Evelyn B. Rosenthal

Radio Talk Shows

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Radio Talk Shows

An all-talk radio station has live programs weekdays from 6 a.m. to midnight. There are seven programs in all, and each starts and ends on the hour or half-hour. Four of the shows have one host, and three have two hosts; the ten hosts are Andy, Chloe, Dave, Don, Ed, Lena, Leonard, Phyllis, Rob, and Ron; last names are Graham, Harris (for two hosts), Jarcho, Kahn, Lipper, Mandel, Quarles, Santo, and Torrance. Can you find the weekday schedule by deducing the beginning and ending times of the programs, as well as each one's host or hosts.

  1. The last program of the day, ending at midnight, is the only one devoted entirely to sports.
  2. Leonard's program is as long as Lipper's and the one beginning at 12:30 p.m. put together.
  3. Quarles's program is as much shorter than the preceding program as it is longer than the following one.
  4. Only two programs begin on the hour; one is the first program of the day, which starts at 6:00 a.m., and the other is the sports program.
  5. Each co-host has the same first initial as his or her partner.
  6. The three longest programs are the ones with two co-hosts each.
  7. Kahn's program is as long as Torrance's and the 6:00 a.m. program put together.
  8. Andy's program, the shortest of the seven, is an hour long.
  9. The all-sports program (which has no female host) is exactly as long as just one other program; all the other programs are different lengths, and shorter than the all-sports program.
  10. Lipper's program is as long as Chloe's and Graham's programs put together.
  11. Rob doesn't host the all-sports program.
  12. Jarcho's program is immediately before that of Santo (who isn't Ron)
  13. Mr. and Mrs. Harris once had Don and Mandel as guests on their program.
  14. Phylis's show is earlier in the day than Ed's.
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