GK 2017 Q15
15. Margot wants to prepare a jogging timetable. She wants to jog exactly twice a week, and on the same days every week. She does not want to jog on two consecutive days. How many different timetables could Margot prepare?
- A 18
- B 16
- C 14
- D 12
- E 10
Grey Kangaroo 2017, Question 15. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 14
Whichever day of the week Margot chooses for her first jogging day, there are four other days she can choose for her second day since she does not want to jog on either the day before or the day after her first chosen day. Therefore there are 7 × 4 = 28 ordered choices of days. However, the order of days does not matter when forming the timetable, only the two days chosen. Hence Margot can prepare 28 ÷ 2 = 14 different timetables.
Solution © UK Mathematics Trust, from the GK 2017 solutions.