PK 2017 Q12
12. Tycho wants to prepare a schedule for his jogging for the next few months. He wants to jog three times per week. Every week, he wants to jog on the same days of the week. He never wants to jog on two consecutive days. How many schedules can he choose from?
- A 6
- B 7
- C 9
- D 10
- E 35
Pink Kangaroo 2017, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 7
Any day when Tycho jogs is immediately followed by a day without a jog. Therefore any period of seven days has three pairs of ‘jog, no-jog’ days and one extra no-jog day. There are seven possibilities for this extra non-jog day, so seven distinct schedules.
Solution © UK Mathematics Trust, from the PK 2017 solutions.