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MathNet 1999 — Part 01 Question 86

Math Olympiad Vault · MathNet 1999 — Part 01

Question 86

Professor Scappavia teaches mathematics in a school where there are 6 hours of lessons a day, from Monday to Friday. Her weekly timetable includes 18 hours of teaching and, for personal reasons, she would like to never teach in the last hour of class. However, the commission that sets the timetable only allows the teacher to choose the daily division of her working hours, after which her timetable will be drawn at random. Which of the following provisions should the teacher choose to have the greatest probability of never having the last hour of class?
  1. $5-5-4-2-2$
  2. $5-4-4-3-2$
  3. $4-4-4-4-2$
  4. 4-4-4-3-3
  5. are all equivalent.