Deduce #40: The market — the solution

The Deduce puzzle from September 23, 2026, worked through clue by clue: 6 clues, 4 rounds of crossing off, and no guessing anywhere.

The puzzle

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

1. Cleo is the one in the wool hat.
2. Rosa is the one at stall 4.
3. The one in the paper hat is exactly 2 stalls after Kit.
4. Cleo is the apples seller.
5. The damsons seller is exactly 2 stalls after the one in the leather hat.
6. The figs seller is the one at stall 4.

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 1, “Cleo is the one in the wool hat”: wool comes off Gwen, Kit and Rosa. That settles it: Cleo’s hat is wool.

Clue 2, “Rosa is the one at stall 4”: stall 4 comes off Gwen, Kit and Cleo. That settles it: Rosa is at stall 4.

Clue 3, “The one in the paper hat is exactly 2 stalls after Kit”: paper comes off Kit; stall 5 comes off Kit.

Clue 4, “Cleo is the apples seller”: apples comes off Gwen, Kit and Rosa. That settles it: Cleo’s fruit is apples.

Clue 5, “The damsons seller is exactly 2 stalls after the one in the leather hat”: damsons comes off Kit; leather comes off Rosa.

Clue 6, “The figs seller is the one at stall 4”: figs comes off Gwen and Kit. That settles it: Kit’s fruit is pears and Rosa’s fruit is figs.

Round 2

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

Pears is Kit’s, so it comes off Gwen. That settles it: Gwen’s fruit is damsons.

Clue 5, “The damsons seller is exactly 2 stalls after the one in the leather hat”: stall 2 comes off Gwen and Kit; leather comes off Gwen; stall 3 comes off Gwen. That settles it: Gwen is at stall 5 and Kit is at stall 3.

Round 3

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

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

stall 5 is Gwen’s, so it comes off Cleo.

stall 3 is Kit’s, so it comes off Cleo. That settles it: Cleo is at stall 2.

Clue 3, “The one in the paper hat is exactly 2 stalls after Kit”: paper comes off Rosa. That settles it: Rosa’s hat is cloth.

Round 4

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

Cloth is Rosa’s, so it comes off Gwen. That settles it: Gwen’s hat is paper.

The answer

Previous: Deduce #39 (Tue, Sep 22)

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.