Deduce #24: The market — the solution

The Deduce puzzle from September 7, 2026, worked through clue by clue: 6 clues, 4 rounds of crossing off, and no guessing anywhere.

The puzzle

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

1. The one in the leather hat is exactly 2 stalls after Gwen.
2. Rosa is not the damsons seller.
3. Gwen is the pears seller.
4. Eve is the one in the wool hat.
5. The one in the leather hat is at a lower stall than Lena.
6. The plums seller is exactly 3 stalls after the one in the felt hat.

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, “The one in the leather hat is exactly 2 stalls after Gwen”: leather comes off Gwen; stall 4 and stall 5 come off Gwen.

Clue 2, “Rosa is not the damsons seller”: damsons comes off Rosa.

Clue 3, “Gwen is the pears seller”: pears comes off Rosa, Eve and Lena. That settles it: Gwen’s fruit is pears.

Clue 4, “Eve is the one in the wool hat”: wool comes off Rosa, Gwen and Lena. That settles it: Eve’s hat is wool.

Clue 5, “The one in the leather hat is at a lower stall than Lena”: leather comes off Lena; stall 5 comes off Rosa; stall 2 comes off Lena.

Clue 6, “The plums seller is exactly 3 stalls after the one in the felt hat”: plums comes off Rosa; felt comes off Lena. That settles it: Rosa’s fruit is cherries and Lena’s hat is straw.

Round 2

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

Cherries is Rosa’s, so it comes off Eve and Lena.

Straw is Lena’s, so it comes off Rosa and Gwen. That settles it: Gwen’s hat is felt.

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

Clue 1, “The one in the leather hat is exactly 2 stalls after Gwen”: stall 3 comes off Rosa and Gwen; stall 2 comes off Rosa. That settles it: Rosa is at stall 4 and Gwen is at stall 2.

Clue 5, “The one in the leather hat is at a lower stall than Lena”: stall 3 and stall 4 come off Lena. That settles it: Lena is at stall 5.

Round 3

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

stall 4 is Rosa’s, so it comes off Eve.

stall 2 is Gwen’s, so it comes off Eve.

stall 5 is Lena’s, so it comes off Eve. That settles it: Eve is at stall 3.

Clue 6, “The plums seller is exactly 3 stalls after the one in the felt hat”: plums comes off Eve. That settles it: Eve’s fruit is damsons.

Round 4

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

Damsons is Eve’s, so it comes off Lena. That settles it: Lena’s fruit is plums.

The answer

Previous: Deduce #23 (Sun, Sep 6) · Next: Deduce #25 (Tue, Sep 8)

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.