Classic Logic & Mini Logic
Each X removes a pairing. When a row has only one open cell, that remaining choice must be the match.
Interactive lesson
Process of Elimination
Remove what cannot be true until the answer becomes certain
You do not always need a clue that states the answer directly. Often, the answer appears after every impossible choice has been crossed out.
Try it yourself
The Three Neighbors
Ava, Ben, and Cora each live in a different colored house and own a different pet.
Follow the clues and decide what each new fact allows you to eliminate.
1 Ben owns the fish.
2 The dog owner lives in the blue house.
3 Ava does not live in the blue house.
4 Ben does not live in the green house.
Who owns which pet?
| Neighbor | Cat | Dog | Fish |
|---|---|---|---|
| Ava | |||
| Ben | |||
| Cora |
Who lives in which house?
| Neighbor | Red | Blue | Green |
|---|---|---|---|
| Ava | |||
| Ben | |||
| Cora |
× impossible ✓ match
Deduction 1 of 3
Clue 1 gives us a direct match. What should we mark?
Choose the deduction that is guaranteed by the highlighted clue.
The key takeaway
An X can be as useful as a checkmark.
No clue directly said that Ava lived in the green house. You proved it by removing Blue and Red until Green was the only possibility left.
AvaGreen house · Cat
BenRed house · Fish
CoraBlue house · Dog
When a clue does not reveal a match, ask:
- What does this make impossible?
- After I mark that X, is only one choice left?
Process of elimination is not guessing. It is proving that every other answer cannot be true.
Use the same thinking
Elimination works across the puzzle room
Binary
Row and column rules eliminate values that would create triples or unequal totals.
Futoshiki
Inequalities and used numbers remove candidates until a cell has only one legal value.
Mastermind
Each response removes color arrangements that cannot match the feedback.