# RE6 | meta/muse-spark-1.1 | run 2

## Prompt

Ann, Beth, and Cara finished a race in distinct positions. Ann did not finish first. Beth finished immediately ahead of Ann. Cara did not finish last. Who finished in each position?

## Response

Cara finished first, Beth second, and Ann third. This is the only distinct ordering that satisfies all three conditions at once.

## Solution

There are only 6 possible orderings for 3 distinct positions. Apply the constraints:

1.  **Ann did not finish first:** Ann's position ≠ 1, so Ann = 2 or 3
2.  **Beth finished immediately ahead of Ann:** Beth's position = Ann's position - 1
3.  **Cara did not finish last:** Cara's position ≠ 3

Testing the two possibilities for Ann:

*   If Ann = 2, then Beth = 1. That leaves Cara = 3. This violates constraint 3.
*   If Ann = 3, then Beth = 2. That leaves Cara = 1. This satisfies all constraints.

| Position | Finisher |
| :--- | :--- |
| 1st | Cara |
| 2nd | Beth |
| 3rd | Ann |

## Verification

*   Ann did not finish first — Ann finished 3rd.
*   Beth immediately ahead of Ann — Beth finished 2nd, directly in front of 3rd.
*   Cara did not finish last — Cara finished 1st.

Do you want me to show you a quick method for solving these types of ordering puzzles with more racers?
