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Mr. Froopaloop's Band
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Hans Ernest Froopaloop, Jr.'s second cousin, Wolfgang Amadeus Froopaloop, is the conductor of the Hans Ernest Froopaloop, Sr. the Third High School band. Five members of the band, Audrey, Brenda, Charlotte, Dawn, and Edith, are girls in grade 9, each one plays a wind instrument, and each wind instrument was rented from a different music store. Each girl has a brother in grade 11 (Victor, Walter, Xavier, Yoshi, and Zeke, in some order) and they each play a different string instrument. From smallest to largest, the string instruments are the violin, the guitar, the cello, the harp, and the piano. Here are some facts:
1. Victor, whose sister isn't the trumpet player, plays the only string instrument larger than that of the boy whose sister rented from the store on the west end of town but smaller than that of Brenda's brother. Brenda didn't rent from the store on the east end of town.
2. Three consecutively sized string instruments, from smallest to largest, are the one played by the saxophone player's brother, the one played by the boy whose sister rented from the store on the east end of town, and the one played by Charlotte's brother. Charlotte didn't rent from the store on the west end of town. Xavier's sister doesn't play the saxophone.
3. Dawn, who isn't the clarinet player, didn't rent from the store on the east end of town. Victor's sister, who isn't Dawn, didn't rent from the store on the north end of town.
4. Xavier doesn't play the violin or the piano. The trombone player's brother isn't Xavier or Yoshi. The brother of the trombone player (who isn't Edith) doesn't play the violin. Edith didn't rent from the store on the east end of town.
5. Victor's sister, who isn't the one who rented from the store in the center of town, doesn't play the clarinet. The saxophone player is neither the one who rented from the store on the north end of town nor Walter's sister.
The question is:
Who plays the flute and who rented from the store on the south end of town?
1. Victor, whose sister isn't the trumpet player, plays the only string instrument larger than that of the boy whose sister rented from the store on the west end of town but smaller than that of Brenda's brother. Brenda didn't rent from the store on the east end of town.
2. Three consecutively sized string instruments, from smallest to largest, are the one played by the saxophone player's brother, the one played by the boy whose sister rented from the store on the east end of town, and the one played by Charlotte's brother. Charlotte didn't rent from the store on the west end of town. Xavier's sister doesn't play the saxophone.
3. Dawn, who isn't the clarinet player, didn't rent from the store on the east end of town. Victor's sister, who isn't Dawn, didn't rent from the store on the north end of town.
4. Xavier doesn't play the violin or the piano. The trombone player's brother isn't Xavier or Yoshi. The brother of the trombone player (who isn't Edith) doesn't play the violin. Edith didn't rent from the store on the east end of town.
5. Victor's sister, who isn't the one who rented from the store in the center of town, doesn't play the clarinet. The saxophone player is neither the one who rented from the store on the north end of town nor Walter's sister.
The question is:
Who plays the flute and who rented from the store on the south end of town?
Answer
Edith plays the flute, which she rented from the store on the south end of town.From fact 1, Victor's sister didn't rent from the store on the west end. From fact 3, it's not on the north end. From fact 5, it's not in the center. From fact 1, Victor's instrument is the next smallest after Brenda's brother's, but from fact 2, the instrument played by the boy whose sister rented from the store on the east end is the next smallest after Charlotte's brother's. So Victor's sister must have rented from the store on the south end.
From fact 1, Brenda couldn't have rented from the store on the east end. From fact 2, it couldn't be Charlotte. From fact 3, it couldn't be Dawn. From fact 4, it couldn't be Edith. So it must be Audrey.
From fact 1, Victor's sister couldn't be Brenda. From fact 3, it couldn't be Dawn. From fact 1, Victor's instrument is the next largest after the one whose sister rented from the store on the west end, but from fact 2, Charlotte's brother's is the next largest after the one whose sister rented from the store on the east end. We have already
determined that Victor's sister rented from the store on the south end, while Audrey rented from the store on the east end. So Victor's sister must be Edith.
Continuing in this fashion, we can determine that there is only one possible solution:
Audrey plays the clarinet, which she rented from the store on the east end of town, and her brother, Xavier, plays the harp.
Brenda plays the saxophone, which she rented from the store in the center of town, and her brother, Yoshi, plays the cello.
Charlotte plays the trombone, which she rented from the store on the north end of town, and her brother, Zeke, plays the piano.
Dawn plays the trumpet, which she rented from the store on the west end of town, and her brother, Walter, plays the violin.
Edith plays the flute, which she rented from the store on the south end of town, and her brother, Victor, plays the guitar.
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