Problem
Logic grid deduction table
Liam, Mia and Noah are each in a different room among Room 1, 2 and 3. Every statement they make is true. Mia is not in Room 1, Noah says Mia is not in Room 3, and Liam says he is not in Room 3. Find Noah's room.
Reasoning · Grade 2-2 Problem Solving with Tables
Your answer
Watch out No clue places Noah, which looks like a dead end — but once the other two are fixed he takes the room left over.
How to solve
Strategy Use Matrix Logic — This is a 'who is where' puzzle with three people and three rooms, so we make a person-by-room grid and mark X for each room a clue rules out. Crossing out the impossible cells leaves exactly one room per person, which pins down Noah.
1STEP 1
Pin down Mia first
Mia is barred from Rooms 1 and 3, so she is in Room 2.
Mia ≠ 1, Mia ≠ 3 → Mia = 2
If a person cannot be in two of the three rooms, the one room that is left must be theirs.
2.OA.A.1Eliminate PossibilitiesSince Mia is barred from two of the three rooms, the one room left has to be hers.
Why?
Mia is in some room, and two of the three have been ruled out, so only one candidate is still standing.
🧱Rule out the rest and the last one is forcedIf every possibility but one has been ruled out, the survivor must be the answer — no further checking is needed.
Why?
Three people fill three rooms with one person each, so fixing one person's room takes that room away from everybody else.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
2STEP 2
Place Liam
Liam is not in Room 3 and Room 2 is taken, so he is in Room 1.
Liam ≠ 3, Room 2 = Mia → Liam = 1
Once one room is used up, the others have fewer choices left, like filling a grid one cell at a time.
2.OA.A.1Introduce A Variable3STEP 3
Noah gets the last room
One room is left, so Noah is in Room 3.
Room 1 = Liam, Room 2 = Mia → Noah = 3
Three people fill three rooms, so the last person simply takes the one empty room.
2.OA.B.2Introduce A VariableAnswer
Room 3
Check all three clues against Liam=Room 1, Mia=Room 2, Noah=Room 3: Liam is not in Room 3 (true), Mia is not in Room 1 (true), and Mia is not in Room 3 (true). All rooms are different. Every statement holds, so the answer is consistent.
Takeaway
Cross out what cannot be true and the answer is whatever is left - that is all the table does for you!
- Pin down Mia first
- Place Liam
- Noah gets the last room