Deduce #49: The library — the solution

The Deduce puzzle from October 2, 2026, worked through clue by clue: 8 clues, 3 rounds of crossing off, and no guessing anywhere.

The puzzle

Four people — Gwen, Wes, Nadia and Pia — and three things to work out about each: their book, bag and time. The clues only ever rule things out.

1. Pia is earlier than the one with the velvet bag.
2. Gwen is not the one at noon.
3. Wes is the one with the novel.
4. Pia is the one with the diary.
5. The one with the novel is not the one with the velvet bag.
6. The one with the cookbook is the one at 10am.
7. Pia is not the one with the leather bag.
8. The one with the diary is exactly 2 hours after the one with the plastic 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, “Pia is earlier than the one with the velvet bag”: velvet comes off Pia; noon comes off Pia.

Clue 2, “Gwen is not the one at noon”: noon comes off Gwen.

Clue 3, “Wes is the one with the novel”: novel comes off Gwen, Nadia and Pia. That settles it: Wes’s book is novel.

Clue 4, “Pia is the one with the diary”: diary comes off Gwen and Nadia. That settles it: Pia’s book is diary.

Clue 5, “The one with the novel is not the one with the velvet bag”: velvet comes off Wes.

Clue 6, “The one with the cookbook is the one at 10am”: 10am comes off Wes and Pia.

Clue 7, “Pia is not the one with the leather bag”: leather comes off Pia.

Clue 8, “The one with the diary is exactly 2 hours after the one with the plastic bag”: plastic comes off Pia; 9am comes off Pia. That settles it: Pia’s bag is tartan and Pia is at 11am.

Round 2

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

Tartan is Pia’s, so it comes off Gwen, Wes and Nadia.

11am is Pia’s, so it comes off Gwen, Wes and Nadia.

Clue 1, “Pia is earlier than the one with the velvet bag”: velvet comes off Gwen; 9am and 10am come off Nadia. That settles it: Nadia is at noon.

Clue 6, “The one with the cookbook is the one at 10am”: cookbook comes off Nadia. That settles it: Gwen’s book is cookbook, Nadia’s book is atlas and Gwen is at 10am.

Clue 8, “The one with the diary is exactly 2 hours after the one with the plastic bag”: plastic comes off Gwen and Nadia; noon comes off Wes. That settles it: Gwen’s bag is leather and Wes is at 9am.

Round 3

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

Leather is Gwen’s, so it comes off Wes and Nadia. That settles it: Wes’s bag is plastic and Nadia’s bag is velvet.

The answer

Previous: Deduce #48 (Thu, Oct 1)

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.