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:

1. Penn Fe finished before Night Marvel and after Wish Bones.
2. If Hallelujah is not tied with Sundae, then Wish Bones is tied 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.

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.

Hint:

Wish Bones must finish strictly before Penn Fe, so they can never tie, which forces one of the other pairs to tie instead.

Answer 1

The Correct Option is C

Clue1: WishBones<PennFe<NightMarvel (strict, so WB&PF can never tie). Clue2: since WB-PF tie is impossible, its 'then' must be forced true only if condition false, meaning Hallelujah IS tied with Sundae. Clue3: since WB always before NightMarvel (from clue1), the gap condition must hold: Sundae sits exactly midway between WB and PF. Checking option (3): WB1st, Sundae&Hallelujah tied 2nd, PennFe 4th, NightMarvel 5th - satisfies all three clues (Hallelujah tied Sundae; WB<PF<NM; equal gaps WB-Sundae and Sundae-PF).

Final Answer: Option (3).