Question 55

# 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 horsesfinished 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?

Solution

After evaluating statement 1 and statement 2, it is clear that Hajiullah tied with Sundae, because if they didn't tie, statement 1 would contradictory as it is clearly given that Pen Fe finished after Wish Bones.

So, with the limited information we have, we can show the positions as-

A

Wish Bones

B

Pen Fe

C

Night Marvel

D

Hajiullah and Sundae can occupy any of the four places marked as A, B, C and D.

Statement 3 tells us that Pen Fe finished after Sundae and Sundae finished after Wish Bones and that the gap between Pen Fe and Sundae is same as that between Sundae and Wish Bones. Only B suffices this information and hence, the final positions of the horses are:

Wish Bones

Hajiullah- Sundae

Pen Fe

Night Marvel

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