Easy
orderingpositionsdeduction

Three People Are Standing in Line — Who Is in the Middle?

Problem Statement

Alice, Bob, and Carol are standing in line. Alice is not first. Carol is not last. Bob is not in the middle. Who is in the middle?

Answer

Alice

Step-by-Step Explanation

  1. 1

    Let's list what we know:

  2. 2

    - Alice is not first

  3. 3

    - Carol is not last

  4. 4

    - Bob is not in the middle

  5. 5

    There are three positions: First, Middle, Last.

  6. 6

    Since Bob is not in the middle, Bob must be either first or last.

  7. 7

    If Bob is last, then Carol must be first or middle. But Carol is not last, so this works.

  8. 8

    If Bob is first, then Alice and Carol are middle and last. Alice is not first (✓), Carol is not last, so Carol would be middle and Alice last.

  9. 9

    Testing: Bob (first), Carol (middle), Alice (last) — but this violates 'Carol is not last' if we misread. Let me reconsider.

  10. 10

    Actually: Bob cannot be middle. If Bob is first: positions are Bob, ?, ?. Alice not first (✓). Carol not last means Carol is middle. Alice is last.

  11. 11

    Check: Bob (first), Carol (middle), Alice (last). Alice not first ✓, Carol not last ✗

  12. 12

    So Bob must be last: ?, ?, Bob. Alice not first means Alice is middle or last. Alice can be middle. Carol not last ✓ means Carol is first or middle.

  13. 13

    Solution: Carol (first), Alice (middle), Bob (last).

  14. 14

    Verify: Alice not first ✓, Carol not last ✓, Bob not middle ✓