Deduce #10: The flats — the solution

The Deduce puzzle from August 24, 2026, worked through clue by clue: 6 clues, 3 rounds of crossing off, and no guessing anywhere.

The puzzle

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

1. The gerbil owner is the flute player.
2. The cat owner is exactly 2 floors after Quinn.
3. Quinn is the tortoise owner.
4. Marco is the cat owner.
5. The cello player is on a lower floor than Sam.
6. The harp player is exactly 2 floors after Sam.

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, “The cat owner is exactly 2 floors after Quinn”: cat comes off Quinn; floor 5 and floor 6 come off Quinn.

Clue 3, “Quinn is the tortoise owner”: tortoise comes off Sam, Cleo and Marco. That settles it: Quinn’s pet is tortoise.

Clue 4, “Marco is the cat owner”: cat comes off Sam and Cleo. That settles it: Marco’s pet is cat.

Clue 5, “The cello player is on a lower floor than Sam”: cello comes off Sam; floor 3 comes off Sam.

Clue 6, “The harp player is exactly 2 floors after Sam”: harp comes off Sam and Quinn; floor 5 and floor 6 come off Sam. That settles it: Sam is on floor 4.

Round 2

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

floor 4 is Sam’s, so it comes off Quinn, Cleo and Marco. That settles it: Quinn is on floor 3.

floor 3 is Quinn’s, so it comes off Cleo and Marco.

Clue 1, “The gerbil owner is the flute player”: flute comes off Quinn and Marco.

Clue 2, “The cat owner is exactly 2 floors after Quinn”: floor 6 comes off Marco. That settles it: Marco is on floor 5.

Clue 5, “The cello player is on a lower floor than Sam”: cello comes off Cleo and Marco.

Clue 6, “The harp player is exactly 2 floors after Sam”: harp comes off Marco; floor 5 comes off Cleo. That settles it: Marco’s instrument is banjo and Cleo is on floor 6.

Round 3

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

Banjo is Marco’s, so it comes off Sam, Quinn and Cleo. That settles it: Sam’s instrument is flute and Quinn’s instrument is cello.

Nobody but Cleo can still have harp, so Cleo’s instrument is harp.

Clue 1, “The gerbil owner is the flute player”: gerbil comes off Cleo. That settles it: Sam’s pet is gerbil and Cleo’s pet is parrot.

The answer

Previous: Deduce #9 (Sun, Aug 23) · Next: Deduce #11 (Tue, Aug 25)

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.