Answer to October 9, 2000 Problem

from The Dell Book of Logic Problems #6
by W.Lee Moss

All in the Family

 
The Marx children grew up in Central City and attended Northeast High School. Each excelled in a different sport. Today, you can find each one coaching at one of Central City's five high schools (one of which is their alma mater, Northeast High), each in his or her chosen sport.

Last year, each Marx-coached team finished its season ranked at a different spot in the top 5 of its respective sport. From the following clues, can you determine each coach's sport, school, ranking, and length of service as coach (one has six years experience)?

  1. Fred is not the man who has coached for eight years.
  2. The third-ranked baseball team's coach has two more years' experience than Gail, and four more years' than Southwest High's coach.
  3. The four-year male coach's team ranked higher than Southeast High, which ranked higher than Carmen's track team.
  4. The fifth-ranked football team's coach has two more years' experience than the Northwest High coach, and four more years' than Mark.
  5. The twelve-year coach's team did not finish fourth.
  6. Josef's team finished lower than the swimming team, which finished one spot below the ten-year coach's team.
  7. The Central High coach's favorite sport has always been basketball.

 

Solution to Problem:

The baseball team ranked 3rd (clue 2).
The football team ranked 5th (clue 4).
Carmen's track team did not rank 1st or 2nd (clue 3), so it ranked 4th.
Carmen has not coached for 8 (clue 1), 4 (clue 3), 12 (clue 5) or 10 years (clue 6); she has coached for 6 years.
The swimming team did not rank 1st (clue 6); by elimination, it ranked 2nd.
Also by elimination, the 1st-ranked team was the basketball team, of Central High (clue 7).
The 8-year coach is a man (clue 1); by clue 2, the baseball coach has 12 years on the job, Gail 10 years, and the 8-year male coach works at Southwest High. By clue 4, he is the football coach, Carmen works at Northwest High, and Mark is the 4-year coach.

Fred does not coach football (clue 1); he is the 12-year baseball coach.
Josef, by elimination, coaches the football team.
By clue 6, Gail is the 1st-place basketball coach at Central High.
Mark, by elimination, is the swimming coach.
By clue 3, Fred works at Southeast High; by elimination, Mark works at Northeast High.

In summary: 

1st: Gail, basketball, 10, Central
2nd: Mark, swimming, 4, Northeast
3rd: Fred, baseball, 12, Southeast 
4th: Carmen, track, 6, Northwest 
5th: Josef, football, 8, Southwest

Correctly solved by:

1. Kirstine Wynn Winchester, VA
2. Bob Hearn Winchester, VA
3. Catherine Roby Winchester, VA
4. Chad McDaniel Winchester, VA