Logic & Reasoning Puzzles
Using systematic approaches to solve puzzles involving age, weight, arrangements and logical deduction.
What is Logic & Reasoning Puzzles?
Logic puzzles test your ability to think systematically and use clues to reach a solution. They are less about calculation and more about reasoning.
In the 11+ exam, logic puzzles may involve age problems, arrangement puzzles, truth/liar puzzles, or problems where you need to use all the given clues to find the answer.
Step-by-Step Method
Read ALL the clues before starting
Do not start solving after reading just one clue. Read everything first to understand the full picture.
Make a table, grid or list
Organise the information visually. For sorting puzzles, a grid with ticks and crosses works well.
Start with the most definite clue
Some clues give you a definite fact. Start with those and work from there.
Use process of elimination
If something is definitely NOT in one position, cross it out. Eventually only one possibility remains.
Check ALL clues are satisfied
When you think you have the answer, go back and verify it works with every single clue.
Worked Examples
Ali is twice as old as Ben. Together their ages add up to 24. How old is each?
Working
- Let Ben’s age = x. Ali’s age = 2x.
- x + 2x = 24.
- 3x = 24.
- x = 8.
- Ben = 8, Ali = 16.
- Check: 16 is twice 8. 16 + 8 = 24. Correct!
Three children – Amy, Beth and Carl – finished a race in 1st, 2nd and 3rd. Amy did not finish last. Beth finished before Amy. Who came 2nd?
Working
- Beth finished before Amy, so Beth is not 3rd and Amy is not 1st.
- Amy did not finish last (3rd), so Amy is 2nd.
- Beth is before Amy, so Beth is 1st.
- Carl is 3rd.
Three friends each have a different pet (cat, dog, fish). Jo does not have a dog. Kim has a fish. Who has the cat?
Working
- Kim has a fish – mark this in the grid.
- So Kim does not have cat or dog.
- Jo does not have a dog – so Jo has a cat or fish.
- Kim already has the fish, so Jo has the cat.
- That leaves the dog for the third friend.
Common Mistakes
Not using all the clues – solving based on just one or two clues.
Every clue is there for a reason. Use them all and check your answer against every clue.
Guessing instead of working systematically.
Make a table or grid. Use logic to eliminate options one by one.
Not checking the final answer against all clues.
Always go back to the original question and verify that every condition is met.
Top Tips
- For age problems, let one age be x and express the other ages in terms of x.
- For arrangement puzzles, a simple grid with ticks and crosses is very effective.
- If you are stuck, try assuming something and see if it leads to a contradiction.
- Work neatly – logic puzzles require clear thinking, and messy notes make errors more likely.
Ready to practise?
Put these techniques into action with our free practice papers.
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