Deduce #13: The bakery line — the solution

The Deduce puzzle from August 27, 2026, worked through clue by clue: 8 clues, 3 rounds of crossing off, and no guessing anywhere.

The puzzle

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

1. The one buying a roll is not the one in the cream coat.
2. The one in the navy coat is exactly 2 places after Nadia.
3. Ben is the one 1st in line.
4. Hugo is the one in the cream coat.
5. Ben is not the one buying a cake.
6. The one buying a donut is the one in the brown coat.
7. The one buying a donut is not the one 1st in line.
8. Nadia is ahead of the one buying a roll.

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, “The one in the navy coat is exactly 2 places after Nadia”: navy comes off Nadia; 3rd and 4th come off Nadia.

Clue 3, “Ben is the one 1st in line”: 1st comes off Hugo, Nadia and Eve. That settles it: Nadia is 2nd in line and Ben is 1st in line.

Clue 4, “Hugo is the one in the cream coat”: cream comes off Nadia, Eve and Ben. That settles it: Hugo’s coat is cream.

Clue 5, “Ben is not the one buying a cake”: a cake comes off Ben.

Clue 6, “The one buying a donut is the one in the brown coat”: a donut comes off Hugo.

Clue 7, “The one buying a donut is not the one 1st in line”: a donut comes off Ben.

Clue 8, “Nadia is ahead of the one buying a roll”: a roll comes off Nadia and Ben. That settles it: Ben’s order is a loaf.

Round 2

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

A loaf is Ben’s, so it comes off Hugo, Nadia and Eve.

2nd is Nadia’s, so it comes off Hugo and Eve.

Clue 1, “The one buying a roll is not the one in the cream coat”: a roll comes off Hugo. That settles it: Hugo’s order is a cake.

Clue 2, “The one in the navy coat is exactly 2 places after Nadia”: navy comes off Ben; 3rd comes off Eve. That settles it: Eve is 4th in line.

Clue 6, “The one buying a donut is the one in the brown coat”: brown comes off Ben. That settles it: Ben’s coat is red.

Round 3

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

A cake is Hugo’s, so it comes off Nadia and Eve. That settles it: Nadia’s order is a donut.

A donut is Nadia’s, so it comes off Eve. That settles it: Eve’s order is a roll.

Red is Ben’s, so it comes off Nadia and Eve. That settles it: Nadia’s coat is brown.

Nobody but Eve can still have navy, so Eve’s coat is navy.

4th is Eve’s, so it comes off Hugo. That settles it: Hugo is 3rd in line.

The answer

Previous: Deduce #12 (Wed, Aug 26) · Next: Deduce #14 (Fri, Aug 28)

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.