Deduce #76: The library — the solution

The Deduce puzzle from October 29, 2026, worked through clue by clue: 7 clues, 4 rounds of crossing off, and no guessing anywhere.

The puzzle

Four people — Yuki, Ana, Arlo and Theo — and three things to work out about each: their book, bag and time. The clues only ever rule things out.

1. Ana is not the one at 1pm.
2. The one with the yearbook is earlier than the one with the corduroy bag.
3. The one with the yearbook is not the one with the burlap bag.
4. Yuki is the one with the corduroy bag.
5. The one with the paper bag is exactly 3 hours after the one with the comic.
6. Arlo is the one at 10am.
7. The one with the manual is the one with the corduroy bag.

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, “Ana is not the one at 1pm”: 1pm comes off Ana.

Clue 4, “Yuki is the one with the corduroy bag”: corduroy comes off Ana, Arlo and Theo. That settles it: Yuki’s bag is corduroy.

Clue 5, “The one with the paper bag is exactly 3 hours after the one with the comic”: paper comes off Ana.

Clue 6, “Arlo is the one at 10am”: 10am comes off Yuki, Ana and Theo. That settles it: Arlo is at 10am.

Clue 7, “The one with the manual is the one with the corduroy bag”: manual comes off Ana, Arlo and Theo. That settles it: Yuki’s book is manual.

Round 2

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

Clue 5, “The one with the paper bag is exactly 3 hours after the one with the comic”: comic comes off Ana and Theo; paper comes off Arlo; 11am and noon come off Theo. That settles it: Theo is at 1pm.

Round 3

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

Nobody but Arlo can still have comic, so Arlo’s book is comic.

Nobody but Theo can still have paper, so Theo’s bag is paper.

1pm is Theo’s, so it comes off Yuki.

Clue 2, “The one with the yearbook is earlier than the one with the corduroy bag”: yearbook comes off Theo; 11am comes off Yuki; noon comes off Ana. That settles it: Theo’s book is textbook, Yuki is at noon and Ana is at 11am.

Clue 3, “The one with the yearbook is not the one with the burlap bag”: burlap comes off Ana. That settles it: Ana’s bag is nylon.

Round 4

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

Textbook is Theo’s, so it comes off Ana. That settles it: Ana’s book is yearbook.

Nylon is Ana’s, so it comes off Arlo. That settles it: Arlo’s bag is burlap.

The answer

Previous: Deduce #75 (Wed, Oct 28) · Next: Deduce #77 (Fri, Oct 30) · All Deduce solutions

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.