Logical Deduction
Eliminate what cannot be true
Logical deduction puzzles give you clues and ask you to find the one possibility that satisfies every clue.
See It in Action
The Problem
Alex, Beth, and Chris each play a different sport: cricket, swimming, and tennis. Alex does not play cricket. Beth does not play swimming. Chris does not play tennis. Who plays cricket?
Common Mistake
Alex doesn't play cricket. So Alex plays swimming or tennis. Beth doesn't play swimming, so Beth plays cricket.
This stops after one inference and doesn't check Chris's constraint. Always verify the full assignment against ALL clues.
Correct Approach
Make a table. From clue 1: Alex plays swimming or tennis. From clue 3: Chris plays cricket or swimming. From clue 2: Beth plays cricket or tennis. Try Beth = cricket: then Chris ≠ cricket (from clue 3 still valid), Chris plays swimming (since tennis is now only for Alex or Beth). But then Alex plays tennis. Check: Alex≠cricket ✓, Beth≠swimming ✓, Chris≠tennis ✓. Consistent!
Answer: Beth plays cricket
Alex: tennis. Beth: cricket. Chris: swimming. Check all clues: Alex≠cricket ✓, Beth≠swimming ✓, Chris≠tennis ✓. ✓
The Core Concept
Logical deduction works through elimination. The correct answer must satisfy ALL clues simultaneously. A common mistake is finding an answer that satisfies ONE clue and stopping. Always test your answer against every single clue.
The most reliable strategy is to set up a table or list all possibilities, then cross out each one that violates any clue. What's left at the end is your answer. For age/ordering puzzles, start with the most restrictive clue (the one that eliminates the most possibilities).
For "only one is true" puzzles, try assuming each statement is the true one, check if the rest are then false, and see which assumption creates a consistent system.
Common Mistakes to Avoid
Stopping after satisfying one clue
The answer must satisfy ALL clues. An assignment that works for clue 1 might violate clue 3. Always check every constraint before accepting an answer.
Not using process of elimination systematically
Random guessing is slow and error-prone. Draw a grid or list, and cross out one option at a time. What's left must be correct.
Misreading "not" in clues
"Alex does not play cricket" means Alex plays swimming OR tennis — not that Alex plays both. One negative clue opens two possibilities, not zero.
Forgetting to check that the assignment is unique
If two answers seem to work, re-read the clues. Either a clue was misunderstood or there's an error. A well-formed logic puzzle has exactly one solution.
Try It Yourself
Four children — Jaya, Kai, Lena, and Max — each prefer a different colour: red, blue, green, yellow. Jaya's favourite is not red or blue. Kai's is not green. Lena's is blue. Who prefers green?
Hint: Start with the most definite clue: Lena's is blue. That eliminates blue for everyone else. Now work through the remaining clues.
Key Tips
Always draw a grid (people as rows, options as columns) and mark X for "impossible" and ✓ for "confirmed."
Start with the most certain clue ("Lena's is blue" is definite; "Alex is not blue" is a restriction).
Check your final answer against EVERY clue, not just the last one you used.
Ready to practise Logical Deduction?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.