Deduce #3: The market — the solution

The Deduce puzzle from August 17, 2026, worked through clue by clue: 8 clues, 3 rounds of crossing off, and no guessing anywhere.

The puzzle

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

1. Vic is the pears seller.
2. Lena is not the one at stall 2.
3. Lena is the one in the wool hat.
4. The one in the paper hat is exactly 3 stalls after Dan.
5. The apples seller is not the one in the wool hat.
6. The one in the cloth hat is at a lower stall than Vic.
7. The pears seller is at a lower stall than the one in the paper hat.
8. Dan is the figs 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 1, “Vic is the pears seller”: pears comes off Lena, Dan and Wes. That settles it: Vic’s fruit is pears.

Clue 2, “Lena is not the one at stall 2”: stall 2 comes off Lena.

Clue 3, “Lena is the one in the wool hat”: wool comes off Vic, Dan and Wes. That settles it: Lena’s hat is wool.

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

Clue 5, “The apples seller is not the one in the wool hat”: apples comes off Lena.

Clue 6, “The one in the cloth hat is at a lower stall than Vic”: cloth comes off Vic; stall 1 comes off Vic.

Clue 7, “The pears seller is at a lower stall than the one in the paper hat”: paper comes off Vic; stall 4 comes off Vic; stall 1 and stall 2 come off Wes. That settles it: Vic’s hat is leather.

Clue 8, “Dan is the figs seller”: figs comes off Lena and Wes. That settles it: Lena’s fruit is plums and Dan’s fruit is figs.

Round 2

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

Plums is Lena’s, so it comes off Wes. That settles it: Wes’s fruit is apples.

Leather is Vic’s, so it comes off Dan and Wes. That settles it: Dan’s hat is cloth.

Cloth is Dan’s, so it comes off Wes. That settles it: Wes’s hat is paper.

stall 1 is Dan’s, so it comes off Lena.

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

Clue 4, “The one in the paper hat is exactly 3 stalls after Dan”: stall 3 comes off Wes. That settles it: Wes is at stall 4.

Round 3

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

stall 4 is Wes’s, so it comes off Lena. That settles it: Lena is at stall 3.

The answer

Previous: Deduce #2 (Sun, Aug 16) · Next: Deduce #4 (Tue, Aug 18)

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.