Solving Logic Grid Puzzles
A logic grid puzzle gives you a handful of clues and never tells you an answer directly. You get there by ruling things out — and the surprising part is that ruling enough things out leaves exactly one possibility standing.
The grid is just somewhere to keep your crossings-out so you do not have to hold them all in your head.
The Puzzle
Four friends — Alice, Bob, Carol and David — each own a dragon. The dragons are red, blue, green and yellow, one each.
The clues:
- Alice's dragon is not red and not blue.
- Bob's dragon is not green.
- Carol owns the red dragon.
- David's dragon is not blue and not yellow.
Setting Up
Draw a grid with the four names down the side and the four colors across the top. Every square is a question: does this person own this color? You will write ✗ for no and ✓ for yes.
Solving It
- Clue 3 first, because it is the only one that says yes. Put ✓ where Carol meets Red. Now fill Carol's whole row with ✗ (she cannot own a second dragon) and the whole Red column with ✗ (nobody else can own the red one).
- Clue 1. Alice is not red — already crossed out — and not blue. Cross Alice/Blue.
- Clue 4. David is not blue and not yellow. Cross both.
- Look at David's row. Red is gone from step 1, blue and yellow from step 3. Only Green is left, so David owns green. ✓ it, then cross out the rest of the Green column.
- Look at Alice's row. Red, blue and now green are all crossed out. Alice owns yellow.
- Bob gets what is left, which is blue. Check it against clue 2 — Bob is not green, and he is not — so nothing is broken.
The order matters. Starting with clue 3 is what makes the rest fall over, because a single ✓ lets you cross out a whole row and a whole column at once.
Which dragon does Alice own?
- The green one
- The yellow one
- The blue one
The Answer
Carol has red, David has green, Alice has yellow and Bob has blue.
Notice that clue 2 was never really needed to find the answer — David's row solved itself from clues 1, 3 and 4. Clue 2 is there to let you check your work. Good puzzles often include one clue like that.
Tips
- Start with any clue that says something is true, not what it is not.
- Every ✓ earns you a full row and a full column of ✗. That is the big one.
- When a row has only one empty square left, that square is a ✓.
- If two clues seem to disagree, you have made a mistake earlier. Go back rather than guess.