Three People Are Standing in Line — Who Is in the Middle?
Problem Statement
Answer
Alice
Step-by-Step Explanation
- 1
Let's list what we know:
- 2
- Alice is not first
- 3
- Carol is not last
- 4
- Bob is not in the middle
- 5
There are three positions: First, Middle, Last.
- 6
Since Bob is not in the middle, Bob must be either first or last.
- 7
If Bob is last, then Carol must be first or middle. But Carol is not last, so this works.
- 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
Testing: Bob (first), Carol (middle), Alice (last) — but this violates 'Carol is not last' if we misread. Let me reconsider.
- 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
Check: Bob (first), Carol (middle), Alice (last). Alice not first ✓, Carol not last ✗
- 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
Solution: Carol (first), Alice (middle), Bob (last).
- 14
Verify: Alice not first ✓, Carol not last ✓, Bob not middle ✓