Deduce #32: The market — the solution

The Deduce puzzle from September 15, 2026, worked through clue by clue: 8 clues, 4 rounds of crossing off, and no guessing anywhere.

The puzzle

Four people — Quinn, Finn, Jonah and Cleo — and three things to work out about each: their fruit, hat and stall. The clues only ever rule things out.

1. The cherries seller is exactly 3 stalls after the one in the leather hat.
2. Finn is the plums seller.
3. The one in the straw hat is not the one at stall 3.
4. The figs seller is at a lower stall than the one in the paper hat.
5. The figs seller is at a lower stall than Quinn.
6. The one in the straw hat is not the one at stall 4.
7. The cherries seller is exactly 2 stalls after Cleo.
8. Jonah is the cherries seller.

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, “Finn is the plums seller”: plums comes off Quinn, Jonah and Cleo. That settles it: Finn’s fruit is plums.

Clue 5, “The figs seller is at a lower stall than Quinn”: figs comes off Quinn; stall 2 comes off Quinn.

Clue 7, “The cherries seller is exactly 2 stalls after Cleo”: cherries comes off Cleo; stall 4 and stall 5 come off Cleo.

Clue 8, “Jonah is the cherries seller”: cherries comes off Quinn. That settles it: Quinn’s fruit is damsons and Jonah’s fruit is cherries.

Round 2

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

Damsons is Quinn’s, so it comes off Cleo. That settles it: Cleo’s fruit is figs.

Clue 1, “The cherries seller is exactly 3 stalls after the one in the leather hat”: leather comes off Quinn and Jonah; stall 2, stall 3 and stall 4 come off Jonah. That settles it: Jonah is at stall 5.

Clue 4, “The figs seller is at a lower stall than the one in the paper hat”: paper comes off Cleo.

Clue 7, “The cherries seller is exactly 2 stalls after Cleo”: stall 2 comes off Cleo. That settles it: Cleo is at stall 3.

Round 3

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

stall 5 is Jonah’s, so it comes off Quinn and Finn.

stall 3 is Cleo’s, so it comes off Quinn and Finn. That settles it: Quinn is at stall 4.

Nobody but Finn can still have stall 2, so Finn is at stall 2.

Clue 1, “The cherries seller is exactly 3 stalls after the one in the leather hat”: leather comes off Cleo.

Clue 3, “The one in the straw hat is not the one at stall 3”: straw comes off Cleo. That settles it: Cleo’s hat is cloth.

Clue 4, “The figs seller is at a lower stall than the one in the paper hat”: paper comes off Finn.

Clue 6, “The one in the straw hat is not the one at stall 4”: straw comes off Quinn.

Round 4

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

Cloth is Cleo’s, so it comes off Quinn, Finn and Jonah. That settles it: Quinn’s hat is paper.

Nobody but Finn can still have leather, so Finn’s hat is leather.

Nobody but Jonah can still have straw, so Jonah’s hat is straw.

The answer

Previous: Deduce #31 (Mon, Sep 14) · Next: Deduce #33 (Wed, Sep 16)

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.