Deduce #51: The bakery line — the solution

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

The puzzle

Four people — Dan, Ben, Lena and Tess — and three things to work out about each: their order, coat and spot. The clues only ever rule things out.

1. Tess is ahead of the one in the cream coat.
2. The one in the red coat is exactly 3 places after Tess.
3. The one buying a bun is the one 4th in line.
4. The one buying a roll is not the one in the red coat.
5. Lena is the one buying a roll.
6. The one buying a loaf is ahead of Dan.
7. Ben is the one in the green coat.

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, “Tess is ahead of the one in the cream coat”: cream comes off Tess; 6th comes off Tess.

Clue 2, “The one in the red coat is exactly 3 places after Tess”: red comes off Tess; 4th and 5th come off Tess. That settles it: Tess is 3rd in line.

Clue 3, “The one buying a bun is the one 4th in line”: a bun comes off Tess.

Clue 5, “Lena is the one buying a roll”: a roll comes off Dan, Ben and Tess. That settles it: Lena’s order is a roll.

Clue 6, “The one buying a loaf is ahead of Dan”: a loaf comes off Dan; 3rd comes off Dan.

Clue 7, “Ben is the one in the green coat”: green comes off Dan, Lena and Tess. That settles it: Ben’s coat is green and Tess’s coat is brown.

Round 2

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

Brown is Tess’s, so it comes off Dan and Lena.

3rd is Tess’s, so it comes off Ben and Lena.

Clue 3, “The one buying a bun is the one 4th in line”: 4th comes off Lena.

Clue 4, “The one buying a roll is not the one in the red coat”: red comes off Lena. That settles it: Lena’s coat is cream.

Round 3

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

Cream is Lena’s, so it comes off Dan. That settles it: Dan’s coat is red.

Clue 2, “The one in the red coat is exactly 3 places after Tess”: 4th and 5th come off Dan. That settles it: Dan is 6th in line.

Clue 3, “The one buying a bun is the one 4th in line”: a bun comes off Dan. That settles it: Dan’s order is a donut, Ben’s order is a bun and Ben is 4th in line.

Round 4

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

A donut is Dan’s, so it comes off Tess. That settles it: Tess’s order is a loaf.

6th is Dan’s, so it comes off Lena. That settles it: Lena is 5th in line.

The answer

Previous: Deduce #50 (Sat, Oct 3)

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.