## Tuesday, July 24, 2007

### The NBA today

A gambler bet on a horse race, but the bookee wouldn't tell him the results of the race. The bookee 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:
• Penuche Fudge finished before Near Miss and after Whispered Promises.
• Whispered Promises tied with Penuche Fudge if and only if Happy Go Lucky did not tie with Skipper's Gal.
• Penuche Fudge finished as many places after Skipper's Gal as Skipper's Gal finished after Whispered Promises if and only if Whispered Promises finished before Near Miss.

The gambler thought for a moment, then answered correctly. How did the five horses finish the race?

1. No answers? That's pretty shocking.

Whispered Promises came in first. Skipper's Gal and Happy Go Lucky tied for second place. Penuche Fudge came in fourth. Near Miss came in fifth.

2. I was about to enter that as my answer, mike, but I realized that I didn't think it met the second criterion. Penuche Fudge finished 4, Skipper's Gal finished 2, and Whispered Promises finished 1. That didn't seem to line up with what number 2 said, since I was looking for the same interval between WP and SG as from SG to PF.

3. Hmmm.... I'm getting myself confused by thinking more about this problem. Since HGL and SG tie for 2nd place, does that means PF is one spot back or two when he finishes in fourth place.

Technically, I think PF is only one spot back, but it certainly is confusing (and I could certainly be wrong).

If you accept that, then the rest works out.

In my solution 2 is true because WP (1) and PF (4) do not tie therefore HGL (2) and SG (2) do tie.

1 is true since PF (4) finished before NM (5) and after WP (1).

3 is true because PF (4) finished as many places after SG (2) as SG (2) finished after WP (1) iff WP (1) finished before NM (5).

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