Deduce #31: The flats — the solution

The Deduce puzzle from September 14, 2026, worked through clue by clue: 8 clues, 3 rounds of crossing off, and no guessing anywhere.

The puzzle

Four people — Rosa, Kit, Dan and Sam — and three things to work out about each: their pet, instrument and floor. The clues only ever rule things out.

1. The cat owner is exactly 2 floors after the piano player.
2. Sam is not the rabbit owner.
3. Dan is on a lower floor than the banjo player.
4. Rosa is the banjo player.
5. Dan is the cat owner.
6. Sam is the one on floor 1.
7. The cello player is not the one on floor 2.
8. The dog owner is the one on floor 2.

The walkthrough

A round is one pass over the clues. Each round applies what the last one settled; every step below is an elimination the clues force, in the order a solver would take them.

Round 1

Start with every possibility open, and take the clues in order.

Clue 2, “Sam is not the rabbit owner”: rabbit comes off Sam.

Clue 3, “Dan is on a lower floor than the banjo player”: banjo comes off Dan; floor 4 comes off Dan.

Clue 4, “Rosa is the banjo player”: banjo comes off Kit and Sam. That settles it: Rosa’s instrument is banjo.

Clue 5, “Dan is the cat owner”: cat comes off Rosa, Kit and Sam. That settles it: Dan’s pet is cat.

Clue 6, “Sam is the one on floor 1”: floor 1 comes off Rosa, Kit and Dan. That settles it: Sam is on floor 1.

Clue 8, “The dog owner is the one on floor 2”: dog comes off Sam; floor 2 comes off Dan. That settles it: Sam’s pet is parrot and Dan is on floor 3.

Round 2

Go back over the clues with the new facts in hand.

Parrot is Sam’s, so it comes off Rosa and Kit.

floor 3 is Dan’s, so it comes off Rosa and Kit.

Clue 1, “The cat owner is exactly 2 floors after the piano player”: piano comes off Kit and Dan.

Clue 3, “Dan is on a lower floor than the banjo player”: floor 2 comes off Rosa. That settles it: Rosa is on floor 4.

Clue 7, “The cello player is not the one on floor 2”: cello comes off Kit. That settles it: Kit’s instrument is drums.

Clue 8, “The dog owner is the one on floor 2”: dog comes off Rosa. That settles it: Rosa’s pet is rabbit, Kit’s pet is dog and Kit is on floor 2.

Round 3

Go back over the clues with the new facts in hand.

Drums is Kit’s, so it comes off Dan and Sam. That settles it: Dan’s instrument is cello.

Cello is Dan’s, so it comes off Sam. That settles it: Sam’s instrument is piano.

The answer

Previous: Deduce #30 (Sun, Sep 13) · Next: Deduce #32 (Tue, Sep 15)

About Deduce

Deduce is Noggin’s daily logic grid: four people, three things to work out about each, and clues that never hand you an answer. Every puzzle has exactly one solution and can be finished by crossing off alone. How to play Deduce, or play today’s.