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)

If Stef, in last place, had been the one to lose 1/3 in Final, then, if x is the amount the 2nd place finisher went into Final with, the winner went in with 5000-x. If the winner was the one to have doubled in Final, then 2(5000-x)-(x+2000)=3000 or 3x=10,000 - 5000, but the right hand side is not divisible by 3. On the other hand if the 2nd finisher were the one to double in Final, 5000-x+2000 - 2x = 3000, or 3x=4000, with the same problem. So Stef, the last finisher, is not the one to lose 1/3 in Final Jeopardy.

So Stef went from 2000 to 4000 in Final Jeopardy, and since Stef is not Ben, this counts as the "adding 2000" rather than the "doubling", so she is Stefanie McNabb.

Again, let x be the amount the 2nd place finisher had going into Final Jeopardy. The first place finisher then must have had 11,000 - x going in.

If the second place finisher were the one to have doubled in Final, and the first place finisher had lost 1/3, then 2(11000-x)/3-2x = 3000, or x=1625. Twice this would still be less than Stef's last place finish, so this is no good.

So the first place finisher was the one to have doubled his money in Final Jeopardy. This works out as 2(11000-x)-2x/3=3000, or 8x=57000, or x=7125.

So the first place went from 3875 to 7750, doubling his money and so was Ben.
The second place went from 7125 to 4750, and was from Summerset.
Last place was Stefanie McNabb, who went from 2000 to 4000.

Since the winner was not Hardy, he was Ben Smith, leaving the second place to Jay Hardy.

Since Smith came from neither Thoreau Falls nor from Summerset, he came from Peyton Park, leaving Thoreau Falls for the last place finisher, Stefanie.

Summary:
Ben Smith from Peyton Park: 3875 to 7750
Jay Hardy of Summerset: 7125 to 4750
Stefanie McNabb of Thoreau Falls: 2000 to 4000

Posted by Charlie on 2003-06-14 04:51:34