Deduce #64: The race — the solution

The Deduce puzzle from October 17, 2026, worked through clue by clue: 7 clues, 4 rounds of crossing off, and no guessing anywhere.

The puzzle

Four people — Remy, Mila, Cal and Rhea — and three things to work out about each: their jersey, club and place. The clues only ever rule things out.

1. Cal is not the Hares runner.
2. The Rovers runner is exactly 3 places after Mila.
3. The one in the pink jersey is exactly 2 places after Cal.
4. Mila is the one in the brown jersey.
5. The one in the purple jersey is not the Hawks runner.
6. The one in the gray jersey is not the Hawks runner.
7. Remy is the one in the purple jersey.

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, “Cal is not the Hares runner”: Hares comes off Cal.

Clue 2, “The Rovers runner is exactly 3 places after Mila”: Rovers comes off Mila; 2nd, 3rd and 4th come off Mila. That settles it: Mila is in 1st.

Clue 3, “The one in the pink jersey is exactly 2 places after Cal”: pink comes off Mila and Cal; 3rd and 4th come off Cal.

Clue 4, “Mila is the one in the brown jersey”: brown comes off Remy, Cal and Rhea. That settles it: Mila’s jersey is brown.

Clue 7, “Remy is the one in the purple jersey”: purple comes off Cal and Rhea. That settles it: Remy’s jersey is purple and Cal’s jersey is gray.

Round 2

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

Gray is Cal’s, so it comes off Rhea. That settles it: Rhea’s jersey is pink.

1st is Mila’s, so it comes off Remy, Cal and Rhea. That settles it: Cal is in 2nd.

2nd is Cal’s, so it comes off Remy and Rhea.

Clue 2, “The Rovers runner is exactly 3 places after Mila”: Rovers comes off Cal.

Clue 3, “The one in the pink jersey is exactly 2 places after Cal”: 3rd comes off Rhea. That settles it: Rhea is in 4th.

Clue 5, “The one in the purple jersey is not the Hawks runner”: Hawks comes off Remy.

Clue 6, “The one in the gray jersey is not the Hawks runner”: Hawks comes off Cal. That settles it: Cal’s club is Kestrels.

Round 3

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

Kestrels is Cal’s, so it comes off Remy, Mila and Rhea.

4th is Rhea’s, so it comes off Remy. That settles it: Remy is in 3rd.

Clue 2, “The Rovers runner is exactly 3 places after Mila”: Rovers comes off Remy. That settles it: Remy’s club is Hares.

Round 4

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

Hares is Remy’s, so it comes off Mila and Rhea. That settles it: Mila’s club is Hawks.

Hawks is Mila’s, so it comes off Rhea. That settles it: Rhea’s club is Rovers.

The answer

Previous: Deduce #63 (Fri, Oct 16) · Next: Deduce #65 (Sun, Oct 18) · 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.