Problem
Logic grid deduction table
Four people are each in a different room, 1 to 4. One person per room and one room per person. Every 'is not' clue must hold at once. Find which room Noah is in.
Reasoning · Grade 3-2 Solving Problems with Tables
Your answer
Watch out No clue names Noah's room, which looks like a dead end — but crossing off every 'is not' leaves one.
How to solve
Strategy Use Matrix Logic — A 4-by-4 grid of people against rooms lets us mark each 'is not' as an X and each known fact as a check. Once Ava fills Room 1, we cross out that column for everyone else, and the remaining X's leave each person only one open room.
1STEP 1
Place Ava and clear her column
Ava takes Room 1, so the others cannot.
Ava = Room 1
Filling one box in a one-to-one table immediately rules out everyone else in that row and column.
K.MD.B.3Introduce A VariablePlacing Ava in her room immediately clears that room for everyone else and clears every other room for her.
Why?
Each person takes one room and each room takes one person, so a filled box empties its whole row and its whole column.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
Every crossing-out shrinks somebody's choices, and when a person is left with one open room that room has to be theirs.
🧱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.
2STEP 2
Find Mia's room
Mia is barred from 2 and 4, so Room 3.
Mia ≠ 1, 2, 4 → Mia = Room 3
When three of the four rooms are crossed out for a person, the one remaining room must be theirs.
K.MD.B.3Eliminate Possibilities3STEP 3
Find Noah's room
That leaves Noah only Room 4.
Noah ≠ 1, 2, 3 → Noah = Room 4
After others claim their rooms, Noah's choices shrink until just one room is open for him.
K.MD.B.3Eliminate PossibilitiesAnswer
Room 4
The final assignment is Ava-1, Liam-2, Mia-3, Noah-4, which uses each room once and obeys every clue: Mia avoids Rooms 2 and 4, and Noah avoids Room 2. So Noah in Room 4 is consistent.
Takeaway
Cross out the rooms each person can't be in on a little grid, and the last open box points straight to the answer!
- Place Ava and clear her column
- Find Mia's room
- Find Noah's room