are a knight… then…". Let them find the contradiction themselves.
Part 1 of 4 · learn, see, practise
True or false?
A statement is a sentence that is either true or false. "7 is odd" is true; "all birds can fly" is false (penguins).
One example that breaks a rule is enough to show an "all" statement is false. To show it is true, you need a reason that works every time.
Think first: Is "the sum of two odd numbers is always even" true? Give a reason, not just examples.
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Stretch 🔥
Answers (for the teacher)
- true
- false
- 33
- true
⭐ Part of Pure Faith Plus
The rest of this lesson is in Plus
Already have Plus? Log in and the whole lesson opens.
You have seen the plan, the warm-up and part 1. With Plus you also get:
- Part 2: Knights and knaves: try every case, with practice at three levels
- Part 3: Grid puzzles: rule things out, with practice at three levels
- Part 4: Assume and look for a contradiction, with practice at three levels
- Class activity 1: Think it through
- Class activity 2: The pet grid
- Class activity 3: Island interviews
- A 8-question quiz
- After-class project: Write your own island puzzle
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
The first 2 lessons of every course, every game and all maths practice stay free.
That is ₹208 a month for every lesson of every course. Prefer a teacher? Ask about live classes.
FAQ
Logic puzzles: knights, knaves and grids: questions
What are knights and knaves puzzles?
Logic puzzles set on an island where knights always tell the truth and knaves always lie. You work out who is who from what they say by testing every case.
How do you solve logical reasoning questions in a maths Olympiad?
Write down every case, check each clue against it, and cross out cases that lead to a contradiction. Grids help when people are matched with things.
Is logical reasoning part of maths Olympiads?
Yes. Most school maths Olympiads have a logical reasoning section, and many problems in the maths section are solved with the same case-by-case thinking.
Start a conversation
Want a teacher to take this class?
Tell us the learner's age and level. A teacher from our network teaches with these lessons; we confirm timing and price first.
- Tell us the learner’s age or grade and goals
- We’ll suggest a suitable class or learning path
- We’ll confirm format, timing and fees with a parent or guardian