Deduce #77: The diner — the solution

The Deduce puzzle from October 30, 2026, worked through clue by clue: 8 clues, 3 rounds of crossing off, and no guessing anywhere.

The puzzle

Four people — Reese, Trey, Mason and Blake — and three things to work out about each: their order, drink and booth. The clues only ever rule things out.

1. Trey is the one who ordered pie.
2. The cocoa drinker is in a lower-numbered booth than Blake.
3. The one who ordered sausage is the milk drinker.
4. The milk drinker is exactly 3 booths after the one who ordered pie.
5. The root beer drinker is in a lower-numbered booth than Blake.
6. Mason is the cocoa drinker.
7. Blake is not the one who ordered sausage.
8. The one who ordered eggs is not the one in booth 4.

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, “Trey is the one who ordered pie”: pie comes off Reese, Mason and Blake. That settles it: Trey’s order is pie.

Clue 2, “The cocoa drinker is in a lower-numbered booth than Blake”: cocoa comes off Blake; booth 3 comes off Blake.

Clue 3, “The one who ordered sausage is the milk drinker”: milk comes off Trey.

Clue 4, “The milk drinker is exactly 3 booths after the one who ordered pie”: booth 4, booth 5 and booth 6 come off Trey. That settles it: Trey is in booth 3.

Clue 5, “The root beer drinker is in a lower-numbered booth than Blake”: root beer comes off Blake.

Clue 6, “Mason is the cocoa drinker”: cocoa comes off Reese and Trey. That settles it: Mason’s drink is cocoa.

Clue 7, “Blake is not the one who ordered sausage”: sausage comes off Blake.

Round 2

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

booth 3 is Trey’s, so it comes off Reese and Mason.

Clue 2, “The cocoa drinker is in a lower-numbered booth than Blake”: booth 6 comes off Mason; booth 4 comes off Blake.

Clue 3, “The one who ordered sausage is the milk drinker”: sausage comes off Mason; milk comes off Blake. That settles it: Reese’s order is sausage, Reese’s drink is milk and Blake’s drink is sweet tea.

Clue 4, “The milk drinker is exactly 3 booths after the one who ordered pie”: booth 4 and booth 5 come off Reese. That settles it: Reese is in booth 6.

Clue 8, “The one who ordered eggs is not the one in booth 4”: eggs comes off Mason. That settles it: Mason’s order is toast.

Round 3

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

Toast is Mason’s, so it comes off Blake. That settles it: Blake’s order is eggs.

Sweet tea is Blake’s, so it comes off Trey. That settles it: Trey’s drink is root beer.

booth 6 is Reese’s, so it comes off Blake. That settles it: Blake is in booth 5.

booth 5 is Blake’s, so it comes off Mason. That settles it: Mason is in booth 4.

The answer

Previous: Deduce #76 (Thu, Oct 29) · Next: Deduce #78 (Sat, Oct 31) · 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.