When the long-time popular TV program "Jeopardy!" filmed a show in the Summerset area recently, host Alex Trebek quizzed three local contestants, including one from Peyton Park, as they vied for cash in the game's three rounds.
During the action, the contestants, including Jay, "questioned answers" against each other during the "Jeopardy!" and "Double Jeopardy!" rounds; each then wagered part or all of the amount he or she had won on a "Final Jeopardy!" question to determine the final sums and game winner.

From the clues below, determine each contestant's full name, home town, and score before and after the final round on the perennial quiz favorite:

1. During "Final Jeopardy!", Ben doubled the money he had won through "Double Jeopardy!" and McNabb added $2,000 in winnings, but the contestant from Summerset missed the final answer and lost 1/3 of the winnings through the first two rounds.
   
   
2. The winner, who isn't Hardy, had $3,000 more than the second-place contestant.
   
   
3. Smith and the contestant from Thoreau Falls both missed the same $2,000 question in the category "Crossword Words" near the end of "Double Jeopardy!".
   
   
4. Stefanie finished in third place with a final total of $4,000.
   
   
5. After the "Double Jeopardy!" round and going into "Final Jeopardy!", the three contestants had amassed $13,000 among them.

(puzzle originally from www.allstarpuzzles.com)

(In reply to solution by Charlie)

As pointed out by Trevor and DJ, I had made an algebraic or arithmetic error in my previous analysis of a couple of cases.

To correct my previous handling of the case where Stefanie lost 1/3 of her money in Final Jeopardy:

If Stef had lost 1/3 in Final, she would have gone from 6000 to 4000. If x is the amount the 2nd place finisher started with, then the first place finisher started Final Jeopardy with 7000-x.

This has two subcases: The first place winner was the one to have doubled his money or the 2nd place winner was the one to have doubled his money.

In the latter case, (7000-x+2000) - 2x = 3000, or 3x = 6000, or x = 2000, meaning the 2nd place finisher had 4000 dollars at the end, the same as the 3rd place finisher, which would mean they were really tied for 2nd/3rd place with no way to distinguish them, so this is no good.

In the former case, 2(7000-x) - (x+2000) = 3000, or 3x = 9000, or x=3000. Then the winner had 4000 going into Final and 8000 after final; the 2nd place finisher 3000 going in, 5000 after; and Stefanie at 6000 going in and 4000 after. Ben was the winner, having doubled his money in Final; the 2nd place finisher was McNabb and Stef was from Summerset. Since the winner was not Hardy, and neither was 2nd place McNabb, third place was Stefanie Hardy (aha!, yes she is indeed better off named Stefanie than Laurel) from Summerset. That leaves Smith in first place, that is Ben Smith, who must be from Peyton Park, leaving Thoreau Falls to 2nd place finisher Jay McNabb.

Summary of this solution:
Ben Smith from Peyton Park, 4000 to 8000
Jay McNabb from Thoreau Falls, 3000 to 5000
Stefanie Hardy from Summerset, 6000 to 4000

This is in addition to the solution I had already found:
Ben Smith from Peyton Park: 3875 to 7750
Jay Hardy of Summerset: 7125 to 4750
Stefanie McNabb of Thoreau Falls: 2000 to 4000

This should be the complete set (2 solutions) as I don't think I made any mistakes in the cases of the first place winner having been the one to lose 1/3 in Final Jeopardy, which does not work out in either of its subcases (2nd place double or 3rd place double).

Posted by Charlie on 2003-06-15 05:28:15