Question

A gambler bet on a horse race, but the bookie wouldn’t tell him the results of the race. The bookie gave clues as to how the five horses finished -which may have included some ties - and wouldn’t pay the gambler off unless the gambler could determine how the five horses finished based on the following clues:
o Penn Fe finished before Night Marvel and after Wish Bones.
o If Hallelujah is not tied with Sundae, then Wish Bones is tied with Penn Fe.
o Penn Fe finished as many places after Sundae as Sundae finished after Wish Bones if and only if Wish Bones finished before Night Marvel.
The gambler thought for a moment, then answered correctly. How did the five horses finish the race?

• A. Sundae came in first. Wish Bones and Hallelujah tied for second place. Penn Fe came in fourth. Night Marvel came in fifth.
• B. Wish Bones came in first. Sundae and Penn Fe tied for second place. Hallelujah came in fourth. Night Marvel came in fifth.
• C. Wish Bones came in first. Sundae and Hallelujah tied for second place. Penn Fe came in fourth. Night Marvel came in fifth.
• D. Penn Fe came in first. Night Marvel and Hallelujah tied for second place. Wish Bones came in fourth. Sundae came in fifth.

Answer 1

The Correct Option is C

The problem provides a series of clues to determine the order in which the horses finished a race. Let's break down each clue to find the solution.

1. Penn Fe finished before Night Marvel and after Wish Bones. 
This implies the order relation: Wish Bones < Penn Fe < Night Marvel.

2. If Hallelujah is not tied with Sundae, then Wish Bones is tied with Penn Fe.
This means that the order dependency is conditional: 
- Case A: Hallelujah ties with Sundae, then Wish Bones and Penn Fe do not tie.
- Case B: Hallelujah does not tie with Sundae, Wish Bones ties with Penn Fe.

3. Penn Fe finished as many places after Sundae as Sundae finished after Wish Bones if and only if Wish Bones finished before Night Marvel.
This infers a symmetric place difference and confirms: Wish Bones < Night Marvel.

Now, let's consider the options. We seek the arrangement meeting all conditions:

1st	Wish Bones
2nd	Sundae & Hallelujah
4th	Penn Fe
5th	Night Marvel

By analyzing:

- Wish Bones is first, satisfying "Penn Fe after Wish Bones."

- Sundae and Hallelujah are tied for second.
- Penn Fe is in fourth, which places Night Marvel in fifth, satisfying "Penn Fe before Night Marvel."

The arrangements adhere to all clues provided, confirming the solution as:

1st	Wish Bones
2nd	Sundae & Hallelujah
4th	Penn Fe
5th	Night Marvel